Portfolio optimization on Dirac

Device: Dirac-1

Introduction

This approach seeks to identify a sub-portfolio of stocks that have superior risk-return profiles compared to the full portfolio. This identifies opportunities for an investor to simplify their investment strategy without sacrificing (and potentially enhancing) the risk-adjusted return. While the expected return on a portfolio is relatively straightforward to optimize by itself, optimizing against risk is more subtle when choosing a set of assets that individually have high returns. The reason that optimizing against risk is more challenging is because asset performances can be correlated. Intuitively, one can see that investing in two highly-correlated assets is more risky than if they are uncorrelated or even anti-correlated. If one of a highly correlated asset is performing poorly, the other in the pair is likely to do so as well. Thus, the variance of a portfolio with both assets can be significantly higher than it would be if they were uncorrelated. Minimizing the overall variance for the return of a portfolio therefore needs to take into account the covariance between the assets, making this a fundamentally quadratic problem, ideal for our Dirac-1 solver.

Importance

Investments need not only give a good return on average, but also need to balance the potential risks. This balance will depend on the goal of the investor. For example, someone investing their retirement fund is likely to favor modest returns with low risks because the consequences of major losses are severe. On the other hand, someone who is day-trading in the hopes of having more money for entertainment might be willing to take more risks. There are of course many other scenarios with other risk levels. In general, the portfolio optimization problem is viewed as being a multi-objective problem. The goal is to balance the objective of maximizing return with the objective of minimizing risk. Even with multiple objectives there is still a sense of optimality, a portfolio is said to be "efficient" or "Pareto optimal" if the only ways to decrease risk would be to also decrease return. Regardless of one's appetite for risk, it never makes sense to invest in a non-Pareto-Optimal portfolio, so our goal is to find those that are Pareto optimal and match the appetite for risk which is parameterized by a term ξ\xi in our description. It is worth noting that this tutorial is based on a relatively simplified but still commonly used model of portfolio optimization. Various efforts exist to take into account more complex structure in the distribution of expected returns, in particular the failure to capture extreme events.

Applications

Portfolios diversification is necessary to achieve satisfactory outcomes for investors, making the kind of portfolio optimization discussed here (and potentially more complex variants) highly important. In spite of its simplicity, the model of diversification presented here, often referred to as modern portfolio theory, is still used. Improvements of the models presented here comprise a subject known as post-modern portfolio theory. One improvement is to consider a quantity known as downside risk instead of variance. Downside risk only takes into account the risk of portfolio elements underperforming a goal, rather than their total variation. Since the goal of diversification is to protect from risk, this approach can yield better performance.

Methodology

Let K be the total number of available stocks to choose from (here K=253K = 253), that is the size of the stock pool. We want to choose a subset of KK^\prime (K<KK^\prime < K) stocks such that the portfolio risk is minimized, while the portfolio expected return is maximized, that is

min{xi}i{1,2,...,K}[E(R)2+ξVAR(R)]\min_{\{x_{i}\}_{i \in \{1, 2,..., K\}}} [-E(R)^2 + \xi VAR(R)]

where RR is the daily returns of the portfolio over some period of time, VAR(R)VAR(R) and E(R)E(R) are the variance and expectation of daily returns, ξ\xi is a hyper-parameter, and {xi}\{x_{i}\} are binary variables representing inclusion or exclusion of a stock. A large value means the focus of optimization is to increase return, whereas a small value indicates the reduction of risk is more important. As we can take both long and short positions on stocks, we assume that x1,x2,...,xKx_1, x_2, ..., x_K corresponds to long positions on stocks 1 to KK.

As we are choosing a subset of KK^\prime stocks, we also need the following constraint,

i=1Kxi=K\sum_{i=1}^{K} x_i = K^\prime

Assuming that the same amount is invested on each of the K' selected stocks, the portfolio daily return at time t over a time period denoted by m can be expanded as follows,

R(m)(t)=1Ki=1Kxiri(m)(t)R^{(m)}(t) =\frac{1}{K^\prime} \sum_{i=1}^{K} x_i r^{(m)}_i(t)

where ri(m)(t)r^{(m)}_i(t) is the daily return of stock i at time tt in time period mm. The expectation of portfolio daily return over time period mm can thus be expanded as,

E(R(m))=1Ki=1KxiE(ri(m))E(R^{(m)}) = \frac{1}{K^\prime} \sum_{i=1}^{K} x_i E(r^{(m)}_i)

and the variance portfolio daily return over time period m is expanded as,

VAR(R(m))=1K2i=1Kj=1KxixjCOV(ri(m),rj(m))VAR(R^{(m)}) = \frac{1}{K^{\prime 2}} \sum_{i=1}^{K} \sum_{j=1}^{K} x_i x_j COV(r^{(m)}_i, r^{(m)}_j)

where COVCOV is the covariant function.

The problem then reduces to

min{xi}xT1K2[Q(m)ξP(m)]x\min_{\{x_i\}} {\bf{x}^T} \frac{1}{K^{\prime 2}} [ Q^{(m)} - \xi P^{(m)}] {\bf{x}}

where

Qij(m)=COV(ri(m),rj(m))Q^{(m)}_{ij} = COV(r^{(m)}_{i}, r^{(m)}_{j})
Pij(m)=E(ri(m))δijP^{(m)}_{ij}= E(r_i^{(m)}) \delta_{ij}

To avoid an over-fit on the portfolio data, we can minimize the average of the cost function over MM overlapping time periods, that is m=1,2,...,Mm=1,2,...,M. The problem becomes,

min{xi}xT1MK2m=1M[Q(m)ξP(m)]x\min_{\{x_i\}} {\bf{x}^T} \frac{1}{MK^{\prime 2}} \sum_{m=1}^{M}[ Q^{(m)} - \xi P^{(m)}] {\bf{x}}

subject to,

i=1Kxi=K\sum_{i=1}^{K} x_i = K^\prime

Implementation

The above-mentioned approach was used to construct an optimal portfolio based on the constituents of the Nasdaq-100 index. The following constituents were used,

In [3]:

  • import pandas as pd
  • from IPython.display import display, HTML
  • df = pd.read_csv("nasdaq100_stocks.csv")
  • display(HTML(df[["Company", "Symbol"]].to_html()))

Out [ ]:

CompanySymbol
0Microsoft CorpMSFT
1Apple IncAAPL
2Amazon.com IncAMZN
3Alphabet IncGOOG
4Alphabet IncGOOGL
5NVIDIA CorpNVDA
6Tesla IncTSLA
7Meta Platforms IncMETA
8PepsiCo IncPEP
9Broadcom IncAVGO
10Costco Wholesale CorpCOST
11Cisco Systems IncCSCO
12T-Mobile US IncTMUS
13Adobe IncADBE
14Texas Instruments IncTXN
15Comcast CorpCMCSA
16Honeywell International IncHON
17Amgen IncAMGN
18Netflix IncNFLX
19QUALCOMM IncQCOM
20Starbucks CorpSBUX
21Intel CorpINTC
22Intuit IncINTU
23Gilead Sciences IncGILD
24Advanced Micro Devices IncAMD
25Automatic Data Processing IncADP
26Intuitive Surgical IncISRG
27Mondelez International IncMDLZ
28Applied Materials IncAMAT
29Analog Devices IncADI
30Regeneron Pharmaceuticals IncREGN
31PayPal Holdings IncPYPL
32Moderna IncMRNA
33Booking Holdings IncBKNG
34Vertex Pharmaceuticals IncVRTX
35CSX CorpCSX
36Fiserv IncFISV
37Lam Research CorpLRCX
38Activision Blizzard IncATVI
39Micron Technology IncMU
40KLA CorpKLAC
41Monster Beverage CorpMNST
42O'Reilly Automotive IncORLY
43Keurig Dr Pepper IncKDP
44ASML Holding NVASML
45Synopsys IncSNPS
46Kraft Heinz Co/TheKHC
47Charter Communications IncCHTR
48American Electric Power Co IncAEP
49Marriott International Inc/MDMAR
50Palo Alto Networks IncPANW
51Cintas CorpCTAS
52Cadence Design Systems IncCDNS
53MercadoLibre IncMELI
54Dexcom IncDXCM
55Exelon CorpEXC
56Biogen IncBIIB
57AstraZeneca PLC ADRAZN
58NXP Semiconductors NVNXPI
59Paychex IncPAYX
60Enphase Energy IncENPH
61Autodesk IncADSK
62Pinduoduo Inc ADRPDD
63Ross Stores IncROST
64Fortinet IncFTNT
65Microchip Technology IncMCHP
66Xcel Energy IncXEL
67Lululemon Athletica IncLULU
68Airbnb IncABNB
69Workday IncWDAY
70PACCAR IncPCAR
71Walgreens Boots Alliance IncWBA
72IDEXX Laboratories IncIDXX
73Electronic Arts IncEA
74Marvell Technology IncMRVL
75Old Dominion Freight Line IncODFL
76GLOBALFOUNDRIES IncGFS
77CoStar Group IncCSGP
78Dollar Tree IncDLTR
79Illumina IncILMN
80Baker Hughes CoBKR
81Copart IncCPRT
82Constellation Energy CorpCEG
83Cognizant Technology Solutions CorpCTSH
84JD.com Inc ADRJD
85Fastenal CoFAST
86Verisk Analytics IncVRSK
87Seagen IncSGEN
88Crowdstrike Holdings IncCRWD
89Diamondback Energy IncFANG
90Sirius XM Holdings IncSIRI
91eBay IncEBAY
92Datadog IncDDOG
93Warner Bros Discovery IncWBD
94ANSYS IncANSS
95Atlassian CorpTEAM
96Rivian Automotive IncRIVN
97Zoom Video Communications IncZM
98Zscaler IncZS
99Align Technology IncALGN
100Lucid Group IncLCID

We got the historical prices of the constituent stocks, as well as those of Nasdaq-100 (NDX) and equal-weighted Nasdaq-100 (QQQE) using the Yahoo Finance Python library,

In [4]:

  • # Import libs
  • import os
  • import pandas as pd
  • import yfinance as yf
  • # Define some parameters
  • OUT_DIR = "data"
  • DROP_STOCKS = []
  • # Get the list of all existing stocks
  • stocks = list(df["Symbol"].unique()) + ["NDX", "QQQE"]
  • for stock in stocks:
  • try:
  • tmp_df = yf.Ticker(stock).history(
  • period="max", interval="1d",
  • )[["Close"]].rename(
  • columns={
  • "Close": stock,
  • }
  • )
  • tmp_df["Date"] = tmp_df.index
  • tmp_df.to_csv(
  • os.path.join(OUT_DIR, "%s.csv" % stock),
  • index=False,
  • )
  • except Exception as exc:
  • print("Could not get price for %s" % stock)
  • print(exc)
  • DROP_STOCKS.append(stock)
  • if tmp_df.shape[0] == 0:
  • DROP_STOCKS.append(stock)

Out [ ]:

- ATVI: No data found, symbol may be delisted
- SGEN: No data found, symbol may be delisted

Let us import some libraries and set some parameters,

In [5]:

  • # Import libs
  • import os
  • import sys
  • import time
  • import datetime
  • import json
  • import warnings
  • from functools import wraps
  • import numpy as np
  • import pandas as pd
  • from qci_client import QciClient
  • warnings.filterwarnings("ignore")
  • ALPHA = 1.0 # The coefficient for penalty term (for linear constraint)
  • N_SAMPLES = 20 # Number of solution samples
  • XI = 5.0 # The xi variable as defined in Methodology
  • K_PRIME = 30 # Number of selected stocks
  • WINDOW_DAYS = 30 # Size of each sliding window in days
  • WINDOW_OVERLAP_DAYS = 15 # Overlap between sliding windows in days
  • IN_SAMPLE_DAYS = 180 # Size of the lookback period in days
  • OUT_OF_SAMPLE_DAYS = 30 # Size of the horizon window in days

We now define a function that calculates daily returns of all constituent stocks,

In [6]:

  • def get_stock_returns(stocks, min_date, max_date):
  • min_date = pd.to_datetime(min_date)
  • max_date = pd.to_datetime(max_date)
  • return_df = None
  • for stock in stocks:
  • stock_df = pd.read_csv("data/%s.csv" % stock)
  • #stock_df["Date"] = stock_df["Date"].astype("datetime64[ns]") # change to fix timezone issue
  • stock_df["Date"] = pd.to_datetime([pd.Timestamp(timestamp).date() for timestamp in stock_df["Date"]])
  • stock_df = stock_df.fillna(method="ffill").fillna(method="bfill")
  • stock_df[stock] = stock_df[stock].pct_change()
  • stock_df = stock_df.dropna()
  • stock_df = stock_df[
  • (stock_df["Date"] >= min_date) & (stock_df["Date"] <= max_date)
  • ]
  • if return_df is None:
  • return_df = stock_df
  • else:
  • return_df = return_df.merge(stock_df, how="outer", on="Date",)
  • return_df = return_df.fillna(method="ffill").fillna(method="bfill")
  • return return_df

And a function that calculates the hamiltonian matrix,

In [7]:

  • def get_hamiltonian(
  • return_df, stocks, min_date, max_date,
  • ):
  • K = len(stocks)
  • # Calculate P and Q
  • Q = np.zeros(shape=(K, K), dtype="d")
  • P = np.zeros(shape=(K, K), dtype="d")
  • m = 0
  • min_date = pd.to_datetime(min_date)
  • max_date = pd.to_datetime(max_date)
  • tmp_date = min_date
  • while tmp_date <= max_date:
  • tmp_min_date = tmp_date
  • tmp_max_date = tmp_date + datetime.timedelta(days=WINDOW_DAYS)
  • tmp_df = return_df[
  • (return_df["Date"] >= tmp_min_date)
  • & (return_df["Date"] <= tmp_max_date)
  • ]
  • r_list = []
  • for i in range(K):
  • r_list.append(np.array(tmp_df[stocks[i]]))
  • Q += np.cov(r_list)
  • for i in range(K):
  • for j in range(K):
  • P[i][j] += np.mean(r_list[i]) * np.mean(r_list[j])
  • tmp_date += datetime.timedelta(
  • days=WINDOW_DAYS - WINDOW_OVERLAP_DAYS,
  • )
  • m += 1
  • fct = m
  • if fct > 0:
  • fct = 1.0 / fct
  • P = fct * P
  • Q = fct * Q
  • # Calculate the Hamiltonian
  • H = -P + XI * Q
  • # make sure H is symmetric up to machine precision
  • H = 0.5 * (H + H.transpose())
  • return H

And, we define a function that yields an optimal portfolio given a hamiltonian HH,

In [9]:

  • def optimize_portfolio(H, stocks, curr_date):
  • beg_time = time.time()
  • K = len(stocks)
  • assert H.shape[0] == K
  • assert H.shape[1] == K
  • # Generate the constraint
  • cons_lhs = np.ones(shape=(K), dtype=np.float32)
  • cons_rhs = np.array([-K_PRIME])
  • constraints = np.hstack([cons_lhs, cons_rhs])
  • # Create json objects
  • objective_json = {
  • "file_name": "objective_tutorial_eq_wt_port_opt.json",
  • "file_config": {
  • "objective": {"data": H, "num_variables": K},
  • }
  • }
  • constraint_json = {
  • "file_name": "constraints_tutorial_eq_wt_port_opt.json",
  • "file_config": {
  • "constraints": {
  • "data": constraints,
  • "num_variables": K,
  • "num_constraints": 1,
  • }
  • }
  • }
  • job_json = {
  • "job_name": "moodys_eqc1_equal_weights",
  • "job_tags": ["moody_nasda100_eqc1_equal_weights",],
  • "params": {
  • "device_type": "csample", #"eqc1",
  • "num_samples": N_SAMPLES,
  • "alpha": ALPHA,
  • },
  • }
  • # Solve the optimization problem
  • token = "your_token"
  • api_url = "https://api.qci-prod.com"
  • qci = QciClient(api_token=token, url=api_url)
  • response_json = qci.upload_file(file=objective_json)
  • objective_file_id = response_json["file_id"]
  • response_json = qci.upload_file(file=constraint_json)
  • constraint_file_id = response_json["file_id"]
  • job_params = {
  • "device_type": "dirac-1",
  • "alpha": ALPHA,
  • "num_samples": N_SAMPLES,
  • }
  • job_json = qci.build_job_body(
  • job_type="sample-constraint",
  • job_params=job_params,
  • constraints_file_id=constraint_file_id,
  • objective_file_id=objective_file_id,
  • job_name=f"tutorial_eqc1",
  • job_tags=["tutorial_eqc1"],
  • )
  • print(job_json)
  • job_response_json = qci.process_job(
  • job_body=job_json
  • )
  • print(job_response_json)
  • results = job_response_json["results"]
  • energies = results["energies"]
  • samples = results["solutions"]
  • is_feasibles = results["feasibilities"]
  • # The sample solutions are sorted by energy
  • sol = None
  • for i, item in enumerate(samples):
  • sol = item
  • is_feasible = is_feasibles[i]
  • if is_feasible:
  • break
  • if not is_feasible:
  • print("Solution is not feasible!")
  • assert len(sol) == K, "Inconsistent solution size!"
  • if sum(sol) != K_PRIME:
  • print(
  • "Expected to select %d stocks, but selected %d!"
  • % (K_PRIME, sum(sol))
  • )
  • sel_stocks = []
  • for i in range(K):
  • if sol[i] > 0:
  • sel_stocks.append(stocks[i])
  • print(
  • "In optimize_portfolio; done with checking constraints; %0.2f seconds!"
  • % (time.time() - beg_time)
  • )
  • return sol, sel_stocks

Results

We can now test the approach over a period of time, for example, between 2020-01-15 to 2023-12-30. We define,

In [10]:

  • def run(curr_date):
  • print("Processing curr date:", curr_date)
  • curr_date = pd.to_datetime(curr_date)
  • min_ins_date = curr_date - datetime.timedelta(days=IN_SAMPLE_DAYS)
  • max_ins_date = curr_date - datetime.timedelta(days=1)
  • min_oos_date = curr_date
  • max_oos_date = curr_date + datetime.timedelta(days=OUT_OF_SAMPLE_DAYS)
  • df = pd.read_csv("nasdaq100_stocks.csv", low_memory=False)
  • stocks = list(set(df["Symbol"]) - set(DROP_STOCKS))
  • ins_return_df = get_stock_returns(stocks, min_ins_date, max_ins_date)
  • oos_return_df = get_stock_returns(stocks, min_oos_date, max_oos_date)
  • ins_return_df = ins_return_df.sort_values("Date")
  • ins_return_df = ins_return_df.fillna(method="ffill").fillna(0)
  • oos_return_df = oos_return_df.sort_values("Date")
  • oos_return_df = oos_return_df.fillna(method="ffill").fillna(0)
  • H = get_hamiltonian(ins_return_df, stocks, min_ins_date, max_ins_date)
  • sol, sel_stocks = optimize_portfolio(H, stocks, curr_date)
  • sel_stock_df = pd.DataFrame()
  • sel_stock_df["Date"] = [curr_date] * len(sel_stocks)
  • sel_stock_df["Stock"] = sel_stocks
  • return sel_stock_df

We can then run a backtest,

In [11]:

  • min_date = pd.to_datetime("2022-01-13")
  • max_date = pd.to_datetime("2022-12-30")
  • SEL_STOCK_OUT_FILE = "selected_stocks.csv"
  • curr_date = min_date
  • while curr_date < max_date:
  • tmp_sel_stock_df = run(curr_date)
  • if os.path.exists(SEL_STOCK_OUT_FILE):
  • tmp_sel_stock_df.to_csv(
  • SEL_STOCK_OUT_FILE, index=False, mode="a", header=False,
  • )
  • else:
  • tmp_sel_stock_df.to_csv(
  • SEL_STOCK_OUT_FILE, index=False,
  • )
  • curr_date += datetime.timedelta(days=OUT_OF_SAMPLE_DAYS + 1)

Out [ ]:

Processing curr date: 2022-01-13 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c2e2f98263204a36575fe', 'objective_file_id': '663c2e2f98263204a36575fc', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 19:00:16 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 19:00:16 - Job submitted: job_id='663c2e30d448b017e54f94d3'
2024-05-08 19:00:16 - QUEUED
2024-05-08 19:00:18 - RUNNING
2024-05-08 19:06:20 - COMPLETED
2024-05-08 19:06:23 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c2e30d448b017e54f94d3', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c2e2f98263204a36575fe', 'objective_file_id': '663c2e2f98263204a36575fc', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T02:00:16.175Z', 'queued_at_rfc3339nano': '2024-05-09T02:00:16.177Z', 'running_at_rfc3339nano': '2024-05-09T02:00:17.157Z', 'completed_at_rfc3339nano': '2024-05-09T02:06:19.26Z'}, 'job_result': {'file_id': '663c2f9b98263204a365760c', 'device_usage_s': 289}}, 'status': 'COMPLETED', 'results': {'counts': [1, 5, 3, 2, 3, 1, 2, 1, 1, 1], 'energies': [-899.8930419210621, -899.8929198507496, -899.8929198507496, -899.8927977804371, -899.8927977804371, -899.8926757101246, -899.8926757101246, -899.8926757101246, -899.8924315694996, -899.8919432882496], 'feasibilities': [True, True, True, True, True, True, True, True, True, True], 'objective_values': [0.10694210024122522, 0.10711688613375814, 0.10713816757050866, 0.10715433158390524, 0.10722590058230652, 0.10727914274376713, 0.10737808437841369, 0.10738215101439265, 0.10759349012139721, 0.1080272879179783], 'solutions': [[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 404.23 seconds!
Processing curr date: 2022-02-13 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c2fc798263204a3657610', 'objective_file_id': '663c2fc698263204a365760e', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 19:07:03 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 19:07:03 - Job submitted: job_id='663c2fc7d448b017e54f94d5'
2024-05-08 19:07:03 - QUEUED
2024-05-08 19:09:31 - RUNNING
2024-05-08 19:15:30 - COMPLETED
2024-05-08 19:15:33 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c2fc7d448b017e54f94d5', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c2fc798263204a3657610', 'objective_file_id': '663c2fc698263204a365760e', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T02:07:03.586Z', 'queued_at_rfc3339nano': '2024-05-09T02:07:03.587Z', 'running_at_rfc3339nano': '2024-05-09T02:09:31.682Z', 'completed_at_rfc3339nano': '2024-05-09T02:15:28.938Z'}, 'job_result': {'file_id': '663c31c098263204a3657620', 'device_usage_s': 289}}, 'status': 'COMPLETED', 'results': {'counts': [1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1], 'energies': [-899.8142022729097, -899.8142022729097, -899.8142022729097, -899.8142022729097, -899.8140802025972, -899.8139581322847, -899.8137139916597, -899.8137139916597, -899.8135919213472, 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1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 547.71 seconds!
Processing curr date: 2022-03-16 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c31ed98263204a3657624', 'objective_file_id': '663c31ec98263204a3657622', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 19:16:13 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 19:16:13 - Job submitted: job_id='663c31edd448b017e54f94d7'
2024-05-08 19:16:13 - QUEUED
2024-05-08 19:18:43 - RUNNING
2024-05-08 19:24:46 - COMPLETED
2024-05-08 19:24:48 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c31edd448b017e54f94d7', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c31ed98263204a3657624', 'objective_file_id': '663c31ec98263204a3657622', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T02:16:13.54Z', 'queued_at_rfc3339nano': '2024-05-09T02:16:13.541Z', 'running_at_rfc3339nano': '2024-05-09T02:18:42.201Z', 'completed_at_rfc3339nano': '2024-05-09T02:24:44.626Z'}, 'job_result': {'file_id': '663c33ec98263204a3657634', 'device_usage_s': 290}}, 'status': 'COMPLETED', 'results': {'counts': [9, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'energies': [-899.7795925257781, -899.7794704554656, -899.7793483851531, -899.7792263148406, -899.7791042445281, -899.7791042445281, -899.7791042445281, -899.7788601039031, -899.7787380335906, -899.7783718226531, -899.7781276820281], 'feasibilities': [True, True, True, True, True, True, True, True, True, True, True], 'objective_values': [0.22038417108175065, 0.22050534780381642, 0.22068812899164647, 0.22073629780553047, 0.22085410560002844, 0.22087060789000373, 0.2209441019202913, 0.22114139951653097, 0.22128187550407075, 0.22169026435936345, 0.2218611331127795], 'solutions': [[1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 552.33 seconds!
Processing curr date: 2022-04-16 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c341898263204a3657638', 'objective_file_id': '663c341798263204a3657636', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 19:25:28 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 19:25:28 - Job submitted: job_id='663c3418d448b017e54f94d9'
2024-05-08 19:25:28 - QUEUED
2024-05-08 19:27:58 - RUNNING
2024-05-08 19:34:00 - COMPLETED
2024-05-08 19:34:03 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c3418d448b017e54f94d9', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c341898263204a3657638', 'objective_file_id': '663c341798263204a3657636', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T02:25:28.74Z', 'queued_at_rfc3339nano': '2024-05-09T02:25:28.74Z', 'running_at_rfc3339nano': '2024-05-09T02:27:57.449Z', 'completed_at_rfc3339nano': '2024-05-09T02:33:59.371Z'}, 'job_result': {'file_id': '663c361798263204a365763c', 'device_usage_s': 288}}, 'status': 'COMPLETED', 'results': {'counts': [14, 2, 3, 1], 'energies': [-899.7645461102991, -899.7643019696741, -899.7640578290491, -899.7640578290491], 'feasibilities': [True, True, True, True], 'objective_values': [0.23549922321350378, 0.2357466216737999, 0.23590463775784443, 0.23598854569161704], 'solutions': [[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 555.70 seconds!
Processing curr date: 2022-05-17 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c364798263204a3657640', 'objective_file_id': '663c364698263204a365763e', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 19:34:47 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 19:34:47 - Job submitted: job_id='663c3647d448b017e54f94da'
2024-05-08 19:34:47 - QUEUED
2024-05-08 19:34:50 - RUNNING
2024-05-08 19:40:50 - COMPLETED
2024-05-08 19:40:52 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c3647d448b017e54f94da', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c364798263204a3657640', 'objective_file_id': '663c364698263204a365763e', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T02:34:47.396Z', 'queued_at_rfc3339nano': '2024-05-09T02:34:47.397Z', 'running_at_rfc3339nano': '2024-05-09T02:34:47.656Z', 'completed_at_rfc3339nano': '2024-05-09T02:40:49.716Z'}, 'job_result': {'file_id': '663c37b198263204a3657642', 'device_usage_s': 288}}, 'status': 'COMPLETED', 'results': {'counts': [13, 2, 2, 1, 1, 1], 'energies': [-899.6566471402217, -899.6566471402217, -899.6560367886592, -899.6559147183467, -899.6555485074092, -899.6554264370967], 'feasibilities': [True, True, True, True, True, True], 'objective_values': [0.3433354284001967, 0.3434022979360825, 0.34393717423579084, 0.3441305781822098, 0.3444755036528773, 0.3445996855621417], 'solutions': [[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 406.72 seconds!
Processing curr date: 2022-06-17 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c37e098263204a3657646', 'objective_file_id': '663c37df98263204a3657644', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 19:41:36 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 19:41:37 - Job submitted: job_id='663c37e1d448b017e54f94db'
2024-05-08 19:41:37 - QUEUED
2024-05-08 19:41:39 - RUNNING
2024-05-08 19:47:39 - COMPLETED
2024-05-08 19:47:42 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c37e1d448b017e54f94db', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c37e098263204a3657646', 'objective_file_id': '663c37df98263204a3657644', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T02:41:37.12Z', 'queued_at_rfc3339nano': '2024-05-09T02:41:37.121Z', 'running_at_rfc3339nano': '2024-05-09T02:41:38.001Z', 'completed_at_rfc3339nano': '2024-05-09T02:47:39.955Z'}, 'job_result': {'file_id': '663c394b98263204a3657648', 'device_usage_s': 289}}, 'status': 'COMPLETED', 'results': {'counts': [15, 2, 1, 2], 'energies': [-899.5422470805225, -899.54066016646, -899.5402939555225, -899.539927744585], 'feasibilities': [True, True, True, True], 'objective_values': [0.45772844079634695, 0.45934757314383895, 0.4597307237517659, 0.46003288145735216], 'solutions': [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 407.07 seconds!
Processing curr date: 2022-07-18 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c397a98263204a365764c', 'objective_file_id': '663c397998263204a365764a', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 19:48:26 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 19:48:26 - Job submitted: job_id='663c397ad448b017e54f94dc'
2024-05-08 19:48:26 - QUEUED
2024-05-08 19:48:29 - RUNNING
2024-05-08 19:54:31 - COMPLETED
2024-05-08 19:54:34 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c397ad448b017e54f94dc', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c397a98263204a365764c', 'objective_file_id': '663c397998263204a365764a', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T02:48:26.817Z', 'queued_at_rfc3339nano': '2024-05-09T02:48:26.818Z', 'running_at_rfc3339nano': '2024-05-09T02:48:27.189Z', 'completed_at_rfc3339nano': '2024-05-09T02:54:29.438Z'}, 'job_result': {'file_id': '663c3ae598263204a365764e', 'device_usage_s': 290}}, 'status': 'COMPLETED', 'results': {'counts': [10, 4, 2, 2, 1, 1], 'energies': [-899.5207858788376, -899.5206638085251, -899.5200534569626, -899.5193210350876, -899.5182224022751, -899.5182224022751], 'feasibilities': [True, True, True, True, True, True], 'objective_values': [0.4792130044740021, 0.47938333898512087, 0.4799653098185577, 0.4806714981361283, 0.4817260375288466, 0.48179708239155056], 'solutions': [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 409.02 seconds!
Processing curr date: 2022-08-18 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c3b1698263204a3657652', 'objective_file_id': '663c3b1598263204a3657650', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 19:55:18 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 19:55:18 - Job submitted: job_id='663c3b16d448b017e54f94dd'
2024-05-08 19:55:18 - QUEUED
2024-05-08 19:55:21 - RUNNING
2024-05-08 20:01:21 - COMPLETED
2024-05-08 20:01:24 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c3b16d448b017e54f94dd', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c3b1698263204a3657652', 'objective_file_id': '663c3b1598263204a3657650', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T02:55:18.634Z', 'queued_at_rfc3339nano': '2024-05-09T02:55:18.635Z', 'running_at_rfc3339nano': '2024-05-09T02:55:18.681Z', 'completed_at_rfc3339nano': '2024-05-09T03:01:20.579Z'}, 'job_result': {'file_id': '663c3c8098263204a3657654', 'device_usage_s': 286}}, 'status': 'COMPLETED', 'results': {'counts': [11, 3, 3, 1, 1, 1], 'energies': [-899.5335581859647, -899.5335581859647, -899.5320933422147, -899.5318492015897, -899.5316050609647, -899.5296519359647], 'feasibilities': [True, True, True, True, True, True], 'objective_values': [0.4664017664446538, 0.4664398583727227, 0.4678700803410983, 0.4681682380335351, 0.4683506506663085, 0.47035568899990987], 'solutions': [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 407.51 seconds!
Processing curr date: 2022-09-18 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c3cb098263204a3657658', 'objective_file_id': '663c3cb098263204a3657656', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 20:02:08 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 20:02:08 - Job submitted: job_id='663c3cb0d448b017e54f94de'
2024-05-08 20:02:08 - QUEUED
2024-05-08 20:02:11 - RUNNING
2024-05-08 20:08:13 - COMPLETED
2024-05-08 20:08:16 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c3cb0d448b017e54f94de', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c3cb098263204a3657658', 'objective_file_id': '663c3cb098263204a3657656', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T03:02:08.963Z', 'queued_at_rfc3339nano': '2024-05-09T03:02:08.964Z', 'running_at_rfc3339nano': '2024-05-09T03:02:09.808Z', 'completed_at_rfc3339nano': '2024-05-09T03:08:11.82Z'}, 'job_result': {'file_id': '663c3e1b98263204a365765a', 'device_usage_s': 291}}, 'status': 'COMPLETED', 'results': {'counts': [8, 3, 4, 1, 2, 1, 1], 'energies': [-899.4227949154381, -899.4224287045006, -899.4221845638756, -899.4221845638756, -899.4215742123131, -899.4209638607506, -899.4196210873131], 'feasibilities': [True, True, True, True, True, True, True], 'objective_values': [0.5772660631608205, 0.5775858384986564, 0.5777806791406422, 0.577840727800031, 0.5784277468822873, 0.5790471550466281, 0.5804146668811597], 'solutions': [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 408.86 seconds!
Processing curr date: 2022-10-19 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c3e4c98263204a365765e', 'objective_file_id': '663c3e4b98263204a365765c', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 20:09:00 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 20:09:00 - Job submitted: job_id='663c3e4cd448b017e54f94df'
2024-05-08 20:09:00 - QUEUED
2024-05-08 20:09:03 - RUNNING
2024-05-08 20:15:06 - COMPLETED
2024-05-08 20:15:08 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c3e4cd448b017e54f94df', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c3e4c98263204a365765e', 'objective_file_id': '663c3e4b98263204a365765c', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T03:09:00.567Z', 'queued_at_rfc3339nano': '2024-05-09T03:09:00.568Z', 'running_at_rfc3339nano': '2024-05-09T03:09:01.075Z', 'completed_at_rfc3339nano': '2024-05-09T03:15:04.053Z'}, 'job_result': {'file_id': '663c3fb898263204a3657660', 'device_usage_s': 293}}, 'status': 'COMPLETED', 'results': {'counts': [9, 5, 3, 1, 1, 1], 'energies': [-899.3300647028726, -899.3299426325601, -899.3296984919351, -899.3289660700601, -899.3288439997476, -899.3285998591226], 'feasibilities': [True, True, True, True, True, True], 'objective_values': [0.669911826241469, 0.6700147349052503, 0.6702868630702825, 0.671054026013198, 0.6711733120148201, 0.6714170867943335], 'solutions': [[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 409.66 seconds!
Processing curr date: 2022-11-19 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c3fe898263204a3657664', 'objective_file_id': '663c3fe898263204a3657662', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 20:15:53 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 20:15:53 - Job submitted: job_id='663c3fe9d448b017e54f94e0'
2024-05-08 20:15:53 - QUEUED
2024-05-08 20:15:55 - RUNNING
2024-05-08 20:21:55 - COMPLETED
2024-05-08 20:21:58 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c3fe9d448b017e54f94e0', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c3fe898263204a3657664', 'objective_file_id': '663c3fe898263204a3657662', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T03:15:53.145Z', 'queued_at_rfc3339nano': '2024-05-09T03:15:53.148Z', 'running_at_rfc3339nano': '2024-05-09T03:15:53.307Z', 'completed_at_rfc3339nano': '2024-05-09T03:21:55.425Z'}, 'job_result': {'file_id': '663c415398263204a3657666', 'device_usage_s': 289}}, 'status': 'COMPLETED', 'results': {'counts': [11, 6, 1, 1, 1], 'energies': [-899.4116445060379, -899.4116445060379, -899.4116445060379, -899.4114003654129, -899.4088368888504], 'feasibilities': [True, True, True, True, True], 'objective_values': [0.5883300061157691, 0.5883418816354902, 0.5883747574303106, 0.5885856769640764, 0.5911926411056718], 'solutions': [[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 407.19 seconds!
Processing curr date: 2022-12-20 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c418298263204a365766a', 'objective_file_id': '663c418298263204a3657668', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
2024-05-08 20:22:43 - Dirac allocation balance = 0 s (unmetered)
2024-05-08 20:22:43 - Job submitted: job_id='663c4183d448b017e54f94e1'
2024-05-08 20:22:43 - QUEUED
2024-05-08 20:22:45 - RUNNING
2024-05-08 20:28:40 - COMPLETED
2024-05-08 20:28:43 - Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '663c4183d448b017e54f94e1', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '663c418298263204a365766a', 'objective_file_id': '663c418298263204a3657668', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-05-09T03:22:43.197Z', 'queued_at_rfc3339nano': '2024-05-09T03:22:43.198Z', 'running_at_rfc3339nano': '2024-05-09T03:22:43.679Z', 'completed_at_rfc3339nano': '2024-05-09T03:28:38.705Z'}, 'job_result': {'file_id': '663c42e698263204a365766c', 'device_usage_s': 289}}, 'status': 'COMPLETED', 'results': {'counts': [12, 3, 1, 2, 1, 1], 'energies': [-899.4937351811574, -899.4934910405324, -899.4930027592824, -899.4923924077199, -899.4917820561574, -899.4914158452199], 'feasibilities': [True, True, True, True, True, True], 'objective_values': [0.5062719196965939, 0.5065549005563347, 0.5070348082132301, 0.5076232649421137, 0.5082234349465327, 0.50856831364782], 'solutions': [[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1]]}}
In optimize_portfolio; done with checking constraints; 401.66 seconds!

We can now calculate the optimal portfolio values over the period of time it was tested.

In [14]:

  • # Import libs
  • import sys
  • import datetime
  • import warnings
  • import numpy as np
  • import pandas as pd
  • import matplotlib.pyplot as plt
  • warnings.filterwarnings("ignore")
  • # Set params
  • INIT_PORT_VAL = 1000000.0
  • OUT_OF_SAMPLE_DAYS = 30
  • K_PRIME = 30
  • XI = 5.0
  • IND_SYMBOL_1 = "QQQE"
  • IND_SYMBOL_2 = "NDX"
  • SEL_STOCK_FILE = "selected_stocks.csv"
  • INDEX_FILE_1 = "data/%s.csv" % IND_SYMBOL_1
  • INDEX_FILE_2 = "data/%s.csv" % IND_SYMBOL_2
  • MIN_DATE = pd.to_datetime("2022-01-01")
  • MAX_DATE = pd.to_datetime("2022-12-31")
  • # Read allocation file
  • df = pd.read_csv(SEL_STOCK_FILE)
  • #df["Date"] = df["Date"].astype("datetime64[ns]")
  • df["Date"] = pd.to_datetime([pd.Timestamp(timestamp).date() for timestamp in df["Date"]])
  • df = df[(df["Date"] >= MIN_DATE) & (df["Date"] <= MAX_DATE)]
  • # Loop through dates and calculate port value
  • beg_port_val = INIT_PORT_VAL
  • df = df.sort_values("Date")
  • adj_dates = sorted(df["Date"].unique())
  • num_adj_dates = len(adj_dates)
  • dates = None
  • port_vals = None
  • for i in range(num_adj_dates):
  • print(
  • "Processing adjustment date %s"
  • % pd.to_datetime(adj_dates[i]).strftime("%Y-%m-%d")
  • )
  • beg_date = pd.to_datetime(adj_dates[i])
  • if i < num_adj_dates - 1:
  • end_date = pd.to_datetime(adj_dates[i + 1])
  • else:
  • end_date = beg_date + datetime.timedelta(days=OUT_OF_SAMPLE_DAYS)
  • tmp_df = df[df["Date"] == beg_date]
  • stocks = tmp_df["Stock"]
  • stocks = list(set(stocks))
  • stocks = list(set(stocks) - set(DROP_STOCKS) - {"FISV"})
  • if end_date > pd.to_datetime("2023-10-20"):
  • stocks = list(set(stocks) - {"ATVI"})
  • all_dates = [beg_date]
  • date0 = beg_date
  • while date0 < end_date:
  • date0 = date0 + datetime.timedelta(days=1)
  • all_dates.append(date0)
  • price_df = pd.DataFrame({"Date": all_dates})
  • for stock in stocks:
  • stock_df = pd.read_csv("data/%s.csv" % stock)
  • #stock_df["Date"] = stock_df["Date"].astype("datetime64[ns]")
  • stock_df["Date"] = pd.to_datetime([pd.Timestamp(timestamp).date() for timestamp in stock_df["Date"]])
  • stock_df = stock_df[
  • (stock_df["Date"] >= beg_date) & (stock_df["Date"] <= end_date)
  • ]
  • if price_df is None:
  • price_df = stock_df
  • else:
  • price_df = price_df.merge(stock_df, on="Date", how="outer")
  • price_df = price_df.fillna(method="ffill").fillna(method="bfill")
  • price_df = price_df.sort_values("Date")
  • tmp_dates = np.array(price_df["Date"])
  • tmp_port_vals = np.zeros(shape=(price_df.shape[0]))
  • assert price_df.shape[0] > 0
  • for stock in stocks:
  • prices = np.array(price_df[stock])
  • beg_price = prices[0]
  • stock_wt = 1.0 / len(stocks)
  • if beg_price <= 0:
  • print(stock)
  • print(price_df[["Date", stock]])
  • assert beg_price > 0, "Error in data for %s" % stock # this assertion was failing, when I comment it out we get all NaN values
  • stock_count = stock_wt * beg_port_val / beg_price
  • tmp_port_vals += stock_count * prices
  • if dates is None:
  • dates = tmp_dates
  • else:
  • dates = np.concatenate([dates, tmp_dates])
  • if port_vals is None:
  • port_vals = tmp_port_vals
  • else:
  • port_vals = np.concatenate([port_vals, tmp_port_vals])
  • beg_port_val = port_vals[-1]

Out [ ]:

Processing adjustment date 2022-01-13
Processing adjustment date 2022-02-13
Processing adjustment date 2022-03-16
Processing adjustment date 2022-04-16
Processing adjustment date 2022-05-17
Processing adjustment date 2022-06-17
Processing adjustment date 2022-07-18
Processing adjustment date 2022-08-18
Processing adjustment date 2022-09-18
Processing adjustment date 2022-10-19
Processing adjustment date 2022-11-19
Processing adjustment date 2022-12-20

We can then plot the optimal portfolio values and compare them with those of Nasdaq-100 and equal-weighted Nasdaq-100 indexes.

In [15]:

  • # note these are the results when the beg price assertion from the previous cell was commented, turn into all NaN values
  • # Plot
  • out_df = pd.DataFrame({"Date": dates, "Port_Val": port_vals})
  • out_df["Date"] = out_df["Date"].astype("datetime64[ns]")
  • ind_df_1 = pd.read_csv(INDEX_FILE_1)
  • #ind_df_1["Date"] = ind_df_1["Date"].astype("datetime64[ns]")
  • ind_df_1["Date"] = pd.to_datetime([pd.Timestamp(timestamp).date() for timestamp in ind_df_1["Date"]])
  • min_date = out_df["Date"].min()
  • max_date = out_df["Date"].max()
  • ind_df_1 = ind_df_1[
  • (ind_df_1["Date"] >= min_date) & (ind_df_1["Date"] <= max_date)
  • ]
  • ind_vals_1 = np.array(ind_df_1[IND_SYMBOL_1])
  • fct = INIT_PORT_VAL / ind_vals_1[0]
  • ind_vals_1 *= fct
  • ind_df_2 = pd.read_csv(INDEX_FILE_2)
  • #ind_df_2["Date"] = ind_df_2["Date"].astype("datetime64[ns]")
  • ind_df_2["Date"] = pd.to_datetime([pd.Timestamp(timestamp).date() for timestamp in ind_df_2["Date"]])
  • min_date = out_df["Date"].min()
  • max_date = out_df["Date"].max()
  • ind_df_2 = ind_df_2[
  • (ind_df_2["Date"] >= min_date) & (ind_df_2["Date"] <= max_date)
  • ]
  • ind_vals_2 = np.array(ind_df_2[IND_SYMBOL_2])
  • fct = INIT_PORT_VAL / ind_vals_2[0]
  • ind_vals_2 *= fct
  • plt.plot(
  • out_df["Date"], out_df["Port_Val"],
  • ind_df_1["Date"], ind_vals_1,
  • ind_df_2["Date"], ind_vals_2,
  • )
  • plt.xlabel("Date")
  • plt.ylabel("Portfolio Value")
  • plt.legend(
  • [
  • "Equal weighted optimal portfolio",
  • "Equal weighted Nasdaq 100",
  • "Nasdaq 100",
  • ]
  • )
  • plt.show()

Out [ ]:

<Figure size 640x480 with 1 Axes>

Conclusion

In this tutorial, we have examined a specific financial application of Dirac related to portfolio optimization. This problem has a naturally quadratic statement, since it relates to minimizing variance of a portfolio based on the covariance between stocks. There is also a natural constraint in the form of the size of the portfolio.

Like feature selection, QBoost, and dimensionality reduction, this tutorial is a variation on the theme of taking advantage of the correlation structure of an underlying data set. Such problems keep arising both because they have important applications, and because they are naturally expressed as QUBOs given the importance of two-body correlations. You may wish to explore other applications of Quadratic linearly constrained binary optimization. Of course you can also get started with your own problems.