This folder contains the data for the paper "Strategies for solving the Fermi-Hubbard model on near-term quantum computers" by Chris Cade, Lana Mineh, Ashley Montanaro and Stasja Stanisic. Data corresponds to the output of numerical experiments attempting to find the ground state of instances of the Hubbard model on varying grids. Output is stored in log files tracking the energy and fidelity achieved against the number of iterations of the optimiser. ## DIRECTORY STRUCTURE ## - exact # Description: Contains results of the runs where we consider no noise and exact measurement of the expectation value of the energy. Directory structure is ansatz type -> grid size -> ansatz depth. Bottom level folders contain optimisation.txt which is a log file for the optimisation. These results are used to produce Figures 7 and 8 in the paper. -- EfficientHamiltonianVariational --- 1x2, 1x3, 1x4, 1x5, 1x6, 1x7, 1x8, 1x9, 1x10, 1x11, 1x12, 2x2, 2x3, 3x3 ---- depth-1 to depth-10 --- 2x4, 3x4 ---- depth-1 to depth-14 --- 2x5 ---- depth-1 to depth-12 --- 2x6 ---- depth-1 to depth-19 -- HamiltonianVariational --- 1x2, 1x3, 1x4, 1x5, 1x6, 1x7, 1x8, 1x9, 1x10, 1x11, 1x12, 2x2, 2x3, 2x4, --- 2x5, 2x6, 3x3, 3x4 ---- depth-1 to depth-10 -- NumberPreserving --- 1x2, 2x2 ---- depth-1 --- 1x3, 1x4 ---- depth-1 to depth-2 --- 1x5, 1x6 ---- depth-1 to depth-3 --- 1x7, 1x9, 2x3 ---- depth-1 to depth-4 --- 1x8, 1x10, 3x3 ---- depth-1 to depth-5 --- 1x11, 2x5 ---- depth-1 to depth-6 --- 2x4 ---- depth-1 to depth-7 - noisy-cd # Description: Contains results of noisy experiments (with and without error detection) on Efficent Hamiltonian Variational anstz with coordinate descent optimisation algorithm. Directory structure is grid size -> noise rate (where e.g. 10-3 represents 10^(-3)) -> error detection. Bottom level folders contain optimisation.txt files that are the log files, along with more detailed logs in optimisation_details.txt. Each experiment has been run 3 times. The optimisation_details.txt file contains six columns. First column ("Neval") matches the "Iter" value from optimisation.txt, and represents the number of "circuit evaluations" (as per the naming convention of the main text of the paper). The second column ("Nmeas") represents the number of (successful, post error-detection) energy measurements. The third column ("Niter") represents the number of iterations of the optimisation algorithm. Fourth column ("Error") gives the error of the energy measurement with ground state energy. Fifth column ("Exact error") gives exact error of energy for the given parameters with ground state energy (calculated using the exact state), matching the "Error" column from optimisation.txt. This value is calculated at the end of a single iteration of the algorithm or at certain pre-specified points within a single iteration. When the value is not calculated, instead of exact error, the energy value is printed. Similarly, sixth column ("1-Fidelity") gives the exact infidelity between the current state and the ground state, and when this value is not calculated the value of 0 is printed. These results are used to produce Figure 10 and Table IV in the paper. -- 1x6, 2x2, 2x3 --- 10-3, 10-4, 10-6 ---- errdet, noerrdet - noisy-spsa # Description: Same as noisy-cd but using the SPSA optimisation algorithm. These results are used to produce Figure 10 and Table IV in the paper. -- 1x6, 2x2, 2x3 --- 10-3, 10-4, 10-6 ---- errdet, noerrdet - real-cd # Description: Contains results of experiments with realistic measurement (but no noise) on Efficient Hamiltonian Variational ansatz with coordinate descent optimisation algorithm. The grid size folders contain details in optimisation.txt and optimisation_details.txt of the 5 times the experiment was run. These results are used to produce Figure 9 and Table III in the paper. -- 1x6, 2x2, 2x3, 3x3 - real-spsa # Description: Same as real-cd but using the SPSA optimisation algorithm. These results are used to produce Figure 9 and Table III in the paper. -- 1x6, 2x2, 2x3, 3x3 - urange # Description: Contains results tracking final fidelity achieved with varying U values for different grid sizes, using the Efficient Hamiltonian Variational ansatz, simulated exact energy measurements, and the L-BFGS optimiser. Directory structure is grid size -> ansatz depth -> U value (between 0 and 8 with step size 0.1). These results are used to produce Figure 15 and 16 in the paper. -- 1x6 --- depth-1 to depth-10 -- 2x2 --- depth-1 to depth-7 -- 3x3 --- depth-1 to depth-14 ---- u-0.0 to u-8.0 - number-preserving # Description: Contains detailed tests on the Number Preserving ansatz with simulated exact energy measurements and the L-BFGS optimiser. -- fermion-placement # Description: Contains data when running the Number Preserving ansatz with different initial fermion placements for 3x3 grid. Directory structure is type of fermion placement -> ansatz depth. These results are used to produce Figure 13 in the paper. --- ground-state, spread, top-corner ---- depth-1 to depth-5 -- pre-initialisation # Description: Contains comparison of running the Number Preserving ansatz with pre-initialised parameters against the ordinary ansatz. Directory structure is grid size -> NP ansatz type -> ansatz depth. These results are used to produce Figure 14 in the paper. --- 2x3, 3x3 ---- ordinary, pre-init ----- depth-1 to depth-5 - spsa-comparison # Description: Contains the results of running standard SPSA vs our three-stage variant for a 1x6 Efficient Hamiltonian Variational depth 5 ansatz. Each experiment was run 5 times. Details of number of measurements are in the optmisation_details.txt files. These results are used to produce Figure 6 in the paper. -- standard, three-stage - stat-error # Description: Contains information on the statistical error in approximating the energy when at the ground state of the Hubbard Hamiltonian vs at the state produced with the Efficient Hamiltonian Variational ansatz depth 6 starting parameters. Bottom level folders contain 2x2_{n}meas.txt where n is the number of measurements carried out on each term of the Hamiltonian. n = 100-1,000 in steps of 100, 2,000-10,000 in steps of 1,000, 20,000-100,000 in steps of 10,000 and 200,000-1,000,000 in steps of 100,000. The data in these files is the error (= estimated - exact) when measuring onsite, horizontal and vertical terms. These results are used to produce Figure 19 in the paper. -- ehv-starting, ground-state - half-fill # Description: Contains results of the runs where the grid is half-filled with fermions. We use the Efficient Hamiltonian Variational ansatz and consider no noise and exact measurement of the expectation value of the energy. Directory structure is grid size -> ansatz depth. Bottom level folders contain optimisation.txt which is a log file for the optimisation. These results are used to produce Figures 17 and 18 in the paper. -- 1x2, 1x3, 1x4, 1x5, 1x6, 1x7, 1x8, 2x2, 2x3, 3x3 --- depth-1 to depth-7 -- 1x9, 1x10, 1x12 --- depth-1 to depth-10 -- 1x11 --- depth-1 to depth-11 -- 2x4 --- depth-1 to depth-13 -- 2x5 --- depth-1 to depth-12 -- 2x6 --- depth-1 to depth-20