Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation

This repository contains the code to reproduce the numerical implementations presented in the manuscript Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation.

Dependences

• Python>=3.11.8

• qibo==0.2.12

• qibojit==0.1.6

• qiskit==1.2.0

Usage

XXZ_folded.py contains a class to generate the circuit to prepare an eigenstate of the XXZ folded model with two domain walls, $N$ bulk sites and $M$ magnons. For $N=5$ and $N=6$ with one magnon, the simplifications explained in the article are implemented.

from XXZ_folded import XXZ_folded_one_domain

N = 6
M = 1
domain_pos = [4,5]

model = XXZ_folded_one_domain(N, M, domain_pos)
model._get_roots()
circ_xx, circ_xxb = model.get_xx_b_circuit()
circ_u0 = model.get_U0_circ()
circ_d = model.get_D_circ()
circ_Psi_M_0 = model.get_Psi_M_0_circ()

circuit = model.get_full_circ()

run_simulation.py performs the simulations explained in the paper for a given eigenstate. The simulation can be customized throught specific command-line arguments.

python run_simulation.py --path result --N 5 --M 1 --domain_pos 3 4 --connectivity google_sycamore --basis_gates cx rz sx x id --boundaries False --lamb 0.003 --n_training_samples 50 --precision single

• path: path to save the data files with the expectaion values and the states.
• N: number of bulk qubits.
• M: number of magnons.
• domain_pos: position of the domain walls.
• connectivity: can be google_sycamore for $N=5$ and $N=6$. None otherwise.
• basis_gates: single-qubit and two-qubit gates used to decompose the circuit.
• boundaries: if True, it extends the final state to $N+2$ qubits.
• lamb: depolarizing parameter used for the noisy simulation.
• n_training_samples: number of near Clifford circuits used in CDR.
• precision single: enables complex64 and double enables complex128.

The structure of the output files is

• path/state.npy: dictionary containing the noiseless and noisy states under the keys noisy and noiseless, respectively.
• path/training_states/training_circuits.npy: list with the training set of near Clifford circuits used in CDR.
• path/training_states/states_i.npy: dictionary containing the noiseless and noisy i-th training state under the keys noisy and noiseless, respectively.
• path/mitigated_values.npy: list of lists. The first element is [[circuit,layout],energy_noiseless,Q1_noiseless,Q2_noiseless], where circuit is the circuit to prepare the eigenstate, layout denotes the mapping from virtual to physical qubits, and energy_noiseless, Q1_noiseless, Q2_noiseless are the noiseless values for the energy, $Q_1$, and $Q_2$, respectively. The second, third and fourth elements have the structure [mit_val, val, optimal_params, train_val]. The second element corresponds to the energy, the third to $Q_1$, and the fourth to $Q_2$. mit_val is the mitigated expectation value, valis the noisy expectation value, optimal params is a list with to elements [a,b] which are the optimal fit parameters from CDR and produce the line $ax+b$, tain_valis a dictionary containing the noiseless and noisy training states under the keys noisy and noiseless, respectively.

The file data.gz contains the files to reproduce the results of the paper.