supermarq.benchmarks.hamiltonian_simulation

Classes

HamiltonianSimulation

Quantum benchmark focused on the ability to simulate 1D

Module Contents

class supermarq.benchmarks.hamiltonian_simulation.HamiltonianSimulation(num_qubits: int, time_step: int = 1, total_time: int = 1)

Bases: supermarq.benchmark.Benchmark

Quantum benchmark focused on the ability to simulate 1D Transverse Field Ising Models (TFIM) of variable length.

Device performance is based on how closely the experimentally obtained average magnetization (along the Z-axis) matches the noiseless value. Since the 1D TFIM is efficiently simulatable with classical algorithms, computing the noiseless average magnetization remains scalable over a large range of benchmark sizes.

circuit() → cirq.Circuit

Generates a circuit to simulate the evolution of an n-qubit TFIM.

The TFIM chain evolves under the Hamiltonian:

H(t) = - Jz * sum_{i=1}^{n-1}(sigma_{z}^{i} * sigma_{z}^{i+1})

• e_ph * cos(w_ph * t) * sum_{i=1}^{n}(sigma_{x}^{i})

where,

w_ph: frequency of E” phonon in MoSe2. e_ph: strength of electron-phonon coupling.

Returns:

The circuit for Hamiltonian simulation.

qiskit_circuit() → qiskit.QuantumCircuit

Generates a circuit to simulate the evolution of an n-qubit TFIM.

The TFIM chain evolves under the Hamiltonian:

H(t) = - Jz * sum_{i=1}^{n-1}(sigma_{z}^{i} * sigma_{z}^{i+1})

• e_ph * cos(w_ph * t) * sum_{i=1}^{n}(sigma_{x}^{i})

where,

w_ph: frequency of E” phonon in MoSe2. e_ph: strength of electron-phonon coupling.

Returns:

The circuit for Hamiltonian simulation.

score(counts: collections.abc.Mapping[str, float]) → float

Compute the average magnetization of the TFIM chain along the Z-axis for the experimental results and via noiseless simulation.

Parameters:

counts – Dictionary of the experimental results. The keys are bitstrings represented the measured qubit state, and the values are the number of times that state of observed.

Returns:

The Hamiltonian simulation benchmark score.

num_qubits

time_step = 1

total_time = 1