[Paper Review] Experimental error mitigation using linear rescaling for variational quantum eigensolving with up to 20 qubits

Eliott Rosenberg, Paul Ginsparg+1 more|arXiv (Cornell University)|Jun 2, 2021

Quantum Computing Algorithms and ArchitectureComputer Science35 references18 citations

TL;DR

This paper proposes and benchmarks linear rescaling as a noise mitigation technique for variational quantum eigensolving (VQE) on noisy intermediate-scale quantum (NISQ) devices. By modeling noise as exponential damping of expectation values and estimating the damping factor via perturbative regimes, the method recovers ground-state energies within 10% of exact values for circuits up to 25 ansatz layers on up to 20 qubits, outperforming zero noise extrapolation and other methods in specific regimes.

ABSTRACT

Quantum computers have the potential to help solve a range of physics and chemistry problems, but noise in quantum hardware currently limits our ability to obtain accurate results from the execution of quantum-simulation algorithms. Various methods have been proposed to mitigate the impact of noise on variational algorithms, including several that model the noise as damping expectation values of observables. In this work, we benchmark various methods, including a new method proposed here. We compare their performance in estimating the ground-state energies of several instances of the 1D mixed-field Ising model using the variational-quantum-eigensolver algorithm with up to 20 qubits on two of IBM's quantum computers. We find that several error-mitigation techniques allow us to recover energies to within 10% of the true values for circuits containing up to about 25 ansatz layers, where each layer consists of CNOT gates between all neighboring qubits and Y-rotations on all qubits.

Motivation & Objective

• To evaluate and benchmark multiple error mitigation techniques for variational quantum eigensolving (VQE) on noisy NISQ devices.
• To assess the performance of linear rescaling via damping factor estimation in recovering accurate ground-state energies for the 1D mixed-field Ising model.
• To compare the effectiveness of linear rescaling against zero noise extrapolation and other noise mitigation techniques on up to 20-qubit quantum circuits.
• To determine whether error mitigation is most effective when applied post-optimization rather than during the variational optimization process.

Proposed method

• Proposes a new method for estimating the damping factor C in the noise model ⟨O⟩_noisy ≈ C⟨O⟩_exact, where C quantifies exponential suppression of expectation values due to noise.
• Estimates the damping factor using the perturbative regime of the Hamiltonian, leveraging analytically solvable limits to calibrate noise suppression.
• Applies linear rescaling to correct noisy expectation values: ⟨O⟩_exact ≈ ⟨O⟩_noisy / C, enabling recovery of near-ideal results.
• Employs zero noise extrapolation (ZNE) by artificially increasing noise through repeated CNOT gates and fitting to an exponential decay model.
• Uses classical optimization to train ansatz circuits before applying error mitigation on quantum hardware, isolating the impact of noise.
• Performs readout error mitigation using uncorrelated readout error models, with error rates derived from IBM’s daily calibrations.

Experimental results

Research questions

• RQ1 How effective is linear rescaling via damping factor estimation in mitigating noise in VQE for the 1D mixed-field Ising model on up to 20 qubits?
• RQ2 How does the performance of linear rescaling compare to zero noise extrapolation and other error mitigation techniques in recovering ground-state energies?
• RQ3 Can the damping factor be reliably estimated from the perturbative regime of the Hamiltonian, and does this lead to improved accuracy?
• RQ4 At what circuit depth (in terms of ansatz layers) does error mitigation become essential for achieving sub-10% energy error?
• RQ5 Does post-optimization error mitigation outperform in-loop mitigation when noise primarily suppresses expectation values?

Key findings

• Linear rescaling using the perturbative regime for damping factor estimation achieves ground-state energy estimates within 10% of the exact value for circuits with up to 25 ansatz layers.
• Zero noise extrapolation (ZNE) with three data points (including the original circuit) provides a strong baseline, but is outperformed by the perturbative method in deep circuits.
• The damping factor estimated from gate fidelities in the backwards light cone overestimates suppression for deep circuits, while the Qiskit Aer noise model underestimates it.
• Readout error mitigation using uncorrelated error models with IBM’s calibration data performs comparably to full readout mitigation, validating its use in large-scale settings.
• For circuits with up to 20 qubits and 25 layers, linear rescaling enables accurate energy estimation even when noise would otherwise render results meaningless.
• The study confirms that post-optimization error mitigation is viable when noise acts primarily as a damping of expectation values, provided the damping factor is accurately estimated.