Error-Mitigated Digital Quantum Simulation

Abstract

Variational algorithms may enable classically intractable simulations on near-future quantum computers. However, their potential is limited by hardware errors. It is therefore crucial to develop efficient ways to mitigate these errors. Here, we propose a stabiliser-like method which enables the detection of up to 60 -80 % of depolarising errors. Our method is suitable for near-term quantum hardware. Simulations show that our method can significantly benefit calculations subject to both stochastic and correlated noise, especially when combined with existing error mitigation techniques.

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

“…In particular, the stabilizer-like method proposed in ref. [125] could enable the detection of up to 60-80 % of depolarizing errors, thus largely improving the results of variational algorithms, as well as Figure 8. Summary of state-of-art experimental digital quantum simulations of spin models.…”

“…In particular, the stabilizer‐like method proposed in ref. [] could enable the detection of up to 60–80 % of depolarizing errors, thus largely improving the results of variational algorithms, as well as of quantum simulations. Theoretical proposals have been developed to demonstrate that the accuracy in the expectation values of computed quantum observables can be improved by suitably interpolating to zero noise the results on a series of experiments at varying noise levels .…”

“…This strategy has been recently applied to suppress incoherent errors in variational calculations on superconducting circuits, see Section 4.2. The combination of these two approaches could further improve the accuracy of the computed observables . We notice that experimental error‐mitigation results, based on probabilistic error cancellation techniques, have also been reported on trapped ions platforms…”

“…[], the largest quantum simulation reported on the actual IBM quantum hardware actually employed five qubits (four encoding the target system, plus one ancilla for correlations readout), showing good agreement with the expected behavior despite the noisy nature of the quantum processors. It is important to note that the accuracy of these results was largely improved by systematic post‐processing corrections based on general properties of the extracted correlation functions, a problem‐specific procedure that could be applied to many other quantum simulations, after analyzing the symmetries of the target Hamiltonian . Fitting of such digitally simulated correlations allows to extract 4D inelastic neutron scattering spectra, a crucial experimental tool to characterize magnetic molecules .…”

“…As mentioned in the first part of Section 4, considerable work is currently focusing on understanding the main sources of error, and on developing error mitigation techniques to enhance the overall quantum simulation fidelities . These theoretical proposals have been recently and successfully applied to improve the accuracy of the observables extracted from VQE calculations on a superconducting chip .…”