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Abstract:

Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum (NISQ) devices. While most conventional QEM schemes assume discrete gate-based circuits with noise appearing either before or after each gate, the assumptions are inappropriate for describing realistic noise that may have strong gate dependence and complicated nonlocal effects, and general computing models such as analog quantum simulators. To address these challenges, we first extend the scenario, where each computation process, being either digital or analog, is described by a continuous time evolution. For noise from imperfections of the engineered Hamiltonian or additional noise operators, we show it can be effectively suppressed by a stochastic QEM method. Since our method assumes only accurate single qubit controls, it is applicable to all digital quantum computers and various analog simulators. Meanwhile, errors in the mitigation procedure can be suppressed by leveraging the Richardson extrapolation method. As we numerically test our method with various Hamiltonians under energy relaxation and dephasing noise and digital quantum circuits with additional two-qubit crosstalk, we show an improvement of simulation accuracy by 2 orders. We assess the resource cost of our scheme and conclude the feasibility of accurate quantum computing with NISQ devices.

Abstract:

The universal quantum homogeniser can transform a qubit from any state to any other state with arbitrary accuracy, using only unitary transformations to perform this task. Here we present an implementation of a finite quantum homogeniser using nuclear magnetic resonance (NMR), with a four-qubit system. We compare the homogenisation of a mixed state to a pure state, and the reverse process. After accounting for the effects of decoherence in the system, we find the experimental results to be consistent with the theoretical symmetry in how the qubit states evolve in the two cases. We analyse the implications of this symmetry by interpreting the homogeniser as a physical implementation of pure state preparation and information scrambling.