Error mitigation with Clifford quantum-circuit data

Abstract

Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data {Xinoisy,Xiexact} via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where Xinoisy and Xiexact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.

Algebraic Bethe Circuits

“…For detailed analysis of the various mitigation techniques we refer the reader to Refs. [50][51][52]. In particular, the implementations here are very similar to those in Ref.…”

“…In order to obtain the best possible results it is necessary to use error mitigation which focuses on reducing the impact of noise rather than removing its effects completely. In this work we implemented three techniques: zero-noise extrapolation (ZNE) [50], Clifford data regression (CDR) [51] and variable noise Clifford data regression (vnCDR) [52]. We used the open source software package Mitiq [53] to execute these methods.…”

Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

“…Training with fermionic linear optics (TFLO) is a method proposed by two of us 25 to mitigate errors in quantum algorithms for simulating fermionic systems, which fits into an overall framework initially introduced by Czarnik et al 59 . The idea is based on producing a set of pairs of noisy and exact energies, which are then used as training data to infer a map from the noisy energy evaluation for the final state produced by VQE to an approximation of the exact energy.…”

“…In Ref. [59], the family of circuits used was Clifford circuits, which can be simulated efficiently classically via the Gottesman-Knill theorem. Here, we use fermionic linear optics (FLO) circuits, which can also be simulated efficiently classically 28 .…”

Quantum error mitigation via matrix product operators

“…Previously studied QEM methods include error extrapolation [10,12,13], quasi-probability method [12,14], quantum subspace expansion [15], symmetry verification [16,17], and several learning-based approaches [18][19][20]. Different techniques can be combined, e.g., combinations of error extrapolation, quasi-probability, and symmetry verification are discussed by Cai [21].…”