Abstract
We propose a method to reliably and efficiently extract the fidelity of many-qubit quantum circuits composed of continuously parametrized two-qubit gates called matchgates. This method, which we call matchgate benchmarking, relies on advanced techniques from randomized benchmarking as well as insights from the representation theory of matchgate circuits. We argue the formal correctness and scalability of the protocol, and moreover deploy it to estimate the performance of matchgate circuits generated by two-qubit XY spin interactions on a quantum processor.
Highlights
Quantum computers promise a revolution in computational power, and a multinational effort is underway to construct them
A variety of techniques have been developed, with the most popular class of techniques known as randomized benchmarking (RB) [1–9], where one characterizes the quality of gates in a gateset by applying random sequences of gates of increasing length, and tracks the corresponding increase in average error
We address this challenge by proposing matchgate benchmarking, an advanced randomized benchmarking procedure based on the general framework given in [10] as well as the recently introduced linear cross-entropy benchmarking [15]
Summary
Matchgate circuits are a continuous class of quantum circuits originally conceived by Valiant [16] and sub-. The two-qubit matchgates are generated by unitaries of the form U (α) = exp(iαP ⊗ P ), where P, P are Pauli X or Y matrices. The n-qubit matchgate group Mn is defined by considering n qubits on a line and composing nearest-neighbor gates of this form, along with single-qubit Z(θ) = exp(iθZ) gates We further extend this group with a Pauli X on the last qubit. The Xn gate maps all γi for i < 2n to themselves but maps γ2n to −γ2n, so it corresponds to a reflection F of the 2n-th axis In this way, matchgate and generalized matchgates unitaries can be efficiently tracked on a classical computer. Since the Majorana operators and their products span the space of n-qubit operators, (generalized) matchgate unitaries are fully determined by the corresponding rotation (and reflection) matrix (up to an overall phase). We note that the addition of the extra bit flip gate, lifting the matchgates to the generalized matchgates, is critical in ensuring the mutual inequivalence of the representations Γk
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