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.
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.
We propose matchgate benchmarking for a Rydberg atom processor. Matchgate benchmarking characterizes a continuously parametrized family of two-qubit gates generated by the XY interaction, and it is both scalable and resistant to state preparation and measurement errors. On the Rydberg platform, the native dipole–dipole interaction between two Rydberg states realizes this XY interaction. We show that the interaction maps to quadratic Majorana operators and therefore generates matchgates, and we describe how the full generalized matchgate set can be realized using the native interaction, single-qubit rotations, and a microwave-driven bit-flip between the two Rydberg states. We implement the protocol in numerical simulations with realistic noise and confirm that it recovers the gate fidelity while remaining resistant to the latter. Our results establish matchgate benchmarking as a practical tool for characterizing Rydberg processors that use the native XY interaction.
Abstract Randomized benchmarking is a technique for estimating the average fidelity of a set of quantum gates. However, if this gateset is not the multi-qubit Clifford group, robustly extracting the average fidelity is difficult. Here, we propose a new method based on representation theory that has little experimental overhead and robustly extracts the average fidelity for a broad class of gatesets. We apply our method to a multi-qubit gateset that includes the T -gate, and propose a new interleaved benchmarking protocol that extracts the average fidelity of a two-qubit Clifford gate using only single-qubit Clifford gates as reference.
Randomized benchmarking (RB) protocols are the most widely used methods for assessing the performance of quantum gates.However, the existing RB methods either do not scale to many qubits or cannot benchmark a universal gate set.Here, we introduce and demonstrate a technique for scalable RB of many universal and continuously parametrized gate sets, using a class of circuits called randomized mirror circuits.Our technique can be applied to a gate set containing an entangling Clifford gate and the set of arbitrary single-qubit gates, as well as gate sets containing controlled rotations about the Pauli axes.We use our technique to benchmark universal gate sets on four qubits of the Advanced Quantum Testbed, including a gate set containing a controlled-S gate and its inverse, and we investigate how the observed error rate is impacted by the inclusion of non-Clifford gates.Finally, we demonstrate that our technique scales to many qubits with experiments on a 27-qubit IBM Q processor.We use our technique to quantify the impact of crosstalk on this 27-qubit device, and we find that it contributes approximately 2=3 of the total error per gate in random many-qubit circuit layers.
Creating scalable, reliable, and well-motivated benchmarks for quantum computers is challenging: straightforward approaches to benchmarking suffer from exponential scaling, are insensitive to important errors, or use poorly-motivated performance metrics. Furthermore, curated benchmarking suites cannot include every interesting quantum circuit or algorithm, which necessitates a tool that enables the easy creation of new benchmarks. In this work, we introduce a software tool for creating scalable and reliable benchmarks that measure a well-motivated performance metric (process fidelity) from user-chosen quantum circuits and algorithms. Our software, called scarab, enables the creation of efficient and robust benchmarks even from circuits containing thousands or millions of qubits, by employing efficient fidelity estimation techniques, including mirror circuit fidelity estimation and subcircuit volumetric benchmarking. scarab provides a simple interface that enables the creation of reliable benchmarks by users who are not experts in the theory of quantum computer benchmarking or noise. We demonstrate the flexibility and power of scarab by using it to turn existing inefficient benchmarks into efficient benchmarks, to create benchmarks that interrogate hardware and algorithmic trade-offs in Hamiltonian simulation, to quantify the in-situ efficacy of approximate circuit compilation, and to create benchmarks that use subcircuits to measure progress towards executing a circuit of interest.
Randomised benchmarking is a widely used experimental technique to characterise the average error of quantum operations. Benchmarking procedures that scale to enable the characterisation of n-qubit circuits rely on efficient procedures for manipulating those circuits and, as such, have been limited to subgroups of the Clifford group. However, universal quantum computers require additional, non-Clifford gates to approximate arbitrary unitary transformations. We define a scalable randomised benchmarking procedure over n-qubit unitary matrices that correspond to protected non-Clifford gates for a class of stabiliser codes. We present efficient methods for representing and composing group elements, sampling them uniformly and synthesising corresponding poly(n)-sized circuits. The procedure provides experimental access to two independent parameters that together characterise the average gate fidelity of a group element. A scalable procedure to determine the error of quantum operations has been developed by researchers in the United States. Andrew Cross and colleagues at the IBM T.J. Watson Research Center have expanded previously used protocols to a broader range of quantum circuits, thereby enabling error benchmarking for all common logical operations used in leading quantum computing protocols. The standard technique for error characterization in these devices is randomized benchmarking, which provides benefits such as insensitivity to measurement errors, but on the other hand only functions in a limited number of circumstances. In their theoretical study, the researchers demonstrate how randomized benchmarking approaches can be expanded to a much broader range of logical operations. The procedure can be readily implemented experimentally, and provides access to important experimental noise parameters in quantum computing.
As quantum processors grow, new performance benchmarks are required to capture the full quality of the devices at scale. While quantum volume is an excellent benchmark, it focuses on the highest quality subset of the device and so is unable to indicate the average performance over a large number of connected qubits. Furthermore, it is a discrete pass/fail and so is not reflective of continuous improvements in hardware nor does it provide quantitative direction to large-scale algorithms. For example, there may be value in error mitigated Hamiltonian simulation at scale with devices unable to pass strict quantum volume tests. Here we discuss a scalable benchmark which measures the fidelity of a connecting set of two-qubit gates over N qubits by measuring gate errors using simultaneous direct randomized benchmarking in disjoint layers. Our layer fidelity can be easily related to algorithmic run time, via γ defined in Ref.\cite{berg2022probabilistic} that can be used to estimate the number of circuits required for error mitigation. The protocol is efficient and obtains all the pair rates in the layered structure. Compared to regular (isolated) RB this approach is sensitive to crosstalk. As an example we measure a N=80(100) qubit layer fidelity on a 127 qubit fixed-coupling "Eagle" processor (ibm\_sherbrooke) of 0.26(0.19) and on the 133 qubit tunable-coupling "Heron" processor (ibm\_montecarlo) of 0.61(0.26). This can easily be expressed as a layer size independent quantity, error per layered gate (EPLG), which is here 1.7×10−2(1.7×10−2) for ibm\_sherbrooke and 6.2×10−3(1.2×10−2) for ibm\_montecarlo.