With the development of controllable quantum systems, fast and practical characterization of multi-qubit gates has become essential for building high-fidelity quantum computing devices. The usual way to fulfill this requirement via randomized benchmarking demands complicated implementation of numerous multi-qubit twirling gates. How to efficiently and reliably estimate the fidelity of a quantum process remains an open problem. This work thus proposes a character-cycle benchmarking protocol and a character-average benchmarking protocol using only local twirling gates to estimate the process fidelity of an individual multi-qubit operation. Our protocols were able to characterize a large class of quantum gates including and beyond the Clifford group via the local gauge transformation, which forms a universal gate set for quantum computing. We demonstrated numerically our protocols for a non-Clifford gate—controlled- ( T X ) and a Clifford gate—five-qubit quantum error-correcting encoding circuit. The numerical results show that our protocols can efficiently and reliably characterize the gate process fidelities. Compared with the cross-entropy benchmarking, the simulation results show that the character-average benchmarking achieves three orders of magnitude improvements in terms of sampling complexity.
With the development of controllable quantum systems, fast and practical characterization of multi-qubit gates has become essential for building high-fidelity quantum computing devices. The usual way to fulfill this requirement via randomized benchmarking demands complicated implementation of numerous multi-qubit twirling gates. How to efficiently and reliably estimate the fidelity of a quantum process remains an open problem. This work thus proposes a character-cycle benchmarking protocol and a character-average benchmarking protocol using only local twirling gates to estimate the process fidelity of an individual multi-qubit operation. Our protocols were able to characterize a large class of quantum gates including and beyond the Clifford group via the local gauge transformation, which forms a universal gate set for quantum computing. We demonstrated numerically our protocols for a non-Clifford gate—controlled- ( T X ) and a Clifford gate—five-qubit quantum error-correcting encoding circuit. The numerical results show that our protocols can efficiently and reliably characterize the gate process fidelities. Compared with the cross-entropy benchmarking, the simulation results show that the character-average benchmarking achieves three orders of magnitude improvements in terms of sampling complexity.
Quantum gate benchmarking is unavoidably influenced by state preparation and measurement errors. Randomized benchmarking addresses this challenge by employing group twirling to regularize the noise channel, then provides a characterization of quantum channels that is robust to these errors through exponential fittings. In practice, local twirling gates are preferred due to their high fidelity and experimental feasibility. However, while existing RB methods leveraging local twirling gates are effective for benchmarking Clifford gates, they face fundamental challenges in benchmarking non-Clifford gates. In this work, we solve this problem by introducing the Pauli Transfer Character Benchmarking. This protocol estimates the Pauli transfer matrix elements for a quantum channel using only local Pauli operations. Building on this protocol, we develop a fidelity benchmarking method for non-Clifford gates U satisfying U2=I. We validate the feasibility of our protocol through numerical simulations applied to Toffoli gates as a concrete example.
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.
Because of the technical difficulty of building large quantum computers, it is important to be able to estimate how faithful a given implementation is to an ideal quantum computer. The common approach of completely characterizing the computation process via quantum process tomography requires an exponential amount of resources, and thus is not practical even for relatively small devices. We solve this problem by demonstrating that twirling experiments previously used to characterize the average fidelity of quantum memories efficiently can be easily adapted to estimate the average fidelity of the experimental implementation of important quantum computation processes, such as unitaries in the Clifford group, in a practical and efficient manner with applicability in current quantum devices. Using this procedure, we demonstrate state-of-the-art coherent control of an ensemble of magnetic moments of nuclear spins in a single crystal solid by implementing the encoding operation for a 3-qubit code with only a 1% degradation in average fidelity discounting preparation and measurement errors. We also highlight one of the advances that was instrumental in achieving such high fidelity control.
Randomized benchmarking is a widely used experimental technique to characterize the average error of quantum operations. Benchmarking procedures that scale to enable characterization 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 randomized benchmarking procedure over n-qubit unitary matrices that correspond to protected non-Clifford gates for a class of stabilizer codes. We present efficient methods for representing and composing group elements, sampling them uniformly, and synthesizing corresponding poly(n)-sized circuits. The procedure provides experimental access to two independent parameters that together characterize the average gate fidelity of a group element.
Group twirling is crucial in quantum information processing, particularly in randomized benchmarking and randomized compiling. While protocols based on Pauli twirling have been effectively crafted to transform arbitrary noise channels into Pauli channels for Clifford gates—thereby facilitating efficient benchmarking and mitigating worst-case errors—the lack of practical twirling groups for multiqubit non-Clifford gates remains a challenge. To address this gap, we study the issue of finding twirling groups for generic quantum gates, focusing on a widely used circuit structure in randomized benchmarking or randomized compiling. Specifically, for multiqubit controlled phase gates, which are essential in quantum algorithms and directly implementable in practice, we determine optimal twirling groups within the realm of classically replaceable unitary operations. Contrasting with the local Pauli twirling group for Clifford gates, the optimal groups for such gates contain nonlocal operations, highlighting the overhead of tailoring noise in global non-Clifford contexts. We design new benchmarking procedures for multiqubit controlled phase gates based on the optimal twirling groups. Our simulation results show that our scheme can improve the precision and accuracy of benchmarking in small-scale systems. Published by the American Physical Society 2024
Accurate and precise control of large quantum systems is paramount to achieve practical advantages on quantum devices. Therefore, benchmarking the hardware errors in quantum computers has drawn significant attention lately. Existing benchmarks for digital quantum computers involve averaging the global fidelity over a large set of quantum circuits and are therefore unsuitable for specific multi-qubit gates used in analog quantum operations. Moreover, average global fidelity is not the optimal figure-of-merit for some of the applications specific to multi-qubit gates and analog devices , such as the study of many-body physics, which often use local observables. In this two-part paper, we develop a new figure-of-merit suitable for multi-qubit quantum gates based on the reduced Choi matrix of the operation. In the first part, we develop an efficient, scalable protocol to completely characterize the reduced Choi matrix. We identify two sources of sampling errors in measurements of the reduced Choi matrix and we show that there are fundamental limits to the rate of convergence of the sampling errors, analogous to the standard quantum limit and Heisenberg limit. A slow convergence rate of sampling errors would mean that we need a large number of experimental shots. We develop protocols using quantum information scrambling, which has been observed in disordered systems for e.g., to speed up the rate of convergence of the sampling error at state preparation Moreover, we develop protocols using squeezed and entangled initial states to enhance the convergence rate of the sampling error at measurement, which results in a metrologically enhanced reduced process tomography protocol.