The standard randomized benchmarking protocol requires access to often complex operations that are not always directly accessible. Compiler optimization does not always ensure equal sequence length of the directly accessible universal gates for each random operation. We introduce a version of the RB protocol that creates Haar-randomness using a directly accessible universal gate set of equal sequence length rather than relying upon a t-design or even an approximate one. This makes our protocol highly resource efficient and practical for small qubit numbers. We exemplify our protocol for creating Haar-randomness in the case of single and two qubits. Benchmarking our result with the standard RB protocol, allows us to calculate the overestimation of the average gate fidelity as compared to the standard technique. We augment our findings with a noise analysis which demonstrates that our method could be an effective tool for building accurate models of experimental noise.
The standard randomized benchmarking protocol requires access to often complex operations that are not always directly accessible. Compiler optimization does not always ensure equal sequence length of the directly accessible universal gates for each random operation. We introduce a version of the RB protocol that creates Haar-randomness using a directly accessible universal gate set of equal sequence length rather than relying upon a t-design or even an approximate one. This makes our protocol highly resource efficient and practical for small qubit numbers. We exemplify our protocol for creating Haar-randomness in the case of single and two qubits. Benchmarking our result with the standard RB protocol, allows us to calculate the overestimation of the average gate fidelity as compared to the standard technique. We augment our findings with a noise analysis which demonstrates that our method could be an effective tool for building accurate models of experimental noise.
Randomized benchmarking (RB) is an efficient and robust method to characterize gate errors in quantum circuits. Averaging over random sequences of gates leads to estimates of gate errors in terms of the average fidelity. These estimates are isolated from the state preparation and measurement errors that plague other methods such as channel tomography and direct fidelity estimation. A decisive factor in the feasibility of randomized benchmarking is the number of sampled sequences required to obtain rigorous confidence intervals. Previous bounds were either prohibitively loose or required the number of sampled sequences to scale exponentially with the number of qubits in order to obtain a fixed confidence interval at a fixed error rate. Here, we show that, with a small adaptation to the randomized benchmarking procedure, the number of sampled sequences required for a fixed confidence interval is dramatically smaller than could previously be justified. In particular, we show that the number of sampled sequences required is essentially independent of the number of qubits and scales favorably with the average error rate of the system under investigation. We also investigate the fitting procedure inherent to randomized benchmarking in light of our results and find that standard methods such as ordinary least squares optimization can give misleading results. We therefore recommend moving to more sophisticated fitting methods such as iteratively reweighted least squares optimization. Our results bring rigorous randomized benchmarking on systems with many qubits into the realm of experimental feasibility.
Randomized benchmarking (RB) protocols are widely used to measure an average error rate for a set of quantum logic gates. However, the standard version of RB is limited because it only benchmarks a processor's native gates indirectly, by using them in composite n -qubit Clifford gates. Standard RB's reliance on n -qubit Clifford gates restricts it to the few-qubit regime, because the fidelity of a typical composite n -qubit Clifford gate decreases rapidly with increasing n . Furthermore, although standard RB is often used to infer the error rate of native gates, by rescaling standard RB's error per Clifford to an error per native gate, this is an unreliable extrapolation. Direct RB is a method that addresses these limitations of standard RB, by directly benchmarking a customizable gate set, such as a processor's native gates. Here we provide a detailed introduction to direct RB, we discuss how to design direct RB experiments, and we present two complementary theories for direct RB. The first of these theories uses the concept of error propagation or scrambling in random circuits to show that direct RB is reliable for gates that experience stochastic Pauli errors. We prove that the direct RB decay is a single exponential, and that the decay rate is equal to the average infidelity of the benchmarked gates, under broad circumstances. This theory shows that group twirling is not required for reliable RB. Our second theory proves that direct RB is reliable for gates that experience general gate-dependent Markovian errors, using similar techniques to contemporary theories for standard RB. Our two theories for direct RB have complementary regimes of applicability, and they provide complementary perspectives on why direct RB works. Together these theories provide comprehensive guarantees on the reliability of direct RB.
Benchmarking methods that can be adapted to multiqubit systems are essential for assessing the overall or "holistic" performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single error rate that quantifies overall performance. But, scaling Clifford RB to many qubits is surprisingly hard. It has only been performed on one, two, and three qubits as of this writing. This reflects a fundamental inefficiency in Clifford RB: the n-qubit Clifford gates at its core have to be compiled into large circuits over the one- and two-qubit gates native to a device. As n grows, the quality of these Clifford gates quickly degrades, making Clifford RB impractical at relatively low n. In this Letter, we propose a direct RB protocol that mostly avoids compiling. Instead, it uses random circuits over the native gates in a device, which are seeded by an initial layer of Clifford-like randomization. We demonstrate this protocol experimentally on two to five qubits using the publicly available ibmqx5. We believe this to be the greatest number of qubits holistically benchmarked, and this was achieved on a freely available device without any special tuning up. Our protocol retains the simplicity and convenient properties of Clifford RB: it estimates an error rate from an exponential decay. But, it can be extended to processors with more qubits-we present simulations on 10+ qubits-and it reports a more directly informative and flexible error rate than the one reported by Clifford RB. We show how to use this flexibility to measure separate error rates for distinct sets of gates, and we use this method to estimate the average error rate of a set of cnot gates.
Benchmarking noise in quantum gates is crucial for developing dependable quantum computers, as noise directly affects gate fidelity and computational accuracy. Randomized benchmarking (RB) protocols, which evaluate performance through random gate sequences, provide a reliable way to quantify average error rates due to their scalability and robustness in averaging out complex, device-specific noise. In this talk, we will discuss several variants of randomized benchmarking protocols including an overview of our recent work in this area.
Randomized benchmarking is routinely used as an efficient method for characterizing the performance of sets of elementary logic gates in small quantum devices. In the measurement-based model of quantum computation, logic gates are implemented via single-site measurements on a fixed universal resource state. Here we adapt the randomized benchmarking protocol for a single qubit to a linear cluster state computation, which provides partial, yet efficient characterization of the noise associated with the target gate set. Applying randomized benchmarking to measurement-based quantum computation exhibits an interesting interplay between the inherent randomness associated with logic gates in the measurement-based model and the random gate sequences used in benchmarking. We consider two different approaches: the first makes use of the standard single-qubit Clifford group, while the second uses recently introduced (non-Clifford) measurement-based 2-designs, which harness inherent randomness to implement gate sequences.
Randomized benchmarking (RB) is a widely used method for estimating the average fidelity of gates implemented on a quantum computing device. The stochastic error of the average gate fidelity estimated by RB depends on the sampling strategy (i.e., how to sample sequences to be run in the protocol). The sampling strategy is determined by a set of configurable parameters (an RB configuration) that includes Clifford lengths (a list of the number of independent Clifford gates in a sequence) and the number of sequences for each Clifford length. The RB configuration is often chosen heuristically and there has been little research on its best configuration. Therefore, we propose a method for fully optimizing an RB configuration so that the confidence interval of the estimated fidelity is minimized while not increasing the total execution time of sequences. By experiments on real devices, we demonstrate the efficacy of the optimization method against heuristic selection in reducing the variance of the estimated fidelity.