Demonstrating scalable benchmarking of universal gate sets.
Jordan Hines, Marie Lu, Ravi Naik, Akel Hashim, Jean-Loup Ville, Bradley Mitchell, David Santiago, Stefan Seritan, Kevin C Young, Robin Blume-Kohout, Irfan A. Siddiqi, K. Birgitta Whaley, Timothy J Proctor
Many-qubit errors such as crosstalk are not apparent in low-width circuits Randomized Benchmarking (RB) [1] and Random Circuit Sampling (RCS) [2] characterize average gate performance • Large gate overhead (RB) • High computational cost for universal gate sets (RB, RCS) Circuit mirroring [3]: Flexible technique for designing scalable benchmarks Scalable Randomized Benchmarking
Many-qubit errors such as crosstalk are not apparent in low-width circuits Randomized Benchmarking (RB) [1] and Random Circuit Sampling (RCS) [2] characterize average gate performance • Large gate overhead (RB) • High computational cost for universal gate sets (RB, RCS) Circuit mirroring [3]: Flexible technique for designing scalable benchmarks Scalable Randomized Benchmarking
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.
The performance of quantum gates is often assessed using some form of randomized benchmarking. However, the existing methods become infeasible for more than approximately five qubits. Here we show how to use a simple and customizable class of circuits-randomized mirror circuits-to perform scalable, robust, and flexible randomized benchmarking of Clifford gates. We show that this technique approximately estimates the infidelity of an average many-qubit logic layer, and we use simulations of up to 225 qubits with physically realistic error rates in the range 0.1%-1% to demonstrate its scalability. We then use up to 16 physical qubits of a cloud quantum computing platform to demonstrate that our technique can reveal and quantify crosstalk errors in many-qubit circuits.
Quantum computers have the potential to bring about a new age of technology, but in order for them to become a reality, the elephant in the room must be addressed, quantum errors. The complexity of quantum errors grows exponentially as the system size is increased; scalable characterization protocols which work under physically realistic noise are therefore needed to assess and optimize control. \n \nRandomized Benchmarking (RB) is a family of characterization protocols with the requisite qualities. RB protocols are independent of state preparation and measurement (SPAM) errors, and because they extract partial information about the error profiles in the form of figures of merit, they are scalable in the number of qubits. In this thesis, we study these figures of merit under various error models, gate-sets, and sample distributions, to further our understanding of their physical meaning, and to fine-tune the best practice for diagnosing errors in basic gate-sets. \n \nThe first study presented in this thesis looks at the physical meaning of the unitarity under physically realistic gate-dependent noise. Numerically, we demonstrate that under these realistic noise models, the unitarity obtained via Extended RB (XRB) overlaps strongly with the average of the unitarity of the errors over the set of individual operations. \n \nThe second study numerically and analytically proves that the Standard RB (SRB) decay parameter p coincides with the decay parameter of the novel figure of merit gate-set circuit fidelity. We also prove that, in the limit of high-fidelity single-qubit experiments, the disconnect between the average gate fidelity and SRB experimental results is caused by a basis mismatch between the gates and the state-preparation and measurement procedures. \n \nIn the third part of this thesis, we compare the results of two variations of the SRB protocol, one that samples uniformly (SRB) and one that samples non-uniformly (NIST RB) from the Clifford group. We prove that NIST RB produces an exponential fidelity curve that gives different infidelity results than SRB. \n \nThe fourth and final study gives a standard for assessing basic gate-sets. Experimental results are given from the assessment run on super-conducting and ion-trap devices. We also experimentally show how the systematic error bounds can be tightened by accounting for the error's degree of coherence, as well as using weaker randomizing sets.
The construction of large scale quantum computing devices might be one of the most exciting \nand promising endeavors of the 21st century, but it also comes with many challenges. \nAs quantum computers are supplemented with more registers, their error profile generally \ngrows in complexity, rendering the enterprise of quantifying the reliability of quantum computations \nincreasingly difficult through naive characterization techniques. In the last decade, \na lot of efforts has been directed toward developing highly scalable benchmarking schemes. \nA leading family of characterization methods built upon scalable principles is known as randomized \nbenchmarking (RB). \nIn this thesis, many tools are presented with the objective of improving the scalability, \nand versatility of RB techniques, as well as demonstrating their reliability under various \nerror models. \nThe first part of this work investigates the connection between the error of individual \ncircuit components and the error of their composition. Before reasoning about intricate circuit \nconstructions, it is shown that there exists a well-motivated way to define decoherent \nquantum channels, and that every channel can be factorized into a unitary-decoherent composition. \nThis dichotomy carries to the circuit evolution of important error parameters by \nassuming realistic error scenarios. Those results are used to improve the confidence interval \nof RB diagnoses and to reconcile experimentally estimated parameters with physically and \noperationally meaningful quantities. \nIn the second part of this thesis, various RB schemes are either developed or more rigorously \nanalyzed. A first result consists of the introduction of “dihedral benchmarking”, a \ntechnique which, if performed in conjunction with standard RB protocols, enables the characterization \nof operations that form a universal gate-set. Finally, rigorous analysis tools are \nprovided to demonstrate the reliability of a highly scalable family of generator-based RB \nprotocols known as direct RB.
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.
In its many variants, randomized benchmarking (RB) is a broadly used technique for assessing the quality of gate implementations on quantum computers. A detailed theoretical understanding and general guarantees exist for the functioning and interpretation of RB protocols if the gates under scrutiny are drawn uniformly at random from a compact group. In contrast, many practically attractive and scalable RB protocols implement random quantum circuits with local gates randomly drawn from some gate-set. Despite their abundance in practice, for those non-uniform RB protocols, general guarantees for gates from arbitrary compact groups under experimentally plausible assumptions are missing. In this work, we derive such guarantees for a large class of RB protocols for random circuits that we refer to as filtered RB. Prominent examples include linear cross-entropy benchmarking, character benchmarking, Pauli-noise tomography and variants of simultaneous RB. Building upon recent results for random circuits, we show that many relevant filtered RB schemes can be realized with random quantum circuits in linear depth, and we provide explicit small constants for common instances. We further derive general sample complexity bounds for filtered RB. We show filtered RB to be sample-efficient for several relevant groups, including protocols addressing higher-order cross-talk. Our theory for non-uniform filtered RB is, in principle, flexible enough to design new protocols for non-universal and analog quantum simulators.