Quantum computing hardware is advancing rapidly toward utility-scale machines that will enable scientific breakthroughs. Many teams are pursuing distinct and difficult-to-compare routes to this goal, using different qubit technologies and logical architectures. Tracking progress toward quantum utility therefore requires rigorous benchmarks that measure computational capability relative to utility-scale challenge problems and enable fair comparison across disparate platforms. Here we demonstrate direct, cross-platform measurement of quantum computational capability using a new benchmark that quantifies the size of the largest computationally relevant quantum circuits that a machine can execute successfully and the speed at which it can execute them. We apply this quantum universal operation performance system (QUOPS) experimentally to leading processors from Quantinuum, Google, and IBM, computing directly on physical qubits. Translating state-of-the-art resource requirements for recognized challenge problems that represent useful quantum computation into effective QUOPS circuit sizes shows that computational capability must grow by 5 orders of magnitude, motivating fault-tolerant approaches. We use the same benchmark to assess the performance of a simple fault-tolerant logical-qubit processor implemented on up to eight [[7,1,3]]-encoded logical qubits using Quantinuum Helios-1, and project the growth of capability across successive generations of fault-tolerant quantum computers to show how QUOPS can track progress toward quantum scientific utility.
Timothy Proctor, Oliver Hart, Oliver Widzowski Maupin et al.· 0 citations
Noisy logic operations on a quantum computational register -- e.g., one or more qubits -- can be described by transfer matrices (a.k.a. CPTP maps or superoperators) that act linearly on the density matrix representing the register's quantum state. Collectively, these operations form a gate set. Gate sets have a gauge freedom; many gate sets that appear different actually predict the same experimental outcomes. A property of a gate set can be observable (and thus physically relevant) only if it is gauge-invariant. Unfortunately, no good gauge-invariant parameterizations of gate sets are known. We introduce the next best thing, a perturbative gauge-invariant parameterization of small Markovian errors in gate sets. We construct vector spaces of properties that are first-order gauge-invariant (FOGI). We show how to construct and understand FOGI properties, how to use them as coordinates to parameterize gate sets without gauge freedom, and how to extract approximately gauge-invariant error metrics.
Juan Gonzalez de Mendoza, Corey I. Ostrove, T. Proctor et al.· 0 citations
Noise characterization methods such as randomized benchmarking (RB) are critical for the development of scalable quantum computers. Modern RB protocols for multiqubit systems extract physically relevant error rates by exploiting the structure of the group representation generated by the set of benchmarked operations. However, existing techniques become prohibitively inefficient for representations that are highly reducible yet decompose into irreducible subspaces of high dimension. These situations prevail when benchmarking high-dimensional systems such as qudits or bosonic modes, where experimental control is limited to implementing a small subset of all possible unitary operations. We introduce a broad framework for enhancing the sample efficiency of RB that is sufficiently powerful to extend the practical reach of RB beyond the multiqubit setting. Our strategy, which applies to any benchmarking group, uses ‘synthetic’ quantum circuits with classical post-processing of both input and output data to leverage the full structure of reducible superoperator representations. To demonstrate the efficacy of our approach, we develop a detailed theory of RB for systems with rotational symmetry. Such systems carry a natural action of the group SU(2), and they form the basis for several novel quantum error-correcting codes. We show that, for experimentally accessible high-spin systems, synthetic RB protocols can reduce the complexity of measuring rotationally invariant error rates by two orders of magnitude relative to standard approaches such as character RB.
Yale Fan, Riley J. Murray, T. Ladd et al.· Quantum Science and Technolo...· 4 citations
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