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arXiv:2312.17418 · Physical Review A

Benchmarking of universal qutrit gates

David Amaro-Alcalá, Barry C. Sanders, Hubert de Guise

Published Jan 29, 2024• 4 citations
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Abstract

We introduce a characterization scheme for a universal qutrit gate set. Motivated by the rising interest in qutrit systems, we apply our criteria to establish that our hyperdihedral group underpins a scheme to characterize the performance of a qutrit T gate. Our resulting qutrit scheme is feasible, as it requires resources and data analysis techniques similar to resources employed for qutrit Clifford randomized benchmarking. Combining our T gate benchmarking procedure for qutrits with known qutrit Clifford-gate benchmarking enables complete characterization of a universal qutrit gate set.

DOI
10.1103/physreva.109.012621

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We introduce a characterization scheme for a universal qutrit gate set. Motivated by the rising interest in qutrit systems, we apply our criteria to establish that our hyperdihedral group underpins a scheme to characterize the performance of a qutrit T gate. Our resulting qutrit scheme is feasible, as it requires resources and data analysis techniques similar to resources employed for qutrit Clifford randomized benchmarking. Combining our T gate benchmarking procedure for qutrits with known qutrit Clifford-gate benchmarking enables complete characterization of a universal qutrit gate set.
Abstract We aim to establish a scalable scheme for characterising diagonal non-Clifford gates for single- and multi-qudit systems; d is a prime-power integer. By employing cyclic operators and a qudit T gate, we generalise the dihedral benchmarking scheme for single- and multi-qudit circuits. Our results establish a path for experimentally benchmarking qudit systems and are of theoretical and experimental interest because our scheme is optimal insofar as it does not require preparation of the full qudit Clifford gate set to characterise a non-Clifford gate. Moreover, combined with Clifford randomised benchmarking, our scheme is useful to characterise the generators of a universal gate set.
Any technology requires precise benchmarking of its components, and the quantum technologies are no exception. Randomized benchmarking allows for the relatively resource economical estimation of the average gate fidelity of quantum gates from the Clifford group, assuming identical noise levels for all gates, making use of suitable sequences of randomly chosen gates. In this work, we report significant progress on randomized benchmarking, by showing that it can be applied individually on a broad class of quantum gates outside the Clifford group, even for varying noise levels per quantum gate. This is possible at little overhead of quantum resources, but at the expense of a significant classical computational cost. At the heart of our analysis is a representation-theoretic framework which we bring into contact with classical estimation techniques based on bootstrapping and matrix pencils. We demonstrate the functioning of the scheme at hand of benchmarking tensor powers of T gates. Apart from its practical relevance, we expect this insight to be relevant as it highlights the role of assumptions made on unknown noise processes when characterizing quantum gates at high precision.
Randomized benchmarking is a widely used experimental technique to characterize the average error of quantum operations. Benchmarking procedures that scale to enable characterization of nnn-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 nnn-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)\mathrm{poly}(n)poly(n)-sized circuits. The procedure provides experimental access to two independent parameters that together characterize the average gate fidelity of a group element.
We describe a practical experimental protocol for robustly characterizing the error rates of non-Clifford gates associated with dihedral groups, including small single-qubit rotations. Our dihedral benchmarking protocol is a generalization of randomized benchmarking that relaxes the usual unitary 2-design condition. Combining this protocol with existing randomized benchmarking schemes enables practical universal gate sets for quantum information processing to be characterized in a way that is robust against state-preparation and measurement errors. In particular, our protocol enables direct benchmarking of the $\ensuremath{\pi}/8$ gate even under the gate-dependent error model that is expected in leading approaches to fault-tolerant quantum computation.
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.
We introduce a scheme to characterise a qudit T gate that has different noise than a set of Clifford gates. We developed our scheme through representation theory and ring theory to generalise non-Clifford interleaved benchmarking to qudit systems. By restricting to the qubit case, we recover the dihedral benchmarking scheme. Our characterisation scheme provides experimental physicists a practical method for characterising universal qudit gate sets and advances randomised benchmarking research by providing the characterisation of a complete qudit library.