Benchmarking quantum devices beyond classical capabilities

TL;DR

This work addresses the scalability bottleneck of the Quantum Volume benchmark, whose heavy-output evaluation historically required costly classical simulations. By introducing parity-preserving (single-parity) and double-parity benchmarks, the authors fix the heavy-output subspace structurally, enabling direct determination of heavy outputs and analytic heavy-output frequencies under noise, with estimators that run efficiently on quantum and classical resources. They validate the approach with experiments on IBM Brisbane and simulations, showing that the new benchmarks reproduce the qualitative scaling of QV while remaining scalable to larger systems. The paper also discusses practical extensions to detect parity-preserving errors and potential cheating, and outlines how these benchmarks can power benchmarking for future, larger quantum computers in an architecture-agnostic and near-term-friendly manner, including extensions to rectangular circuit families.

Abstract

Rapid development of quantum computing technology has led to a wide variety of sophisticated quantum devices. Benchmarking these systems becomes crucial for understanding their capabilities and paving the way for future advancements. The Quantum Volume (QV) test is one of the most widely used benchmarks for evaluating quantum computer performance due to its architecture independence. However, as the number of qubits in a quantum device grows, the test faces a significant limitation: classical simulation of the quantum circuit, which is indispensable for evaluating QV, becomes computationally impractical. In this work, we propose modifications of the QV test that allow for direct determination of the most probable outcomes of a quantum circuit, eliminating the need for expensive classical simulations. This approach resolves the scalability problem of the Quantum Volume test beyond classical computational capabilities, while still examining key features of universal quantum computing.

Figures (12)

• Figure 1: Quantum circuit used in the quantum volume test, consisting of $T$ layers and $N$ qubits, includes permutations $\Pi$ followed by two-qubit random gates BishopCross2019.
• Figure 2: Outputs for three-qubit QV circuit represented as vertices of a cube, each edge corresponds to one bit flip, with heavy output subspace denoted in red: (a) exemplary realization and (b) parity preserving case - bit flip always sends a state out of heavy subspace, as there are no edges connecting red vertices.
• Figure 3: Diagram of the modified quantum volume circuit with hidden parity preservation (only first two layers presented for clarity). The global parity conservation is enforced by a cancellation scheme using single-qubit gates. Each two-qubit gate provided to quantum computer (for example the dashed region) consists of parity-preserving 2-qubit gate (eg. $U_6$) surrounded by single-qubit gates (eg. $B^{-1}, D^{-1},K,L$), which are cancelled by their inverses immersed in neighbouring layers. This ensures the overall circuit preserves parity, even though individual constituent gates do not.
• Figure 4: Comparison of single parity ($p$), double parity ($dp$) and standard ($s$) quantum volume ($QV$) tests. Heavy output probability $h_U$ as a function of number of layers $T$ for 6 qubits on a) quantum device IBM Brisbane, b) simulator of this computer with error parameters rescaled by factor $\lambda = 0.5$, to obtain $\log_2(QV) = 6$. The dashed line indicate $h_U = 2/3$ threshold. c) Ranges of the scaling factor $\lambda$ for passing different tests -- for any noise level proposed benchmarks (parity and double parity) exhibit the same behavior as the original QV test.
• Figure 5: An example of parity preserving circuit for $N=3$ qubits and $T=2$ layers. We mark $m=2$ parity preserving qubits by $^*$. Gate $X$ is applied on the first qubit only. As first two qubits keep parity $B_1$ is a random matrix of the type $U_2^{\{00,11\}} \oplus U_2^{\{01, 10\}}$ and $C_1$ is arbitrary. The permutation $(1,2,3)$ maps the first qubit to the second place, second to the third and third to the first. Finally, matrix $B_2$ is of the type $U_2^{\{00,10\}} \oplus U_2^{\{01, 11\}}$ and $C_2$ is diagonal to preserve parity. The parity subset at the end of the circuit equals $\mathcal{M}_2 = \{1,3\}$, hence, if the circuit is noiseless we should measure one of the following bit-strings $100, 110, 001, 011$.