Many-body Quantum Score: a scalable benchmark for digital and analog quantum processors and first test on a commercial neutral atom device

TL;DR

The paper tackles the challenge of benchmarking quantum processors on their ability to simulate genuine many-body dynamics in a scalable, device-agnostic way. It introduces the Many-Body Quantum Score (MBQS), which uses a global quench in the one-dimensional transverse-field Ising model and the surge time $t_*$—when two-point connected correlations $g^{(2)}_\ell(t)$ peak across distances—to define a quantitative score based on the relative error against exact Ising results. The authors provide a detailed protocol, analytical insights (including a Lehmann representation and surge-time analysis) and numerical demonstrations, and report experimental results on a commercial neutral-atom QPU (Ruby) with error mitigation to illustrate practicality. MBQS offers a scalable, interpretable benchmark that tests state preparation, Hamiltonian control, coherence, and measurement fidelity, and it enables cross-platform comparisons for current and near-future quantum devices tackling many-body physics problems. The work also lays the groundwork for extending the benchmark to gate-based QPUs and larger system sizes as hardware quality improves, contributing a practical tool for guiding hardware development and assessing near-term quantum advantage in many-body simulations.

Abstract

We propose the Many-body Quantum Score (MBQS), a practical and scalable application-level benchmark protocol designed to evaluate the capabilities of quantum processing units (QPUs)--both gate-based and analog--for simulating many-body quantum dynamics. MBQS quantifies performance by identifying the maximum number of qubits with which a QPU can reliably reproduce correlation functions of the transverse-field Ising model following a specific quantum quench. This paper presents the MBQS protocol and highlights its design principles, supported by analytical insights, classical simulations, and experimental data. It also displays results obtained with Ruby, an analog QPU based on Rydberg atoms developed by the Pasqal company. These findings demonstrate MBQS's potential as a robust and informative tool for benchmarking near-term quantum devices for many-body physics.

Figures (26)

• Figure 1: Proposed benchmark protocol.
• Figure 2: Antipodal $2$-point connected correlation functions $g^{(2)}_{\lfloor L/2 \rfloor}(t)$ for the Ising and Rydberg models with $a = \qty{7.5}{\micro m}$ ($J \approx \qty{1.22}{rad \cdot \micro s^{-1}}$), $g = 1$, $L \in [3, 20]$, for the Ising and Rydberg Hamiltonians. The time evolution is displayed up to $1.1 \times t_*(L)$.
• Figure 3: Spacetime plot of $2$-point connected correlation functions $g^{(2)}_\ell(t)$ for the Ising model with $a = \qty{7.5}{\micro m}$ ($J \approx \qty{1.22}{rad \cdot \micro s^{-1}}$), $g = 1$, $L = 20$. See \ref{['fig:2pt-corr-all-plus']} for another representation of this information. The maximal velocity is defined in \ref{['eq:max-velocity']}.
• Figure 4: Surge times for the Ising and Rydberg models with $g = 1$, $a = \qty{7.5}{\micro m}$ ($J \approx \qty{1.22}{rad \cdot \micro s^{-1}}$), $\ket{\psi_{\text{ini}}} = \ket{+ \cdots +}$. The cross and plus mark the values computed by finding the maximum of the antipodal $2$-point connected correlation functions. The linear regressions are indicated by lines ($R^2 = 0.99996$ for both), and the yellow shadowed area indicates the width of the peak at 75 height. Finally, we also show the time computed from the Lieb--Robinson velocity.
• Figure 5: Von Neumann entropy for a partition of the chain in two equal parts and at the surge time $t_*$ plotted as a function the system size $L$.