AppQSim: Application-oriented benchmarks for Hamiltonian simulation on a quantum computer

TL;DR

AppQSim delivers an application-oriented benchmarking framework for Hamiltonian simulation on quantum hardware, spanning material dynamics, static low-temperature observables, NMR spectroscopy, molecular ground-state preparation, and classical optimization. A central contribution is the distinguishability cost $\mathcal{S}$, the minimal total two-qubit gates a perfect computer must execute to certify incorrectness of hardware outputs via a chi-square test, enabling cross-task hardware comparison even when exact solutions are inaccessible. The suite includes concrete protocols such as a compact free-fermion encoding on a square lattice, adiabatic Kagome-lattice ground-state preparation, benzene NMR-era FID spectroscopy, hydrogen-chain adiabatic state preparation with a randomized Hamiltonian evolution, and a Max-Cut adiabatic benchmark on 3-regular graphs, each with task-specific scoring rules. These benchmarks emphasize diverse circuit depths, connectivities, and measurement strategies, offering a practical path toward assessing and guiding quantum hardware toward real-world quantum advantage in Hamiltonian simulation tasks.

Abstract

We introduce AppQSim, a benchmarking suite for quantum computers focused on applications of Hamiltonian simulation. We consider five different settings for which we define a precise task and score: condensed matter and material simulation (dynamic and static properties), nuclear magnetic resonance simulation, chemistry ground state preparation, and classical optimization. These five different benchmark tasks display different resource requirements and scalability properties. We introduce a metric to evaluate the quality of the output of a tested quantum hardware, called distinguishability cost, defined as the minimal number of gates that a perfect quantum computer would have to run to certify that the output of the benchmarked hardware is incorrect.

Figures (9)

• Figure 1: Square lattice after the compact fermion encoding. Blue circles indicate sites of the original lattice and red circles indicate ancillas.
• Figure 2: Left: Curve $\langle \mathcal{O}\rangle$ as a function of Trotter step number, on a system of size $L=4\times 4$, for different depolarizing noise levels $p$ per two-qubit gate. The curves are averaged over $20$ different analog trajectories as described in granet2024analog. The black continuous curve is the exact value. Right: Exact noiseless curve $\langle \mathcal{O}\rangle$ as a function of number of Trotter steps divided by $L$, for different system sizes $L$.
• Figure 3: Top: Value of the score (in the legend) obtained in size $L=4\times 4$ for different noise levels $p$ and for different number of shots $N_S$ (cyan: $p=0.01$ and $N_S=10^3$, teal: $p=0.001$ and $N_S=50$, purple: $p=0.0001$ and $N_S=50$, orange: $p=0.00001$ and $N_S=10^3$). Bottom: Score obtained in size $L=4\times 4$ as a function of number of shots per time point, for different noise levels. Here, the error bars indicate an estimated standard deviation of the score over different experiments (which is different from $\delta x$ in the top panel defined in \ref{['deltax']}).
• Figure 4: Top: Kagome lattice with $L_x=3$ and $L_y=2$. Bottom: Energy density as a function of number of Trotter steps in the benchmark setup, for different system sizes and different noise levels. Dashed lines indicate the minimum reached by the curve with the same color, and correspond to the benchmark score.
• Figure 5: Depiction of the benzene molecule. The spinful atoms are indicated with a green circle. The numbering of the different spinful nuclei is given in red.