Benchmarks
QESEM has been tested on a wide variety of use cases and applications. The following examples can assist you with assessing which types of workloads you can run with QESEM.
A key figure of merit for quantifying the hardness of both error mitigation and classical simulation for a given circuit and observable is active volume: the number of CNOT gates affecting the observable in the circuit. The active volume depends on the circuit depth and width, on the observable weight, and on the circuit structure, which determines the light cone of the observable. For further details, see the talk from the 2024 IBM Quantum Summit. QESEM provides particularly large value in the high-volume regime, giving reliable results for generic circuits and observables.
| Application | Number of qubits | Device | Circuit description | Accuracy | Total time | Runtime usage |
|---|---|---|---|---|---|---|
| VQE circuit | 8 | Eagle (r3) | 21 total layers, 9 measurement bases, 1D chain | 98% | 35 min | 14 min |
| Kicked Ising | 28 | Eagle (r3) | 3 unique layers x 3 steps, 2D heavy-hex topology | 97% | 22 min | 4 min |
| Kicked Ising | 28 | Eagle (r3) | 3 unique layers x 8 steps, 2D heavy-hex topology | 97% | 116 min | 23 min |
| Trotterized Hamiltonian simulation | 40 | Eagle (r3) | 2 unique layers x 10 Trotter steps, 1D chain | 97% | 3 hours | 25 min |
| Trotterized Hamiltonian simulation | 119 | Eagle (r3) | 3 unique layers x 9 Trotter steps, 2D heavy-hex topology | 95% | 6.5 hours | 45 min |
| Kicked Ising | 136 | Heron (r2) | 3 unique layers x 15 steps, 2D heavy-hex topology | 99% | 52 min | 9 min |
Accuracy is measured here relative to the ideal value of the observable: \(\frac{\langle O \rangle_{ideal} - \epsilon}{\langle O \rangle_{ideal}}\), where '\(\epsilon\)' is the absolute precision of the mitigation (set by the user input), and \(\langle O \rangle_{ideal}\) is the observable at the noiseless circuit. 'Runtime usage' measures the usage of the benchmark in batch mode (sum over usage of individual jobs), whereas 'total time' measures usage in session mode (experiment wall time), which includes additional classical and communication times. QESEM is available for execution in both modes, so that users can make the best use of their available resources.
The 28-qubit Kicked Ising circuits simulate the Discrete Time Quasicrystal studied by Shinjo et al. (see arXiv 2403.16718 and Q2B24 Tokyo) on three connected loops of ibm_kawasaki. The circuit parameters taken here are \((\theta_x, \theta_z) = (0.9 \pi, 0)\), with a ferromagnetic initial state \(| \psi_0 \rangle = | 0 \rangle ^{\otimes n}\). The measured observable is the absolute value of the magnetization \(M = |\frac{1}{28} \sum_{i=0}^{27} \langle Z_i \rangle|\). The utility-scale Kicked Ising experiment was run on the 136 best qubits of ibm_fez; this particular benchmark was run at the Clifford angle \((\theta_x, \theta_z) = (\pi, 0)\), at which the active volume grows slowly with circuit depth, which - together with the high device fidelities - enables high accuracy at a short runtime.
Trotterized Hamiltonian simulation circuits are for a Transverse-Field Ising model at fractional angles: \((\theta_{zz}, \theta_x) = (\pi / 4, \pi /8)\) and \((\theta_{zz}, \theta_x) = (\pi / 6, \pi / 8)\) correspondingly (see Q2B24 Tokyo). The utility-scale circuit was run on the 119 best qubits of ibm_brisbane, whereas the 40-qubit experiment was run on the best available chain. The accuracy is reported for the magnetization; high-accuracy results were obtained for higher-weight observables as well.
The VQE circuit was developed together with researchers from the Center for Quantum Technology and Applications at the Deutsches Elektronen-Synchrotron (DESY). The target observable here was a Hamiltonian consisting of a large number of non-commuting Pauli strings, emphasizing QESEM's optimized performance for multi-basis observables. Mitigation was applied to a classically-optimized ansatz; although these results are still unpublished, results of the same quality will be obtained for different circuits with similar structural properties.
Next Steps
- Install QESEM client library.