Improving the efficiency of learning-based error mitigation
1Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA.
2Institute of Theoretical Physics, Jagiellonian University, Krakow, Poland.
3Information Sciences, Los Alamos National Laboratory, Los Alamos, NM, USA.
4Quantum Science Center, Oak Ridge, TN 37931, USA.
| Published: | 2025-05-05, volume 9, page 1727 |
| Editor: | Xin Wang |
| Eprint: | arXiv:2204.07109v2 |
| Doi: | https://doi.org/10.22331/q-2025-05-05-1727 |
| Citation: | Quantum 9, 1727 (2025). |
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Abstract
Error mitigation will play an important role in practical applications of near-term noisy quantum computers. Current error mitigation methods typically concentrate on correction quality at the expense of frugality (as measured by the number of additional calls to quantum hardware). To fill the need for highly accurate, yet inexpensive techniques, we introduce an error mitigation scheme that builds on Clifford data regression (CDR). The scheme improves the frugality by carefully choosing the training data and exploiting the symmetries of the problem. We test our approach by correcting long range correlators of the ground state of XY Hamiltonian on IBM Toronto quantum computer. We find that our method is an order of magnitude cheaper while maintaining the same accuracy as the original CDR approach. The efficiency gain enables us to obtain a factor of $10$ improvement on the unmitigated results with the total budget as small as $2\cdot10^5$ shots. Furthermore, we demonstrate orders of magnitude improvements in frugality for mitigation of energy of the LiH ground state simulated with IBM's Ourense-derived noise model.
Featured image: Improved Clifford Data Regression method. Circuit of interest together with observable $O$ are used to generate training data $\{ O^{\rm exact}_i, O^{\rm noisy}_i \}_i$ made out of observables computed from classically simulable circuits similar to the circuit of interest. They are evaluated on both, classical ($O^{\rm exact}_i$) and noisy quantum ($O^{\rm noisy}_i$) computers, as shown in the upper panel. Previous methods for generating training circuits resulted in data clustering, a situation in which the majority of training circuits share similar $O^{\rm exact}$, as depicted in a cartoon in the left part of the middle panel where the green circles are the training data and pink ring represents $(O^{\rm exact},O^{\rm noisy})$ for the circuit of interest. This effect necessitates the use of large training data sets to maintain high-quality correction $O^{\rm mitigated}$. We solve that problem by distributing and symmetrizing the training data, as depicted in the right part of the middle panel. That is achieved by generating the training circuits with a large variance of $O^{\rm exact}$ using classical computation. Our approach significantly reduces the shot cost of data-driven error mitigation techniques while preserving their high correction quality. Symmetries of the problem, if present, can be used to enhance the data further, i.e., to generate additional data (the blue squares) from initially generated (the green circles) one, at no extra cost. Finally, a learned ansatz (the red line) is used to correct $O$ for the circuit of interest.
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