We proposed a general methodology for evaluating the optimal resource cost required for error mitigation.
Ryuji Takagi (distinguished visiting researcher) from QunaSys Inc. proposed a general methodology for evaluating the optimal resource cost required for one of the most promising error mitigation methods for near-term devices, employing ideas and techniques developed in the field known as quantum resource theories. The preprint is available on arXiv:
"Optimal resource cost for error mitigation",
The recent technological development pushes us toward the realization of quantum information processing in a fully controlled manner, and a near-term cornerstone is to make use of noisy intermediate-scale quantum (NISQ) devices. Although the size of the circuit is much smaller than that for fault-tolerant quantum computation, the effect of noise becomes a serious obstacle to find a practical application of NISQ devices. To deal with this crucial noise effect within the reach of current technology, a number of error mitigation techniques have been proposed, and in particular the probabilistic error cancellation method has gained much attention as a promising candidate that may be feasibly implemented on near-term noisy devices.
Mitigating noise, however, comes with a cost. The most demanding resource cost paid for the probabilistic error cancellation method is the sampling cost; the required number of samples tends to grow exponentially with respect to the size of the circuit and quickly becomes out of hand. Therefore, estimating the smallest cost for ensuring the desired accuracy is crucial. However, due to an infinite number of suboptimal strategies that near-term devices can realize, evaluating such optimal cost is extremely challenging, and only heuristic approaches realizing certain costs were discussed on a case-by-case basis, without knowing their optimality whatsoever.
CONTRIBUTION AND RESULT
To overcome this problem, we provided a general methodology for evaluating the optimal resource cost for running probabilistic error cancellation for a given noisy device that allows us to obtain its rigorous bounds. We achieved this by establishing a novel connection between error mitigation and another field of quantum information theory known as quantum resource theories. Resource theories are general frameworks that deal with quantities that are considered “precious’’ under a given setting, including quantum entanglement for two separate parties Alice and Bob as an example. In our setting for error mitigation, a “clean” quantum gate can be considered as a precious resource, and this “resourcefulness” may be quantified. We find that the optimal sampling cost for probabilistic error cancellation is directly related to the resource quantification in our framework, which can be rigorously analyzed via tools developed in resource theories. We applied our method to several important noise models and presented their exact optimal costs and effective bounds, as well as to a general class of noise channels that provides us with a systematic evaluation of its optimal resource cost.
Our work not only provides insights into the potential and limitations on feasible error mitigation on near-term devices but also displays an application of resource theories as a useful theoretical framework. Our consideration may also be combined with other techniques for probabilistic error cancellation, allowing us to make a precise assessment of the realization of error-mitigated NISQ devices in practice. We also expect that our results can be extended to a broad class of problems even beyond error mitigation such as efficient measurement for variational algorithms and classical simulation of noisy quantum circuits.