Error mitigation and quantum-assisted simulation in the error corrected regime
Due to the fragility of quantum information, quantum error correction is
a prerequisite of large-scale quantum computing. A standard paradigm is
that of state injection, where a set of fault-tolerant core operations
are promoted to universal quantum computation by injecting so-called
magic states. The latter require complex distillation schemes, so they
come at a limited rate and are noisy.
After an introduction, I will discuss error mitigation in this setting
and present a quantity, the Quantum-assisted Robustness of Magic (QRoM),
which measures the distance between ideal and available magic states. We
show how the QRoM quantifies the sampling overhead of (quasiprobability
based) error mitigation algorithms as a function of the noise parameter,
interpolating between classical simulation and ideal QC. Furthermore,
classical simulation and error mitigation can be seen as special
instances of quantum-assisted simulation. In this task, fewer, noisier
quantum resources boost simulations of a larger, ideal quantum
computation with an overhead quantified by the QRoM.
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