Quantum Error Suppression with Subgroup Stabilisation Projectors
arxiv(2024)
摘要
Quantum state purification is the functionality that, given multiple copies
of an unknown state, outputs a state with increased purity. This is an
essential building block for near- and middle-term quantum ecosystems before
the availability of full fault tolerance, where one may want to suppress errors
not only in expectation values but also in quantum states. We propose an
effective state purification gadget with a moderate quantum overhead by
projecting M noisy quantum inputs to their symmetric subspace defined by a
set of projectors forming a symmetric subgroup with order M. Our method,
applied in every short evolution over M redundant copies of noisy states, can
suppress both coherent and stochastic errors by a factor of 1/M. This reduces
the circuit implementation cost M times smaller than the state projection to
the full symmetric subspace proposed more than two decades ago by Barenco et
al. We also show that our gadget purifies the depolarised inputs with
probability p to asymptotically O(p^2) with an optimal choice
of M when p is small. Our method provides flexible choices of state
purification depending on the hardware restrictions before fully fault-tolerant
computing is available. Our method may also find its application in designing
robust verification protocols for quantum outputs.
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