Uniformly Decaying Subspaces for Error Mitigated Quantum Computation
arxiv(2024)
摘要
We present a general condition to obtain subspaces that decay uniformly in a
system governed by the Lindblad master equation and use them to perform error
mitigated quantum computation. The expectation values of dynamics encoded in
such subspaces are unbiased estimators of noise-free expectation values. In
analogy to the decoherence free subspaces which are left invariant by the
action of Lindblad operators, we show that the uniformly decaying subspaces are
left invariant (up to orthogonal terms) by the action of the dissipative part
of the Lindblad equation. We apply our theory to a system of qubits and qudits
undergoing relaxation with varying decay rates and show that such subspaces can
be used to eliminate bias up to first order variations in the decay rates
without requiring full knowledge of noise. Since such a bias cannot be
corrected through standard symmetry verification, our method can improve error
mitigation in dual-rail qubits and given partial knowledge of noise, can
perform better than probabilistic error cancellation.
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