Error Suppression for Hamiltonian Quantum Computing in Markovian Environments

Abstract

Hamiltonian quantum computing, such as the adiabatic and holonomic models, can be protected against decoherence using an encoding into stabilizer subspace codes for error detection and the addition of energy penalty terms. This method has been widely studied since it was first introduced by Jordan, Farhi, and Shor (JFS) in the context of adiabatic quantum computing. Here we extend the original result to general Markovian environments, not necessarily in Lindblad form. We show that the main conclusion of the original JFS study holds under these general circumstances: assuming a physically reasonable bath model, it is possible to suppress the initial decay out of the encoded ground state with an energy penalty strength that grows only logarithmically in the system size, at a fixed temperature.

updated to published version

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• Continuous quantum error correction for evolution under time-dependent Hamiltonians
• Superconducting qubit circuit emulation of a vector spin-1/2
• Arbitrary-time error suppression for Markovian adiabatic quantum computing using stabilizer subspace codes
• From Ansätze to Z-gates: a NASA View of Quantum Computing
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• Robust universal Hamiltonian quantum computing using two-body interactions
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• Suppressing decoherence in quantum state transfer with unitary operations
• Families of $d=2$ 2D subsystem stabilizer codes for universal Hamiltonian quantum computation with two-body interactions