Kavli Affiliate: Matthew P. A. Fisher
| First 5 Authors: Yaodong Li, Matthew P. A. Fisher, , ,
| Summary:
We explore a class of "open" quantum circuit models with local decoherence
("noise") and local projective measurements, each respecting a global Z_2
symmetry. The model supports a spin glass phase where the Z_2 symmetry is
spontaneously broken (not possible in an equilibrium 1d system), a paramagnetic
phase characterized by a divergent susceptibility, and an intermediate
"trivial" phase. All three phases are also stable to Z_2-symmetric local
unitary gates, and the dynamical phase transitions between the phases are in
the percolation universality class. The open circuit dynamics can be purified
by explicitly introducing a bath with its own "scrambling" dynamics, as in
[Bao, Choi, Altman, arXiv:2102.09164], which does not change any of the
universal physics. Within the spin glass phase the circuit dynamics can be
interpreted as a quantum repetition code, with each stabilizer of the code
measured stochastically at a finite rate, and the decoherences as effective
bit-flip errors. Motivated by the geometry of the spin glass phase, we devise a
novel decoding algorithm for recovering an arbitrary initial qubit state in the
code space, assuming knowledge of the history of the measurement outcomes, and
the ability of performing local Pauli measurements and gates on the final
state. For a circuit with L^d qubits running for time T, the time needed to
execute the decoder scales as O(L^d T) (with dimensionality d). With this
decoder in hand, we find that the information of the initial encoded qubit
state can be retained (and then recovered) for a time logarithmic in L for a 1d
circuit, and for a time at least linear in L in 2d below a finite error
threshold. For both the repetition and toric codes, we compare and contrast our
decoding algorithm with earlier algorithms that map the error model to the
random bond Ising model.
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