Papers › Topological order and entanglement dynamics in the measurement-only XZZX quantum code
Topological order and entanglement dynamics in the measurement-only XZZX quantum code
Kai Klocke, Michael Buchhold
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We examine the dynamics of a (1+1)-dimensional measurement-only circuit defined by the stabilizers of the [[5,1,3]] quantum error correcting code interrupted by single-qubit Pauli measurements. The code corrects arbitrary single-qubit errors and it stabilizes an area law entangled state with a D₂ = ℤ₂ ×ℤ₂ symmetry protected topological (SPT) order, as well as a symmetry breaking (SB) order from a two-fold bulk degeneracy. The Pauli measurements break the topological order and induce a phase transition into a trivial area law phase. Allowing more than one type of Pauli measurement increases the measurement-induced frustration, and the SPT and SB order can be broken either simultaneously or separately at nonzero measurement rate. This yields a rich phase diagram and unanticipated critical behavior at the phase transitions. Although the correlation length exponent ν=43 and the dynamical critical exponent z=1 are consistent with bond percolation, the prefactor of the logarithmic entanglement growth may take non-integer multiples of the percolation value. Remarkably, we identify a robust transient scaling regime for the purification dynamics of L qubits. It reveals a modified dynamical critical exponent z^*≠z, which is observable up to times t∼L^(z^*) and is reminiscent of the relaxation of critical systems into a prethermal state.
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