Topological order and entanglement dynamics in the measurement-only XZZX quantum code

Journal Article · Fri Sep 23 00:00:00 EDT 2022 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.106.104307· OSTI ID:1982785

Klocke, Kai ^[1]; Buchhold, Michael ^[2]

---

1. Univ. of California, Berkeley, CA (United States)
2. Univ. of Cologne (Germany)

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 $D_2={\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry protected topological (SPT) order, as well as a symmetry breaking (SB) order from a twofold 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 $\nu =\frac{4}{3}$ and the dynamical critical exponent $z=1$ are consistent with bond percolation, the prefactor of the logarithmic entanglement growth may take noninteger 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 $z^{*}\ne z$ , which is observable up to times $t~L^{z^{*}}$ and is reminiscent of the relaxation of critical systems into a prethermal state.

• Research Organization: National Quantum Information Science (QIS) Research Centers (United States). The Quantum Science Center (QSC)
• Sponsoring Organization: German Research Foundation (DFG); USDOE Office of Science (SC)
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1982785
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 10 Vol. 106; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
Physics
quantum entanglement
quantum phase transitions
symmetry protected topological states