Confinement Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory

By Chenyang Wang, J. Harrington, John Preskill. 2002

343 citations recorded by the source corpus.

We study the ±J random-plaquette Z_2 gauge model (RPGM) in three spatial dimensions, a three-dimensional analog of the two-dimensional ±J random-bond Ising model (RBIM). The model is a pure Z_2 gauge theory in which randomly chosen plaquettes (occurring with concentration p) have couplings with the “wrong sign” so that magnetic flux is energetically favored on these plaquettes. Excitations of the model are one-dimensional “flux tubes” that terminate at “magnetic monopoles” located inside lattice cubes that contain an odd number of wrong-sign plaquettes. Electric confinement can be driven by thermal fluctuations of the flux tubes, by the quenched background of magnetic monopoles, or by a combination of the two. Like the RBIM, the RPGM has enhanced symmetry along a “Nishimori line” in the p–T plane (where T is the temperature). The critical concentration p_c of wrong-sign plaquettes at the confinement-Higgs phase transition along the Nishimori line can be identified with the accuracy threshold for robust storage of quantum information using topological error-correcting codes: if qubit phase errors, qubit bit-flip errors, and errors in the measurement of local check operators all occur at rates below p_c, then encoded quantum information can be protected perfectly from damage in the limit of a large code block. Through Monte-Carlo simulations, we measure p_(c0), the critical concentration along the T=0 axis (a lower bound on p_c), finding p_(c0)=.0293±.0002. We also measure the critical concentration of antiferromagnetic bonds in the two-dimensional RBIM on the T=0 axis, finding p_(c0)=.1031±.0001. Our value of p_(c0) is incompatible with the value of p_c=.1093±.0002 found in earlier numerical studies of the RBIM, in disagreement with the conjecture that the phase boundary of the RBIM is vertical (parallel to the T axis) below the Nishimori line. The model can be generalized to a rank-r antisymmetric tensor field in d dimensions, in the presence of quenched disorder.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/d809eb03385e569be2e2f5451abef8b0e122f193

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Citations in the corpus

A quantum processor based on coherent transport of entangled atom arrays (2021, positive): “rays will allow efficient, parallel execution of transversal entangling gates between many logical qubits [37, 46].”
Quantum error correction for quantum memories (2013, positive): “Numerical studies by Wang, Harrington, and Preskill (2003) (using minimum-weight decoding) showed a threshold of p c ≈ 2 .”
Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects (2012, background): “9% [58]), for a gate-based error model (the threshold error probability per gate is 0.”
Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States (2024, neutral): “The summation over the replica index s = 1 , 2 , · · · , t − 1 is kept implicit.”
The XZZX surface code (2020, methodology): “[39] and, unless otherwise stated, error bars are obtained by jackknife resampling over code distance.”
Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory (2023, methodology): “In the Toric code and other topological codes with local errors, the statistical mechanical model for the optimal decoding algorithm always satisfies the Nishimori condition [10, 18–22 , 72 ].”
Quantum memories at finite temperature (2014, background): “Moreover, the study of decoding has foundations in the study of glassy statistical mechanical models (Andrist et al., 2014; Bombin et al., 2012; Dennis et al., 2002; Wang et al., 2003).”