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Topological Quantum Spin Glass Order and its realization in qLDPC codes
Benedikt Placke, Tibor Rakovszky, Nikolas P. Breuckmann +1
Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, an…
Bottlenecks in quantum channels and finite temperature phases of matter
Tibor Rakovszky, Benedikt Placke, Nikolas P. Breuckmann +1
We prove an analog of the "bottleneck theorem," well-known for classical Markov chains, for Markovian quantum channels. In particular, we show that if two regions (subspaces) of Hi…
Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
Zihan Cheng, Eric Huang, Vedika Khemani +2
Unitary -designs are distributions of unitary gates that match the Haar distribution up to its -th statistical moment. They are a crucial resource for randomized quantum prot…
LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations
Wojciech De Roeck, Vedika Khemani, Yaodong Li +2
We generalize the proof of stability of topological order, due to Bravyi, Hastings and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity check (LDPC) codes…
Absorbing state transitions with long-range annihilation
Nicholas O'Dea, Sayak Bhattacharjee, Sarang Gopalakrishnan +1
We introduce a family of classical stochastic processes describing diffusive particles undergoing branching and long-range annihilation in the presence of a parity constraint. The…
Rare Events and Griffiths Phases in Topological Quantum Error Correction
Adithya Sriram, Nicholas O'Dea, Yaodong Li +2
The performance of quantum error correcting (QEC) codes are often studied under the assumption of spatio-temporally uniform error rates. On the other hand, experimental implementat…
Perturbative stability and error correction thresholds of quantum codes
Yaodong Li, Nicholas O'Dea, Vedika Khemani
Topologically-ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stabi…
Phases and phase transition in Grover's algorithm with systematic noise
Sasanka Dowarah, Chuanwei Zhang, Vedika Khemani +1
While limitations on quantum computation by Markovian environmental noise are well-understood in generality, their behavior for different quantum circuits and noise realizations ca…
The Physics of (good) LDPC Codes II. Product constructions
Tibor Rakovszky, Vedika Khemani
We continue the study of classical and quantum low-density parity check (LDPC) codes from a physical perspective. We focus on constructive approaches and formulate a general framew…