Related papers: Single-Shot Quantum Error Correction in Intertwine…
We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC), which is a generalization of the stabilizer toric code. The 3D STC can be realized by measuring geometrically-local parity checks of weight at…
Subsystem quantum error-correcting codes typically involve measuring a sequence of non-commuting parity check operators. They can sometimes exhibit greater fault-tolerance than conventional subspace codes, which use commuting checks.…
For quantum error correction codes the required number of measurement rounds typically increases with the code distance when measurements are faulty. Single-shot error correction allows for an error threshold with only one round of noisy…
Quantum error correction typically requires repeated syndrome extraction due to measurement noise, which results in substantial time overhead in fault-tolerant computation. Single-shot error correction aims to suppress errors using only one…
While quantum low-density parity check (qLDPC) codes are a low-overhead means of quantum information storage, it is valuable for quantum codes to possess fault-tolerant features beyond this resource efficiency. In this work, we introduce…
Topological subsystem codes in three spatial dimensions allow for quantum error correction with no time overhead, even in the presence of measurement noise. The physical origins of this single-shot property remain elusive, in part due to…
Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here I show that for suitable topological codes a single round of local measurements is…
The Kitaev toric code is widely considered one of the leading candidates for error correction in fault-tolerant quantum computation. However, direct methods to increase its logical dimensions, such as lattice surgery or introducing…
We propose a unifying paradigm for analyzing and constructing topological quantum error correcting codes as dynamical circuits of geometrically local channels and measurements. To this end, we relate such circuits to discrete fixed-point…
Topological stabilizer codes, such as the toric and surface codes, are leading candidates for fault-tolerant quantum computation. While their decodability under stochastic noise has been extensively studied, the effects of coherent errors,…
A toric quantum error-correcting code construction procedure is presented in this work. A new class of an infinite family of toric quantum codes is provided by constructing a classical cyclic code on the square lattice $\mathbb{Z}_{q}\times…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction…
We present a family of simple three-dimensional stabilizer codes, called the chiral color codes, that realize fermionic and chiral topological orders. In the qubit case, the code realizes the topological phase of a single copy of the…
Single-shot error correction is a technique for correcting physical errors using only a single round of noisy check measurements, such that any residual noise affects a small number of qubits. We propose a general theory of single-shot…
In this work we study the single-shot performance of higher dimensional hypergraph product codes decoded using belief-propagation and ordered-statistics decoding [Panteleev and Kalachev, 2021]. We find that decoding data qubit and syndrome…
Single-shot error correction corrects data noise using only a single round of noisy measurements on the data qubits, removing the need for intensive measurement repetition. We introduce a general concept of confinement for quantum codes,…
Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces. More…
Quantum hardware rarely suffers equal amounts of bit-flip ($X$) and phase-flip ($Z$) errors; one type is often much more common than the other. A code that is ``bias-tailored'' can exploit this imbalance, lowering the fault-tolerance…
We investigate the stability of logical information in quantum stabilizer codes subject to coherent unitary errors. Beginning with a logical state, we apply a random unitary error channel and subsequently measure stabilizer checks,…