Related papers: Optimal local unitary encoding circuits for the su…
The surface code is unarguably the leading quantum error correction code for 2-D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and…
Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not…
Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating…
Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…
We consider realistic, multi-parameter error models and investigate the performance of the surface code for three possible fault-tolerant superconducting quantum computer architectures. We map amplitude and phase damping to a diagonal Pauli…
To avoid prohibitive overheads in performing fault-tolerant quantum computation, the decoding problem needs to be solved accurately and at speeds sufficient for fast feedback. Existing decoding systems fail to satisfy both of these…
Noise poses a challenge for any real-world implementation in quantum information science. The theory of quantum error correction deals with this problem via methods to encode and recover quantum information in a way that is resilient…
We consider the problem of preparing topologically ordered states using unitary and non-unitary circuits, as well as local time-dependent Hamiltonian and Liouvillian evolutions. We prove that for any topological code in $D$ dimensions, the…
Locally recoverable codes (LRCs) are classical error-correcting codes widely used in large scale distributed and cloud storage systems. Quantum locally recoverable codes (quantum LRCs) are the quantum counterpart of classical LRCs. They…
Local decoders provide a promising approach to real-time quantum error-correction by replacing centralized classical decoding, with significant hardware constraints, by a fully distributed architecture based on a simple, local update rule.…
We propose a systematic and efficient quantum circuit composed solely of Clifford gates for simulating the ground state of the surface code model. This approach yields the ground state of the toric code in $\lceil…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
One of the main challenge for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing…
We propose a simplified version of the Kitaev's surface code in which error correction requires only three-qubit parity measurements for Pauli operators XXX and ZZZ. The new code belongs to the class of subsystem stabilizer codes. It…
We propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. We show how to use our method to analyze hypothetical quantum computers with various…
Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity…
Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct…
A code over a finite field is called locally recoverable code (LRC) if every coordinate symbol can be determined by a small number (at most r, this parameter is called locality) of other coordinate symbols. For a linear code with length n,…