Related papers: Efficient Verification of Stabilizer Code Subspace…
Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting…
The implementation of large-scale fault-tolerant quantum computers calls for the integration of millions of physical qubits, with error rates of physical qubits significantly below 1%. This outstanding engineering challenge may benefit from…
Self-testing was originally introduced as a device-independent method of certification of entangled quantum states and local measurements performed on them. Recently, in [F. Baccari \textit{et al.}, arXiv:2003.02285] the notion of state…
Quantum low density parity check (qLDPC) codes are an attractive alternative to the surface code due to their relatively high code rate and distance. However, unlike the surface code which has simple, geometrically local, stabilizer checks,…
The efficient and reliable certification of quantum states is essential for various quantum information processing tasks as well as for the general progress on the implementation of quantum technologies. In the last few years several…
$k$-uniform states are valuable resources in quantum information, enabling tasks such as teleportation, error correction, and accelerated quantum simulations. The practical realization of $k$-uniform states, at scale, faces major obstacles:…
We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph…
We discuss two methods to encode one qubit into six physical qubits. Each of our two examples corrects an arbitrary single-qubit error. Our first example is a degenerate six-qubit quantum error-correcting code. We explicitly provide the…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
We introduce a quantum strategy from nonlocal games to improve the stabilizer approximation we proposed previously. The resulting approach turns out to be a qubit-by-qubit gauging procedure for standard stabilizers, which could involve…
Realizing universal fault-tolerant quantum computation is a key goal in quantum information science. By encoding quantum information into logical qubits utilizing quantum error correcting codes, physical errors can be detected and…
Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve…
We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…
Two-dimensional quantum colour codes hold significant promise for quantum error correction, offering advantages such as planar connectivity and low overhead logical gates. Despite their theoretical appeal, the practical deployment of these…
Self-testing of quantum devices based on observed measurement statistics is a method to certify quantum systems using minimal resources. In Ref. [Phys. Rev. \textbf{A} 101, 032106 (2020)], a scheme based on observing measurement statistics…
The quantum stabilizer formalism became foundational for understanding error correction soon after the realization of the first useful quantum error correction codes. Stabilizers provide a way to describe sets of quantum states which are…
Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
Quantum low-density parity-check (QLDPC) codes with good parameters are promising candidates for low-overhead fault-tolerant quantum computing, but their non-local stabilizers require long-range connectivity and frequent qubit movement,…