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Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are…
Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion…
The five-qubit quantum error correcting code encodes one logical qubit to five physical qubits, and protects the code from a single error. It was one of the first quantum codes to be invented, and various encoding circuits have been…
We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code.…
Quantum error-correcting codes (QECCs) is at the heart of fault-tolerant quantum computing. As the size of quantum platforms is expected to grow, one of the open questions is to design new optimal codes of ever-increasing size. A related…
Dynamical stabilizer codes may offer a practical route to large-scale quantum computation. Such codes are defined by a schedule of error-detecting measurements, which allows for flexibility in their construction. In this work, we ask how…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realised in the near term, uses…
Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…
We investigate stabilizer codes with carrier qudits of equal dimension $D$, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding…
Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits…
Quantum low-density parity-check (qLDPC) codes are quantum stabilizer codes where each stabilizer acts on a constant number of qubits and each qubit is acted on by a constant number of stabilizers. We study qLDPC codes constructed from…
Quantum Error Correction (QEC) decoding faces a fundamental accuracy-efficiency tradeoff. Classical methods like Minimum Weight Perfect Matching (MWPM) exhibit variable performance across noise models and suffer from polynomial complexity,…
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…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
Quantum error correction is indispensable for scalable quantum computation. Although encoding logical qubits substantially enhances noise resilience, achieving logical error rates low enough for practical algorithms remains challenging on…
The low coding rate of quantum stabilizer codes results in formidable physical qubit overhead when realizing quantum error correcting in engineering. In this letter, we propose a new class of hypergraph-product code called…
The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it…
We explore what the integrated use of quantum spatial distribution (QSD), or more specifically, superposition of both spin and position states of particles, and gauge symmetry (GS) within stabilizer formalism provides for quantum error…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…