相关论文: Graphical CSS Code Transformation Using ZX Calculu…
We provide a simplified, yet rigorous presentation of the ideas from Bomb\'{i}n's paper "Gauge Color Codes" [arXiv:1311.0879v3]. Our presentation is self-contained, and assumes only basic concepts from quantum error correction. We provide…
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…
We present a complete optimization procedure for hybrid quantum-classical circuits with classical parity logic. While common optimization techniques for quantum algorithms focus on rewriting solely the pure quantum segments, there is…
We introduce an enhanced technique for strong classical simulation of quantum circuits which combines the `sum-of-stabilisers' method with an automated simplification strategy based on the ZX-calculus. Recently it was shown that quantum…
The topological color code and the toric code are two leading candidates for realizing fault-tolerant quantum computation. Here we show that the color code on a $d$-dimensional closed manifold is equivalent to multiple decoupled copies of…
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…
Graphs and recently hypergraphs have been known as an important tool for considering different properties of quantum many-body systems. In this paper, we study a mapping between an important class of quantum systems namely quantum…
The study of holographic bulk-boundary dualities has led to the construction of novel quantum error correcting codes. Although these codes have shed new light on conceptual aspects of these dualities, they have widely been believed to lack…
Color codes are a class of topological quantum codes with a high error threshold and large set of transversal encoded gates, and are thus suitable for fault tolerant quantum computation in two-dimensional architectures. Recently,…
Mapping fermionic systems to qubits on a quantum computer is often the first step for algorithms in quantum chemistry and condensed matter physics. However, it is difficult to reconcile the many different approaches that have been proposed,…
The Reed-Muller codes are a family of error-correcting codes that have been widely studied in coding theory. In 2020, Wei Yan and Sian-Jheng Lin introduced a variant of Reed-Muller codes so called symmetric Reed-Muller codes. We investigate…
Reducing the number of non-Clifford quantum gates present in a circuit is an important task for efficiently implementing quantum computations, especially in the fault-tolerant regime. We present a new method for reducing the number of…
Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However,…
In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural…
Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes $\mathcal{C}$, $\mathcal{D}$…
Surface codes are a popular choice for implementing fault-tolerant quantum computing. Two-qubit gates may be realised in these codes using only nearest-neighbour interactions, either by lattice surgery or by braiding defects around each…
A binary extended 1-perfect code $\mathcal C$ folds over its kernel via the Steiner quadruple systems associated with its codewords. The resulting folding, proposed as a graph invariant for $\mathcal C$, distinguishes among the 361…
Calderbank-Shor-Steane (CSS) quantum error-correcting codes are based on pairs of classical codes which are mutually dual containing. Explicit constructions of such codes for large blocklengths and with good error correcting properties are…
Recent discoveries in asymptotically good quantum codes have intensified research on their application in quantum computation and fault-tolerant operations. This study focuses on the addressability problem within CSS codes: what circuits…
We generalize the concept of folding from surface codes to CSS codes by considering certain dualities within them. In particular, this gives a general method to implement logical operations in suitable LDPC quantum codes using transversal…