Related papers: The color code, the surface code, and the transver…
flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…
Extensive quantum error correction is necessary in order to scale quantum hardware to the regime of practical applications. As a result, a significant amount of decoding hardware is necessary to process the colossal amount of data required…
An algorithm is presented for error correction in the surface code quantum memory. This is shown to correct depolarizing noise up to a threshold error rate of 18.5%, exceeding previous results and coming close to the upper bound of 18.9%.…
Quantum error correction codes (QECCs) are critical for realizing reliable quantum computing by protecting fragile quantum states against noise and errors. However, limited research has analyzed the noise resilience of QECCs to help select…
Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the…
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…
In this paper we investigate the colorful components framework, motivated by applications emerging from comparative genomics. The general goal is to remove a collection of edges from an undirected vertex-colored graph $G$ such that in the…
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
Transversal gates are logical gate operations on encoded quantum information that are efficient in gate count and depth, and are designed to minimize error propagation. Efficient encoding circuits for quantum codes that admit transversal…
The problem of computing distances of error-correcting codes is fundamental in both the classical and quantum settings. While hardness for the classical version of these problems has been known for some time (in both the exact and…
Learning-based image compression has improved to a level where it can outperform traditional image codecs such as HEVC and VVC in terms of coding performance. In addition to good compression performance, device interoperability is essential…
Quantum Approximate Optimization Algorithm (QAOA) is studied primarily to find approximate solutions to combinatorial optimization problems. For a graph with $n$ vertices and $m$ edges, a depth $p$ QAOA for the Max-cut problem requires…
Surface codes are promising for practical quantum error correction due to their high threshold and experimental feasibility. However, their performance under realistic noise conditions, particularly those involving correlated errors,…
NP-hard problems such as the maximum clique or minimum vertex cover problems, two of Karp's 21 NP-hard problems, have several applications in computational chemistry, biochemistry and computer network security. Adiabatic quantum annealers…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
The NP-hard problem of decoding random linear codes is crucial to both coding theory and cryptography. In particular, this problem underpins the security of many code based post-quantum cryptographic schemes. The state-of-art algorithms for…
We prove improved inapproximability results for hypergraph coloring using the low-degree polynomial code (aka, the 'short code' of Barak et. al. [FOCS 2012]) and the techniques proposed by Dinur and Guruswami [FOCS 2013] to incorporate this…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
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…