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We develop novel protocols for generating loss-tolerant quantum codes; these are central for safeguarding information against qubit losses, with most crucial applications in quantum communications. Contrary to current proposals, our method…
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…
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…
Discovering low-overhead quantum error-correcting codes is of significant interest for fault-tolerant quantum computation. For hardware capable of long-range connectivity, the bivariate bicycle codes offer significant overhead reduction…
The non-local interactions in several quantum device architectures allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will…
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
We consider experimentally feasible chains of trapped ions with pseudo-spin 1/2, and find models that can potentially be used to implement error-resistant quantum computation. Similar in spirit to classical neural networks, the…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
Quantum error correction promises a viable path to fault-tolerant computations, enabling exponential error suppression when the device's error rates remain below the protocol's threshold. This threshold, however, strongly depends on the…
Quantum error correction (QEC) plays a critical role in preventing information loss in quantum systems and provides a framework for reliable quantum computation. Identifying quantum codes with nice code parameters for physically motivated…
While quantum low-density parity check (qLDPC) codes are a low-overhead means of quantum information storage, it is valuable for quantum codes to possess fault-tolerant features beyond this resource efficiency. In this work, we introduce…
High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…
Decoded Quantum Interferometry (DQI) is a recently proposed quantum algorithm for approximating solutions to combinatorial optimization problems by reducing instances of linear satisfiability to bounded-distance decoding over superpositions…
A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound and, for some codes, upon the Hartmann-Tzeng (HT) bound. Several Boston bounds are special…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…
Generalized quasi-cyclic (GQC) codes with arbitrary lengths over the ring $\mathbb{F}_{q}+u\mathbb{F}_{q}$, where $u^2=0$, $q=p^n$, $n$ a positive integer and $p$ a prime number, are investigated. By the Chinese Remainder Theorem,…
Quantum low-density parity-check (QLDPC) codes are among the most promising candidates for future quantum error correction schemes. However, a limited number of short to moderate-length QLDPC codes have been designed and their decoding…
The standard algebraic decoding algorithm of cyclic codes $[n,k,d]$ up to the BCH bound $t$ is very efficient and practical for relatively small $n$ while it becomes unpractical for large $n$ as its computational complexity is $O(nt)$. Aim…