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In universal fault-tolerant quantum computing, implementing logical non-Clifford gates often demands substantial spacetime resources for many error-correcting codes, including the high-threshold surface code. A critical mission for…
Unrolling a decoding algorithm allows to achieve extremely high throughput at the cost of increased area. Look-up tables (LUTs) can be used to replace functions otherwise implemented as circuits. In this work, we show the impact of…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical error in plausible hardware implementations of quantum error-correcting codes (QECC). In this work, we consider logical error rates…
Practical quantum advantage is expected to depend on fault-tolerant quantum computing, although the architectural overhead needed to support fault tolerance is still extremely high. Prior FTQC designs generally emphasize either fast…
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions…
Fault-tolerant quantum computing (FTQC) is essential for achieving large-scale practical quantum computation. Implementing arbitrary FTQC requires the execution of a universal gate set on logical qubits, which is highly challenging.…
In this article, we present a new construction of codes from algebraic curves. Given a curve over a non-prime finite field, the obtained codes are defined over a subfield. We call them Cartier Codes since their construction involves the…
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…
Encoding logical quantum information in harmonic oscillator modes is a promising and hardware-efficient approach to the realization of a quantum computer. In this work, we propose to encode logical qubits in grid states of an ensemble of…
Recently Haah introduced a new quantum error correcting code embedded on a cubic lattice. One of the defining properties of this code is the absence of string logical operator. We present new codes with similar properties by relaxing the…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…
With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting codes designed to address a single dominant error type.…
Transversal Pauli $Z$ rotations provide a natural route to fault-tolerant logical diagonal gates in quantum CSS codes, but their capability is inherently constrained. We develop a homological framework that organizes transversal diagonal…
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…
Classical locally recoverable codes, which permit highly efficient recovery from localized errors as well as global recovery from larger errors, provide some of the most useful codes for distributed data storage in practice. In this paper,…
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…
Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow…
Quantum computers show promise to solve select problems otherwise intractable on classical computers. However, noisy intermediate-scale quantum (NISQ) era devices are currently prone to various sources of error. Quantum error correction…