Related papers: Toward Constructing a Continuous Logical Operator …
Transversal gates play a crucial role in suppressing error propagation in fault-tolerant quantum computation, yet they are intrinsically constrained: any nontrivial code encoding a single logical qubit admits only a finite subgroup of…
This paper proves the threshold result, which asserts that quantum computation can be made robust against errors and inaccuracies, when the error rate, $\eta$, is smaller than a constant threshold, $\eta_c$. The result holds for a very…
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…
Recent advancements in quantum computing have enabled practical use of quantum error detecting and correcting codes. However, current architectures and future proposals of quantum computer design suffer from limited qubit counts,…
The Eastin-Knill theorem is a central result of quantum error correction theory and states that a quantum code cannot correct errors exactly, possess continuous symmetries, and implement a universal set of gates transversely. As a way to…
Quantum computers will require encoding of quantum information to protect them from noise. Fault-tolerant quantum computing architectures illustrate how this might be done but have not yet shown a conclusive practical advantage. Here we…
Quantum information is very fragile to environmentally and operationally induced imperfections. Therefore, the construction of practical quantum computers requires quantum error-correction techniques to protect quantum information. In…
Following the introduction of the task of reference frame error correction, we show how, by using reference frame alignment with clocks, one can add a continuous Abelian group of transversal logical gates to any error-correcting code. With…
Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead. Potentially high encoding rates and large distance relative to their block size make them…
We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits by means of geometrically local quantum operations and efficient classical computation. We prove that circuit-level local stochastic noise…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
We present a family of quantum error-correcting codes that support a universal set of transversal logic gates using only local operations on a two-dimensional array of physical qubits. The construction is a subsystem version of color codes…
Quantum computing holds the promise of solving classically intractable problems. Enabling this requires scalable and hardware-efficient quantum processors with vanishing error rates. This perspective manuscript describes how bosonic codes,…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
Certain types of quantum computing platforms, such as those realized using Rydberg atoms or Kerr-cat qubits, are natively more susceptible to Pauli-Z noise than Pauli-X noise, or vice versa. On such hardware, it is useful to ensure that…
Steane's 7-qubit quantum error-correcting code admits a set of fault-tolerant gates that generate the Clifford group, which in itself is not universal for quantum computation. The 15-qubit Reed-Muller code also does not admit a universal…
Logical qubit encoding and quantum error correction (QEC) have been experimentally demonstrated in various physical systems with multiple physical qubits, however, logical operations are challenging due to the necessary nonlocal operations.…
The resource overhead required to achieve net computational benefits from quantum error correction (QEC) limits its utility while current systems remain constrained in size, despite exceptional progress in experimental demonstrations. In…
Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the…
Quantum error correction represents a significant advancement in large-scale quantum computing. However, achieving fault-tolerant implementations of non-Clifford logical gates with reduced overhead remains a challenge in the popular surface…