Related papers: Permutation-invariant codes: a numerical study and…
Quantum synchronisation errors are a class of quantum errors that change the number of qubits in a quantum system. The classical error correction of synchronisation errors has been well-studied, including an insertion-deletion equivalence…
Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal…
Modular quantum computing architectures require error correction schemes that remain effective in the presense of noisy inter-processor operations. We introduce a distributed quantum error correction framework based on approximate codes to…
Error correcting codes protect quantum information and form the basis of fault tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transverse non-Clifford…
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…
Decoded Quantum Interferometry (DQI) defines a duality that pairs decoding problems with optimization problems. The original work on DQI considered Reed-Solomon decoding, whose dual optimization problem, called Optimal Polynomial…
Ternary quantum systems are being studied because these provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the…
This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…
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…
All known qudit-based prepare-and-measure quantum key distribution (PM-QKD) schemes are more error resilient than their qubit-based counterparts. Their high error resiliency comes partly from the careful encoding of multiple bits of signals…
We introduce a decoder for the 3D color code with boundaries, which is a variation of the restriction decoder introduced by Kubicka and Delfosse. Specifically, we adapt the lift procedure to efficiently find a correction on qubits adjacent…
Quantum error correction (QEC) is essential for protecting quantum information against noise, yet understanding the structure of the Knill-Laflamme (KL) coefficients $\lambda_{ij}$ from the condition $PE_i^\dagger E_j P = \lambda_{ij} P$…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
We develop a framework for constructing quantum error-correcting codes and logical gates for three types of spaces -- composite permutation-invariant spaces of many qubits or qudits, composite constant-excitation Fock-state spaces of many…
We present a lower bound for Pauli Manipulation Detection (PMD) codes, a class of quantum codes that detect every Pauli error with high probability. Our lower bound reveals the first trade-off between the error parameter and the coding…
We introduce and explicitly construct a quantum code we coin a "Pauli Manipulation Detection" code (or PMD), which detects every Pauli error with high probability. We apply them to construct the first near-optimal codes for two tasks in…
The promise of quantum computers hinges on the ability to scale to large system sizes, e.g., to run quantum computations consisting of more than 100 million operations fault-tolerantly. This in turn requires suppressing errors to levels…
We analyze the performance of a quantum error correction code subject to physically motivated noise modeled by a Lindblad master equation. We consider dissipative and coherent single-qubit terms and two-qubit crosstalk, studying how…
We propose quaternion-based strategies for quantum error correction by extending quantum mechanics into quaternionic Hilbert spaces. Building on the properties of quaternionic quantum states, we define quaternionic analogues of Pauli…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…