Related papers: The Near-optimal Performance of Quantum Error Corr…
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg…
This paper shows that Knill-Laflamme condition, known as a necessary and sufficient condition for quantum error-correction, can be applied to quantum errors where the number of particles changes before and after the error. This fact shows…
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…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
In order to achieve fault-tolerant quantum computing, we make use of quantum error correction schemes designed to protect the logical information of the system from decoherence. A promising way to preserve such information is to use the…
We study channel fidelity for the high-fidelity approach in the Knill-Laflamme-Milburn (KLM) scheme. We examine an optimal channel fidelity $f_{opt}$ and identify the corresponding KLM ancilla state. In the limit of large $n$, where $2n$ is…
In Ref. [1], we proved a duality between two optimizations problems. The primary one is, given two quantum channels M and N, to find a quantum channel R such that RN is optimally close to M as measured by the worst-case entanglement…
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…
The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors.…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
The ultimate goal of quantum error correction is to create logical qubits with very low error rates (e.g. 1e-12) and assemble them into large-scale quantum computers capable of performing many (e.g. billions) of logical gates on many (e.g.…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
Autonomous quantum error correction utilizes the engineered coupling of a quantum system to a dissipative ancilla to protect quantum logical states from decoherence. We show that the Knill-Laflamme condition, stating that the environmental…
Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterise noise. The experiment is…
Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with…
To implement fault-tolerant quantum computation with continuous variables, the Gottesman--Kitaev--Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
Quantum error detection (QED) offers a promising pathway to fault tolerance in near-term quantum devices by balancing error suppression with minimal resource overhead. However, its practical utility hinges on optimizing design…
Quantum metrology aims to maximize measurement precision on quantum systems, with a wide range of applications in quantum sensing. Achieving the Heisenberg limit (HL) - the fundamental precision bound set by quantum mechanics - is often…
Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software and hardware developments. Similarly to the classical setting,…