Related papers: A new approximate Eastin-Knill theorem
We present for the first time a general theory of error correction for permutation invariant (PI) codes. Using representation theory of the symmetric group we construct efficient algorithms that can correct any correctible error on any PI…
Fault-tolerant quantum error correction is essential for implementing quantum algorithms of significant practical importance. In this work, we propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of…
We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect non-stabilizer gates. We prove…
Achieving scalable, fault-tolerant quantum computation requires quantum memory architectures that minimize error correction overhead while preserving coherence. This work presents a framework for high-dimensional qudit memory in…
Identifying stabilizer codes that admit fault-tolerant implementations of the full logical Clifford group would significantly advance fault-tolerant quantum computation. Motivated by this goal, we study several classes of fault-tolerant…
We present analytic estimates of the performances of various approximate quantum error correction schemes for the generalized amplitude damping (GAD) qubit channel. Specifically, we consider both stabilizer and nonadditive quantum codes.…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
The requirements for fault-tolerant quantum error correction can be simplified by leveraging structure in the noise of the underlying hardware. In this work, we identify a new type of structured noise motivated by neutral atom qubits,…
Classical simulations of noisy quantum circuits are instrumental to our understanding of the behavior of real-world quantum systems and the identification of regimes where one expects quantum advantage. In this work, we present a highly…
Implementing large-scale quantum algorithms with practical advantage will require fault-tolerance achieved through quantum error correction, but the associated overhead is a significant cost. The overhead can be reduced by engineering…
Bosonic codes offer hardware-efficient approaches to logical qubit construction and hosted the first demonstration of beyond-break even logical quantum memory. However, such accomplishments were done for idling information, and realization…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
Quantum neural networks (QNNs) have been a promising framework in pursuing near-term quantum advantage in various fields, where many applications can be viewed as learning a quantum state that encodes useful data. As a quantum analog of…
Bias-tailored quantum error correcting codes (QECCs) offer a higher error threshold than standard QECCs and have the potential to achieve lower logical errors with less space overhead. The spin-cat qubit, encoded in a large nuclear spin-$F$…
Knill demonstrated a fault-tolerant quantum computation scheme based on concatenated error-detecting codes and postselection with a simulated error threshold of 3% over the depolarizing channel. %We design a two-dimensional architecture for…
We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
Single-shot error correction corrects data noise using only a single round of noisy measurements on the data qubits, removing the need for intensive measurement repetition. We introduce a general concept of confinement for quantum codes,…
To perform reliable quantum computation, quantum error correction is indispensable. In certain cases, continuous covariance symmetry of the physical system can make exact error correction impossible. In this work we study the approximate…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…