Related papers: Quantum computation and quantum error correction: …
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…
We calculate the fidelity with which an arbitrary state can be encoded into a [7,1,3] CSS quantum error correction code in a non-equiprobable Pauli operator error environment with the goal of determining whether this encoding can be used…
We identify gauge freedoms in quantum error correction (QEC) codes and introduce strategies for optimal control algorithms to find the gauges which allow the easiest experimental realization. Hereby, the optimal gauge depends on the…
We present a generalization of the tilted Bell inequality for quantum [[n,k,d]] error-correcting codes and explicitly utilize the simplest perfect code, the [[5,1,3]] code, the Steane [[7,1,3]] code, and Shor's [[9,1,3]] code, to…
We present an approach to one-way quantum computation (1WQC) that can compensate for single-qubit errors, by encoding the logical information residing on physical qubits into five-qubit error-correcting code states. A logical two-qubit…
In this paper an extended scalability condition is proposed to achieve the ground-state stability for a class of multipartite quantum systems which may involve two-body interactions, and an explicit procedure to construct the dissipation…
The typical model for measurement noise in quantum error correction is to randomly flip the binary measurement outcome. In experiments, measurements yield much richer information - e.g., continuous current values, discrete photon counts -…
We present a theoretical framework for state-adaptive quantum error correction that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we…
Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic…
Error mitigation has enabled quantum computing applications with over one hundred qubits and deep circuits. The most general error mitigation methods rely on a faithful characterization of the noise channels of the hardware. However,…
Quantum error correction is an essential ingredient in the development of quantum technologies. Its subject is to investigate ways to embed quantum Hilbert spaces into a physical system such that this subspace is robust against small…
We analyse a generalised quantum error correction code against photon loss where a logical qubit is encoded into a subspace of a single oscillator mode that is spanned by distinct multi-component cat states (coherent-state superpositions).…
Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are…
Quantum states are inherently fragile, making their storage a major concern for many practical applications and experimental tests of quantum mechanics. The field of quantum memories is concerned with how this storage may be achieved,…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Quantum error correcting (QEC) stabilizer codes enable protection of quantum information against errors during storage and processing. Simulation of noisy QEC codes is used to identify the noise parameters necessary for advantageous…
Building reliable quantum computers requires protecting fragile quantum states from inevitable environmental noise and operational errors. While quantum error correction codes like the Steane $[\![7,1,3]\!]$ code provide elegant theoretical…