Related papers: Performance analysis of GKP error correction
Quantum Error Mitigation (QEM) enables the extraction of high-quality results from the presently-available noisy quantum computers. In this approach, the effect of the noise on observables of interest can be mitigated using multiple…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
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 consider the task of performing shadow tomography of a logical subsystem defined via the Gottesman-Kitaev-Preskill (GKP) error correcting code. Our protocol does not require the input state to be a code state but is implemented by…
We construct stabilizer states and error-correcting codes on combinations of discrete- and continuous-variable systems, generalizing the Gottesman-Kitaev-Preskill (GKP) quantum lattice formalism. Our framework absorbs the discrete phase…
Quantum computing potentially offers exponential speed-ups over classical computing for certain tasks. A central, outstanding challenge to making quantum computing practical is to achieve fault tolerance, meaning that computations of any…
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…
Quantum effect enables enhanced estimation precision in metrology, with the Heisenberg limit (HL) representing the ultimate limit allowed by quantum mechanics. Although the HL is generally unattainable in the presence of noise, quantum…
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…
This paper investigates quantum error correction schemes for fully-correlated noise channels on an $n$-qubit system, where error operators take the form $W^{\otimes n}$, with $W$ being an arbitrary $2\times 2$ unitary operator. In previous…
Computational power in measurement-based quantum computing stems from the symmetry-protected topological (SPT) order of entangled resource states. However, resource states are prone to preparation errors. We introduce a quantum error…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Quantum error-correcting codes are many-body entangled states that are prepared and measured using complex sequences of entangling operations. Each element of such an entangling sequence introduces noise to delicate quantum information…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…
Quantum error correction is important to quantum information processing, which allows us to reliably process information encoded in quantum error correction codes. Efficient quantum error correction benefits from the knowledge of error…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
Quantum system characterization techniques represent the front line in the identification and mitigation of noise in quantum computing, but can be expensive in terms of quantum resources and time to repeatedly employ. Another challenging…
We present a general-purpose quantum error correction primitive based on state purification via the SWAP test, which we refer to as purification quantum error correction (PQEC). This method operates on $N$ noisy copies, requires minimally…
With sub-threshold quantum error correction on quantum hardware still out of reach, quantum error mitigation methods are currently deemed an attractive option for implementing certain applications on near-term noisy quantum devices. One…