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Motivated by the close relationship between quantum error-correction, topological order, the holographic AdS/CFT duality, and tensor networks, we initiate the study of approximate quantum error-detecting codes in matrix product states…
We formalize the problem of dissipative quantum encoding, and explore the advantages of using Markovian evolution to prepare a quantum code in the desired logical space, with emphasis on discrete-time dynamics and the possibility of exact…
With the intense interest in small, noisy quantum computing devices comes the push for larger, more accurate -- and hence more useful -- quantum computers. While fully fault-tolerant quantum computers are, in principle, capable of achieving…
Stabilization of encoded logical qubits using quantum error correction is key to the realization of reliable quantum computers. While qubit codes require many physical systems to be controlled, oscillator codes offer the possibility to…
An important topic in quantum information is the theory of error correction codes. Practical situations often involve quantum systems with states in an infinite dimensional Hilbert space, for example coherent states. Motivated by these…
Quantum error correction is a fundamental primitive of fault-tolerant quantum computing. But in order for error correction to proceed, one must first prepare the codespace of the underlying error-correcting code. A popular method for…
We propose a new method to autonomously correct for errors of a logical qubit induced by energy relaxation. This scheme encodes the logical qubit as a multi-component superposition of coherent states in a harmonic oscillator, more…
Entanglement is known to be an essential resource for many quantum information processes. However, it is now known that some quantum features may be acheived with quantum discord, a generalized measure of quantum correlation. In this paper,…
The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at…
Standard approaches to quantum error correction (QEC) require active maintenance using measurements and classical processing. Passive QEC, by contrast, has so far been established only in unphysical spatial dimensions. Here, we give an…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Up to now every good quantum error-correcting code discovered has had the structure of an eigenspace of an Abelian group generated by tensor products of Pauli matrices; such codes are known as stabilizer or additive codes. In this letter we…
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We…
We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…
A universal set of quantum gates is constructed for the recently developed jump-error correcting quantum codes. These quantum codes are capable of correcting errors arising from the spontaneous decay of distinguishable qubits into…
Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits…
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…