Related papers: Unitary application of the quantum error correctio…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
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…
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
Quantum error correcting codes have been developed to protect a quantum computer from decoherence due to a noisy environment. In this paper, we present two methods for optimizing the physical implementation of such error correction schemes.…
Advances in single photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have losses low enough to be correctable using a quantum error correcting code. Such error-corrected…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Recently a framework for assisted quantum error correction was proposed in which a specific type of error is allowed to occur on auxiliary qubits, which is in contrast to standard entanglement assistance that requires noiseless auxiliary…
This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…
We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., single-qubit operations and CNOT), we focus on the…
We investigate the use of Quantum Neural Networks for discovering and implementing quantum error-correcting codes. Our research showcases the efficacy of Quantum Neural Networks through the successful implementation of the Bit-Flip quantum…
We present a protocol for transferring arbitrary continuous-variable quantum states into a few discrete-variable qubits and back. The protocol is deterministic and utilizes only two-mode Rabi-type interactions which are readily available in…
Efficient verification of the functioning of quantum devices is a key to the development of quantum technologies, but is a daunting task as the system size increases. Here we propose a simple and general framework for verifying unitary…
An efficient coding circuit is given for the perfect quantum error correction of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The circuit presented employs a double `classical' code, i.e., one for bit flips and one…
This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known…
We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit to avoid resource escalation typical of multi-qubit codes. These codes can be customized to the specific physical errors on the qudit,…
By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting…
We propose a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the…
The universal quantum computer is a device capable of simulating any physical system and represents a major goal for the field of quantum information science. Algorithms performed on such a device are predicted to offer significant gains…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment.…