相关论文: Improving the efficiency of decoding quantum error…
The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new…
A new class of error-correcting quantum codes is introduced capable of stabilizing qubits against spontaneous decay arising from couplings to statistically independent reservoirs. These quantum codes are based on the idea of using an…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
We develop the theory of entanglement-assisted quantum error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional…
Qubit loss is a major source of error in quantum computation, as it invalidates the algebraic structure of the standard stabilizer formalism for quantum error-correcting codes. On the one hand, it complicates decoding; on the other hand, it…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
Certain physical aspects of quantum error correction are discussed for a quantum computer (n-qubit register) in contact with a decohering environment. Under rather plausible assumptions upon the form of the computer-environment interaction,…
We study a quantum analogue of locally decodable error-correcting codes. A q-query locally decodable quantum code encodes n classical bits in an m-qubit state, in such a way that each of the encoded bits can be recovered with high…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
Lowering the resource overhead needed to achieve fault-tolerant quantum computation is crucial to building scalable quantum computers. We show that adapting conventional maximum likelihood (ML) decoders to a small subset of efficiently…
Recent years have seen rapid development in the subject of quantum coding theory, with breakthroughs on many exciting classes of codes, including quantum LDPC codes, quantum locally testable codes, and quantum codes with interesting…
The overheads of classical decoding for quantum error correction on superconducting quantum systems grow rapidly with the number of logical qubits and their correction code distance. Decoding at room temperature is bottle-necked by…
Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
We provide a self-contained introduction for entanglement-assisted quantum error-correcting codes in this book chapter.
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
We investigate effective noise channels for encoded quantum systems with and without active error correction. Noise acting on physical qubits forming a logical qubit is thereby described as a logical noise channel acting on the logical…
In this work, we develop an efficient decoding method for graph codes, a class of stabilizer quantum error-correcting codes constructed from graph states. While optimal decoding is generally NP-hard, we propose a faster decoder exploiting…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…