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This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
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 introduce the concept of quantum locally recoverable codes (qLRCs) with intersecting recovery sets. We derive a singleton-like bound for these codes by leveraging the additional information provided by the intersecting recovery sets.…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…
Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct…
Quantum computing offers significant speedups, but the large number of physical qubits required for quantum error correction introduces engineering challenges for a monolithic architecture. One solution is to distribute the logical quantum…
We investigate the possibility of correcting errors occurring on a multipartite system through a feedback mechanism that acquires information from partial access to the environment. A partial control scheme of this kind might be useful when…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…
Powerful techniques have been developed in quantum field theory that employ algebras of local operators, yet local operators cannot create physical charged states in gauge theory or physical nonzero-energy states in perturbative quantum…
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in…
Quantum state tomography is a daunting challenge of experimental quantum computing even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the…
The development of prototype quantum information processors has progressed to a stage where small instances of logical qubit systems perform better than the best of their physical constituents. Advancing towards fault-tolerant quantum…
Several information measures have recently been defined which capture the notion of "recoverability." In particular, the fidelity of recovery quantifies how well one can recover a system $A$ of a tripartite quantum state, defined on systems…
Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple…
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…