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Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction…

We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…

Quantum computers promise to solve certain problems exponentially faster than possible classically but are challenging to build because of their increased susceptibility to errors. Remarkably, however, it is possible to detect and correct…

Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…

The hypergraph states are pure multipartite quantum states corresponding to a hypergraph. It is an equal superposition of the states belonging to the computational basis. Given any hypergraph, we can construct a hypergraph state determined…

We present two economical one-step error-correction protocols for multipartite polarization-entangled systems in a Greenberger-Horne-Zeilinger state. One uses spatial entanglement to correct errors in the polarization entanglement of an…

Today ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. The standard circuit model of quantum computing requires a universal set…

The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The…

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…

We optimize fault-tolerant quantum error correction to reduce the number of syndrome bit measurements. Speeding up error correction will also speed up an encoded quantum computation, and should reduce its effective error rate. We give both…

The performance of a given quantum error correction (QEC) code depends upon the noise model that is assumed. Independent Pauli noise, applied after each quantum operation, is a simplistic noise model that is easy to simulate and understand…

In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural…

Boolean functions have important applications in cryptography and coding theory. Two famous classes of binary codes derived from Boolean functions are the Reed-Muller codes and Kerdock codes. In the past two decades, a lot of progress on…

Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…

In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat…

Neutral atom quantum processors are a promising platform for large-scale quantum computing. Integrating them with an optical cavity enables fast nondestructive qubit readout and access to fast remote entanglement generation for quantum…

The present thesis deals with various methods of quantum error correction. It is divided into two parts. In the first part, dynamical decoupling methods are considered which have the task of suppressing the influence of residual…

Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large…

A major outstanding problem for many quantum clock synchronization protocols is the hidden assumption of the availability of synchronized clocks within the protocol. In general, quantum operations between two parties do not have consistent…

Compared with entanglement with multiple types of noise, entanglement including only one type of error is a favorable fundamental resource not only for quantum communication but also for distributed quantum computation. We consider protocol…