相关论文: Mathematical Foundations of Holonomic Quantum Comp…

Quantum computers use quantum mechanical phenomena to perform conventionally intractable calculations for specific problems. Despite being universal machines, quantum computers are not expected to replace classical computers, but rather, to…

The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many…

Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only…

There has been no lack of coverage in the past few years in scientific journals of the topic of quantum computation. Rightly so, as this is a novel idea with--so far--at least one very important practical application (prime factorisation)…

Holonomic quantum computation exploits a quantum state's non-trivial, matrix-valued geometric phase (holonomy) to perform fault-tolerant computation. Holonomies arising from systems where the Hamiltonian traces a continuous path through…

This paper provides a short introduction to the mathematical foundation of quantum computation for researchers in computer science by providing an introduction fo the mathematical basis of calculations. This paper concerns the mathematical…

We describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and…

In this paper the idea of holonomic quantum computation is realized within quantum optics. In a non-linear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices and interferometers…

We develop a scalable architecture for quantum computation using controllable electrons of double-dot molecules coupled to a microwave stripline resonator on a chip, which satisfies all Divincenzo criteria. We analyze the performance and…

Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…

We show how to realize, by means of non-abelian quantum holonomies, a set of universal quantum gates acting on decoherence-free subspaces and subsystems. In this manner we bring together the quantum coherence stabilization virtues of…

Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can…

The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…

A theorem from control theory relating the Lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to Holonomic Quantum Computation. Conditions for deriving the holonomy algebra…

Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…

The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems.…

In this research notebook in the four-part, quantum computation and applications, quantum computation and algorithms, quantum communication protocol, and universal quantum computation for quantum engineers, researchers, and scientists, we…

We consider an example of a quantum algorithm from the point of view of the de Broglie-Bohm formulation of quantum mechanics. For concreteness we look at two particular implementations: one using spin-1/2 particles as described by a simple…

In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse the Fourier--Hadamard and Walsh supports of those functions…

We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This…