Related papers: Quantum Algorithms for Quantum Field Theories
As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a…
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials science, statistical mechanics, quantum information,…
This article introduces quantum computation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
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)…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…
We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for…
The role of acceleration in particle physics can provide an alternative method for probing the properties of quantum gravity. To analyze acceleration-induced processes one utilizes the formalism of quantum field theory in curved spacetime.…
The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…
Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can only find the solution of hard problems probabilistically. Thus the efficiency of the…
We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…