相关论文: Grover's algorithm on a Feynman computer

The origin and nature of time in complex systems is explored using quantum (or 'Feynman') clocks and the signals produced by them. Networks of these clocks provide the basis for the evolution of complex systems. The general concept of…

Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…

In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it…

Grover's algorithm is usually described in terms of the iteration of a compound operator of the form $Q = - H I_{0} H I_{x_0}$. Although it is quite straightforward to verify the algebra of the iteration, this gives little insight into why…

We revisit a recent proposal for a definition of time in quantum cosmology, to investigate the effects of having more than one possible type of clock "at the same time". We use as test tube an extension of Einstein gravity with a massless…

Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…

Logic entailment is essential to reasoning, but entailment checking has the worst-case complexity of an exponential of the variable size. With recent development, quantum computing when mature may allow an effective approach for various…

Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as…

Grover's quantum search algorithm promises a quadratic speedup for unstructured search over its classical counterpart. But this advantage is affected by noise acting on the search space. Here, we show that a quantum switch can act as a…

We summarize our investigation of the extent to which the choice of internal clock influences the dynamics in quantum models of gravity. Firstly, at the classical level, we define an extension to the Hamilton-Jacobi theory of contact…

The Rodeo Algorithm is a quantum computing method for computing the energy spectrum of a Hamiltonian and preparing its energy eigenstates. We discuss how to improve the performance of the rodeo algorithm for each of these two applications.…

We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…

A flagship application of quantum computers is the simulation of other quantum systems, including quantum field theories. In this article, we show how quantum computers can be employed to naturally calculate Feynman diagrams and their…

This research presents a novel approach in quantum computing by transforming ARM assembly instructions for use in quantum algorithms. The core achievement is the development of a method to directly map the ARM assembly language, a staple in…

We motivate the use of quantum algorithms in particle physics and provide a brief overview of the most recent applications at high-energy colliders. In particular, we discuss in detail how a quantum approach reduces the complexity of jet…

In order to study the "problem of time", Rovelli proposed a model of a two harmonic oscillator system where one of the oscillators can be thought of as a 'clock' for the other oscillator. In this paper we examine a model where the…

In quantum information theory, there is an explicit mapping between general unitary dynamics and Hermitian ground state eigenvalue problems known as the Feynman-Kitaev Clock. A prominent family of methods for the study of quantum ground…

We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system described by an N dimensional Hilbert space with a Hamiltonian of the form $E |w >< w|$ where…

Grover's quantum search algorithm, involving a large number of qubits, is highly sensitive to errors in the physical implementation of the unitary operators. This poses an intrinsic limitation to the size of the database that can be…