Related papers: Stochastic Simulation of Grover's Algorithm
We review the basic theoretical underpinnings of the Grover algorithm, providing a rigorous and well motivated derivation. We then present a generalization of Grover's algorithm that searches an arbitrary subspace of the multi-dimensional…
We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for…
We study the effects of dissipation or leakage on the time evolution of Grover's algorithm for a quantum computer. We introduce an effective two-level model with dissipation and randomness (imperfections), which is based upon the idea that…
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm…
We present novel algorithms to estimate outcomes for qubit quantum circuits. Notably, these methods can simulate a Clifford circuit in linear time without ever writing down stabilizer states explicitly. These algorithms outperform previous…
Classical simulation of quantum computers is an irreplaceable step in the design of quantum algorithms. Exponential simulation costs demand the use of high-performance computing techniques, and in particular distribution, whereby the…
$ $In its usual form, Grover's quantum search algorithm uses $O(\sqrt{N})$ queries and $O(\sqrt{N} \log N)$ other elementary gates to find a solution in an $N$-bit database. Grover in 2002 showed how to reduce the number of other gates to…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
We describe and analyze algorithms for classically simulating measurement of an $n$-qubit quantum state $\psi$ in the standard basis, that is, sampling a bit string $x$ from the probability distribution $|\langle x|\psi\rangle|^2$. Our…
An examination of the concept of using classical degrees of freedom to drive the evolution of quantum computers is given. Specifically, when externally generated, coherent states of the electromagnetic field are used to drive transitions…
We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the…
We investigate the performance and accuracy of digital quantum algorithms for the study of static and dynamic properties of the fermionic Hubbard model at half-filling with next-nearest neighbour hopping terms. We provide quantum circuits…
Simulating physical systems has been an important application of classical and quantum computers. In this article we present an efficient classical algorithm for simulating time-dependent quantum mechanical Hamiltonians over constant…
Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and…
A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…
One of the first proposals for the use of quantum computers was the simulation of quantum systems. Over the past three decades, great strides have been made in the development of algorithms for simulating closed quantum systems and the more…
We introduce the concepts of Grover operators and Grover kernels to systematically analyse Grover's searching algorithms. Then, we investigate a one-parameter family of quantum searching algorithms of Grover's type and we show that the…
In this brief comment on `Grover search with pairs of trapped Ions' [Phys. Rev. A 63, 052308, (2001)], we show that Grover's algorithm may be performed exactly using the gate set given provided that small changes are made to the gate…
We present a method for constructing numerical schemes with up to 3rd strong convergence order for solution of a class of stochastic differential equations, including equations of the Langevin type. The construction proceeds in two stages.…
Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum simulation of strongly correlated fermionic…