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Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…
A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…
In this work, we consider the performance of using a quantum algorithm to predict a result for a binary classification problem if a machine learning model is an ensemble from any simple classifiers. Such an approach is faster than classical…
The energy gap is calculated for the ground state quantum computer circuit, which was recently proposed by Mizel et.al. When implementing a quantum algorithm by Hamiltonians containing only pairwise interaction, the inverse of energy gap…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a…
When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this…
This paper gives the first separation of quantum and classical pure (i.e., non-cryptographic) computing abilities with no restriction on the amount of available computing resources, by considering the exact solvability of a celebrated…
We propose a polynomial-time algorithm for simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between…
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…
Simulating noninteracting fermion systems is a common task in computational many-body physics. In absence of translational symmetries, modeling free fermions on $N$ modes usually requires poly$(N)$ computational resources. While often…
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…
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts…
We give a general method of construting quantum circuit for random \QTR{it}{satisfiability} (SAT) problems with the basic logic gates such as multi-qubit controlled-NOT and NOT gates. The sizes of these circuits are almost the same as the…
A major goal of developing high-precision control of many-body quantum systems is to realise their potential as quantum computers. Probably the most significant obstacle in this direction is the problem of "decoherence": the extreme…