Related papers: Quantum Advantage via Solving Multivariate Polynom…
The Polynomial-Time Hierarchy ($\mathsf{PH}$) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to ''quantum advantage'' analyses for near-term quantum computers.…
Traditional cryptography is facing great challenges with the development of quantum computing. Not only public-key cryptography, the applications of quantum algorithms to symmetric cryptanalysis has also drawn more and more attention. In…
We present a quasi-Newton method for unconstrained stochastic optimization. Most existing literature on this topic assumes a setting of stochastic optimization in which a finite sum of component functions is a reasonable approximation of an…
A fast quantum search algorithm for continuous variables is presented. The result is the quantum continuous variable analog of Grover's algorithm originally proposed for qubits. A continuous variable analog of the Hadamard (i.e., Fourier…
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
The quantum switch is a quantum computational primitive that provides computational advantage by applying operations in a superposition of orders. In particular, it can reduce the number of gate queries required for solving promise problems…
In this work, we propose a novel key reconciliation protocol for the quantum key distribution (QKD). Based on Newton's polynomial interpolation, the proposed protocol aims to correct all erroneous bits at the receiver without revealing…
We develop a hybrid classical-quantum algorithm to solve a type of linear reaction-diffusion equation, the neutron diffusion (generalized) k-eigenvalue problem that establishes nuclear criticality. The algorithm handles an equation with…
Quantum annealing has emerged as a promising approach for solving NP-hard optimization problems, leveraging quantum phenomena such as quantum tunneling to navigate complex energy landscapes. However, the extent to which quantum tunneling…
The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the…
Quantum algorithms offer an exponential advantage with respect to the number of dependent variables for solving certain nonlinear ordinary differential equations (ODEs). These algorithms typically begin by transforming the original…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…
We derive a sufficient condition for advantage distillation to be secure against collective attacks in device-independent quantum key distribution (DIQKD), focusing on the repetition-code protocol. In addition, we describe a semidefinite…
An overarching milestone of quantum machine learning (QML) is to demonstrate the advantage of QML over all possible classical learning methods in accelerating a common type of learning task as represented by supervised learning with…
Quantum cryptography and quantum key distribution (QKD) have been the most successful applications of quantum information processing, highlighting the unique capability of quantum mechanics, through the no-cloning theorem, to protect the…
Decision of whether a Boolean equation system has a solution is an NPC problem and finding a solution is NP hard. In this paper, we present a quantum algorithm to decide whether a Boolean equation system FS has a solution and compute one if…