Related papers: A New Quantum Lower Bound Method, with Application…
Quantum hypothesis testing concerns the discrimination between quantum states. This paper introduces a novel lower bound for asymmetric quantum hypothesis testing that is based on the Nussbaum-Szko{\l}a mapping. The lower bound provides a…
We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
The quantum approximate optimization algorithm is commonly used to solve combinatorial optimization problems. While unconstrained problems map naturally into the algorithm, incorporating constraints typically requires penalizing constraint…
We show a practical application of an well-known nonequilibrium relation, the Jarzynski equality, in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
We investigate a hybrid quantum-classical solution method to the mean-variance portfolio optimization problems. Starting from real financial data statistics and following the principles of the Modern Portfolio Theory, we generate…
Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the…
In the rapidly advancing domain of quantum optimization, the confluence of quantum algorithms such as Quantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) with robust optimization methodologies presents a…
We study the problem of finding $K$ collision pairs in a random function $f : [N] \rightarrow [N]$ by using a quantum computer. We prove that the number of queries to the function in the quantum random oracle model must increase…
By leveraging the principles of quantum mechanics, QML opens doors to novel approaches in machine learning and offers potential speedup. However, machine learning models are well-documented to be vulnerable to malicious manipulations, and…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
In this note, we show that quantum lower bounds obtained using the adversary method hold in the Hamiltonian oracle model.
Many combinatorial optimization problems admit a maximin fairness variant, where the aim is to find a distribution over possible solutions which maximizes an expected worst-case outcome. However, the support for an optimal distribution may…
The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problem's hardness. We study the quantum…
We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…
The Quantum Approximate Optimization Algorithm (QAOA) is designed to run on a gate model quantum computer and has shallow depth. It takes as input a combinatorial optimization problem and outputs a string that satisfies a high fraction of…
The Quantum Approximate Optimisation Algorithm is a $p$ layer, time-variable split operator method executed on a quantum processor and driven to convergence by classical outer loop optimisation. The classical co-processor varies individual…