Related papers: An algorithm for solving unconstrained unitary qua…
We introduce a quantum approximate optimization algorithm (QAOA) for continuous optimization. The algorithm is based on the dynamics of a quantum system moving in an energy potential which encodes the objective function. By approximating…
A quantum algorithm for combinatorial search is presented that provides a simple framework for utilizing search heuristics. The algorithm is evaluated in a new case that is an unstructured version of the graph coloring problem. It performs…
Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum…
Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms. Motivated by existing deterministic and random methods, we present a hybrid approach, where Hamiltonians with large amplitude are…
We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly…
Simulation of quantum matters is a significant application of quantum computers. In contrast to the unitary operation which can be realized naturally on a quantum computer, the implementation of nonunitary operation, widely used in…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
Given a parameterized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
Low-energy estimation and state preparation for general $k$-local Hamiltonians are fundamental challenges in quantum complexity theory. For constant relative accuracy, Buhrman et al. (PRL 2025) recently broke the natural Grover bound…
Time symmetry in quantum mechanics, where the current quantum state is determined jointly by both the past and the future, offers a more comprehensive description of physical phenomena. This symmetry facilitates both forward and backward…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
The Grover algorithm is a crucial solution for addressing unstructured search problems and has emerged as an essential quantum subroutine in various complex algorithms. By using a different approach with previous studies, this research…
Variational quantum algorithms are viewed as promising candidates for demonstrating quantum advantage on near-term devices. These approaches typically involve the training of parameterized quantum circuits through a classical optimization…
Grover's algorithm can be employed in global optimization methods providing, in some cases, a quadratic speedup over classical algorithms. This paper describes a new method for continuous global optimization problems that uses a classical…
We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses ($p$-spin model), and $k$-local…
We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time.…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
We provide a tight analysis of Grover's recent algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine…