Related papers: Fixed-point quantum continuous search algorithm wi…
The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. Quantum search algorithm can be described as the rotation of state vectors in…
The standard quantum search lacks a feature, enjoyed by many classical algorithms, of having a fixed point, i.e. monotonic convergence towards the solution. Recently a fixed point quantum search algorithm has been discovered, referred to as…
Grover's quantum search and its generalization, quantum amplitude amplification, provide quadratic advantage over classical algorithms for a diverse set of tasks, but are tricky to use without knowing beforehand what fraction $\lambda$ of…
Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an…
In this paper, we study the generalized problem that minimizes or maximizes a multi-order complex quadratic form with constant-modulus constraints on all elements of its optimization variable. Such a mathematical problem is commonly…
Fixed-point quantum search algorithms succeed at finding one of $M$ target items among $N$ total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster…
Grover recently presented the fixed-point search algorithm. In this letter, we study the fixed-point search algorithm obtained by replacing equal phase shifts of $\pi /3$ by different phase shifts.
Solving eigenvalue problems is crucially important for both classical and quantum applications. Many well-known numerical eigensolvers have been developed, including the QR and the power methods for classical computers, as well as the…
The Traveling Salesman Problem (TSP) is a classical NP-hard problem that plays a crucial role in combinatorial optimization. In this paper, we are interested in the quantum search framework for the TSP because it has robust theoretical…
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…
We introduce a structured quantum search algorithm that leverages entanglement maps and a fixed-point method to minimize oracle query complexity in unsorted datasets. By partitioning qubits into rows based on their entanglement order, the…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
For the unsorted database quantum search with the unknown fraction $\lambda$ of target items, there are mainly two kinds of methods, i.e., fixed-point or trail-and-error. (i) In terms of the fixed-point method, Yoder et al. [Phys. Rev.…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
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…
Building quantum devices using fixed operators is a must to simplify the hardware construction. Quantum search engine is not an exception. In this paper, a fixed phase quantum search algorithm that searches for M matches in an unstructured…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…