Quantum search algorithms, such as Grover’s algorithm, are anticipated to efficiently solve constrained combinatorial optimization problems. However, applying these algorithms to the traveling salesman problem (TSP) on a quantum circuit presents a significant challenge. Existing quantum search algorithms for the TSP typically assume that an initial state—an equal superposition of all feasible solutions satisfying the […]
We assess the convergence of the Carleman linearization of advection–diffusion–reaction (ADR) equations with a logistic nonlinearity. It is shown that five Carleman iterates provide a satisfactory approximation of the original ADR across a broad range of parameters and strength of nonlinearity. To assess the feasibility of a quantum algorithm based on this linearization, we analyze […]
The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over classical computers, quantum algorithms for the solution of DEs have received a lot of attention. Particularly interesting are algorithms that offer advantages […]
In some quantum secret sharing schemes, it is known that some shares can be distributed to participants before a secret is given to the dealer. However, it is unclear whether some shares can be distributed before a secret is given in the ramp quantum secret sharing schemes with the highest coding rate. This article proposes […]
In this article, we introduce a generalization of one-way superdense coding to two-way communication protocols for transmitting classical bits by using entangled quantum pairs. The proposed protocol jointly addresses the provision of entangled pairs and superdense coding, introducing an integrated approach for managing entanglement within the communication protocol. To assess the performance of the proposed […]
Relaxation is a common way for dealing with combinatorial optimization problems. Quantum random-access optimization (QRAO) is a quantum-relaxation-based optimizer that uses fewer qubits than the number of bits in the original problem by encoding multiple variables per qubit using quantum random-access code (QRAC). Reducing the number of qubits will alleviate physical noise (typically, decoherence), and […]
Relaxation is a common way for dealing with combinatorial optimization problems.
The reliable provision of entangled qubits is an essential precondition in a variety of schemes for distributed quantum computing. This is challenged by multiple nuisances, such as errors during the transmission over quantum links, but also due to degradation of the entanglement over time due to decoherence. The latter can be seen as a constraint […]
Grover adaptive search (GAS) is a quantum exhaustive search algorithm designed to solve binary optimization problems. In this article, we propose higher order binary formulations that can simultaneously reduce the numbers of qubits and gates required for GAS. Specifically, we consider two novel strategies: one that reduces the number of gates through polynomial factorization, and […]
Variational quantum optimization algorithms, such as the variational quantum eigensolver (VQE) or the quantum approximate optimization algorithm (QAOA), are among the most studied quantum algorithms. In our work, we evaluate and improve an algorithm based on the VQE, which uses exponentially fewer qubits compared to the QAOA. We highlight the numerical instabilities generated by encoding […]