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Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared…
Variational quantum algorithms have found success in the NISQ era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers. In our study we introduce the dynamic ansatz in the Variational…
We present a distributed algorithm and implementation of the variational quantum eigensolver (VQE), termed distributed VQE (DVQE). DVQE, provided as an open-source Python package, enables the execution of parameterized quantum circuits…
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
We compare the circuit depths for five different gate sets to implement a quantum algorithm solving a drift-diffusion equation in two spatial dimensions. Our algorithm uses diagonalisation by the quantum Fourier transform. The gate sets…
We propose a simple quantum algorithm for implementing the diffusion step of grid-based Bayesian filters. The method encodes the advected state density and the process noise density into quantum registers and realizes diffusion using a…
We present a quantum variational algorithm based on a novel circuit that generates all permutations that can be spanned by one- and two-qubits permutation gates. The construction of the circuits follows from group-theoretical results, most…
Electron-molecule collisions play a central role in both natural processes and modern technological applications, particularly in plasma processing. Conventional computational strategies such as the R-matrix method have been widely adopted…
We present two experimental schemes that can be used to implement the Factorized Quantum Lattice-Gas Algorithm for the 1D Diffusion Equation with Persistent-Current Qubits. One scheme involves biasing the PC Qubit at multiple flux bias…
Variational quantum algorithms are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a…
The characterization of quantum phase transitions is a fundamental task for the understanding of quantum phases of matter, with a number of potential applications in quantum technologies. In this work, we use digital quantum simulation as a…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
Optimization problems are critical across various domains, yet existing quantum algorithms, despite their great potential, struggle with scalability and accuracy due to excessive reliance on entanglement. To address these limitations, we…
Variational quantum algorithms (VQAs) have emerged as a promising approach for achieving quantum advantage on current noisy intermediate-scale quantum devices. However, their large-scale applications are significantly hindered by…
Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report…
We propose a quantum-classical hybrid algorithm to simulate the non-equilibrium steady state of an open quantum many-body system, named the dissipative-system Variational Quantum Eigensolver (dVQE). To employ the variational optimization…
We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the…
This work studies the variational quantum eigensolver algorithm, designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. Methods of reducing the number of required qubit…
Scaling quantum computers, i.e., quantum processing units (QPUs) to enable the execution of large quantum circuits is a major challenge, especially for applications that should provide a quantum advantage over classical algorithms. One…