Related papers: An Analytic Solution to Wahba's Problem
Optimal quantum linear equation solvers provide complexity $O(\kappa\log(1/\epsilon))$, where $\kappa$ is the condition number and $\epsilon$ is the allowable error. The optimal solver using a discrete adiabatic approach [PRX Quantum 3,…
The Quantum Approximate Optimization Algorithm (QAOA) has shown promise in solving combinatorial optimization problems by leveraging quantum computational power. We propose a simple approach, the Two-Step QAOA, which aims to improve the…
We retrace Davenport's solution to Wahba's classic problem of aligning two pointclouds using the formalism of Geometric Algebra (GA). GA proves to be a natural backdrop for this problem involving three-dimensional rotations due to the…
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Quantum algorithms have gained increasing attention for addressing complex combinatorial problems in finance, notably portfolio optimization. This study systematically benchmarks two prominent variational quantum approaches, Variational…
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Spacecraft attitude control using only magnetic torques is a periodic time-varying system as the Earth magnetic field in the spacecraft body frame changes periodically while the spacecraft circles around the Earth. The optimal controller…
By exploiting the invariance of the molecular Hamiltonian by a unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in the Variational Quantum Eigensolver (VQE) algorithm by…
The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is…
Stochastic, iterative search methods such as Evolutionary Algorithms (EAs) are proven to be efficient optimizers. However, they require evaluation of the candidate solutions which may be prohibitively expensive in many real world…
This paper presents a computationally efficient optimization algorithm for solving nonconvex optimal control problems that involve discrete logic constraints. Traditional solution methods for these constraints require binary variables and…
In recent years, Variational Quantum Algorithms (VQAs) have emerged as a promising approach for solving optimization problems on quantum computers in the NISQ era. However, one limitation of VQAs is their reliance on fixed-structure…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…
Finding a Hadamard matrix of a specific order using a quantum computer can lead to a demonstration of practical quantum advantage. Earlier efforts using a quantum annealer were impeded by the limitations of the present quantum resource and…
Fast and robust quantum control protocols are often based on an idealised approximate description of the relevant quantum system. While this may provide a performance which is close to optimal, improvements can be made by incorporating…
We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic…
Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…
Orbital optimization procedure is widely called in electronic structure simulation. To efficiently find the orbital optimization solution, we developed a new second order orbital optimization algorithm, co-iteration augmented Hessian (CIAH)…
We introduce SamBa-GQW, a novel quantum algorithm for solving binary combinatorial optimization problems of arbitrary degree with no use of any classical optimizer. The algorithm is based on a continuous-time quantum walk on the solution…