11 citations · 18 across the 8 of their papers we have counts for
9 papers
Adiabatic tracking and optimal schedules for classical and quantum Gibbs-state preparation
Pedro C. S. Costa, Mauro E. S. Morales, Dong An +1
We develop a discrete adiabatic framework for Gibbs-state preparation in classical and quantum optimisation algorithms. For finite time-inhomogeneous reversible Markov chains, we d…
Constant Factor Analysis of Optimal Quantum Linear Solvers in Practice
Pedro C. S. Costa, Alexander M. Dalzell, Dong An +1
Optimal quantum linear equation solvers provide complexity , where is the condition number and is the allowable error. The optimal solver using a discrete ad…
Unitary Quantum Cellular Automata for Density Classification
Pedro C. S. Costa, Yuval R. Sanders, Pedro Paulo Balbi +1
We investigate the density classification task (DCT) -- determining the majority bit in a one-dimensional binary lattice -- within a quantum cellular automaton (CA) framework. Whil…
Large time-step discretisation of adiabatic quantum dynamics
Dong An, Pedro C. S. Costa, Dominic W. Berry
Adiabatic quantum computing is a general framework for preparing eigenstates of Hamiltonians on quantum devices. However, its digital implementation requires an efficient Hamiltoni…
On a class of left ideals of nest algebras
Pedro Costa, Martim Ferreira, Lina Oliveira
We introduce a class of left ideals (and subalgebras) of nest algebras determined by totally ordered families of partial isometries on a complex Hilbert space . Let $\mathcal{E}…
Assessing Quantum and Classical Approaches to Combinatorial Optimization: Testing Quadratic Speed-ups for Heuristic Algorithms
Pedro C. S. Costa, Mauro E. S. Morales, Dong An +1
Many recent investigations conclude, based on asymptotic complexity analyses, that quantum computers could accelerate combinatorial optimization (CO) tasks relative to a purely cla…
Quantum Linear System Solvers: A Survey of Algorithms and Applications
Mauro E. S. Morales, Lirandë Pira, Philipp Schleich +7
Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve t…
Further improving quantum algorithms for nonlinear differential equations via higher-order methods and rescaling
Pedro C. S. Costa, Philipp Schleich, Mauro E. S. Morales +1
The solution of large systems of nonlinear differential equations is needed for many applications in science and engineering. In this study, we present three main improvements to e…
The discrete adiabatic quantum linear system solver has lower constant factors than the randomized adiabatic solver
Pedro C. S. Costa, Dong An, Ryan Babbush +1
The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition numbe…