6 papers
Logarithmic-depth quantum state preparation of polynomials
Baptiste Claudon, Alexis Lucas, Jean-Philip Piquemal +2
Quantum state preparation is a central primitive in many quantum algorithms, yet it is generally resource intensive, with efficient constructions known only for structured families…
Quantum algorithm for anisotropic diffusion and convection equations with vector norm scaling
Julien Zylberman, Thibault Fredon, Nuno F. Loureiro +1
In this work, we tackle the resolution of partial differential equations (PDEs) on digital quantum computers. Two fundamental PDEs are addressed: the anisotropic diffusion equation…
Trotter-based quantum algorithm for solving transport equations with exponentially fewer time-steps
Julien Zylberman, Thibault Fredon, Nuno F. Loureiro +1
The extent to which quantum computers can simulate physical phenomena and solve the partial differential equations (PDEs) that govern them remains a central open question. In this…
Real-Space Chemistry on Quantum Computers: A Fault-Tolerant Algorithm with Adaptive Grids and Transcorrelated Extension
César Feniou, Christopher Cherfan, Julien Zylberman +3
First-quantized, real-space formulations of quantum chemistry on quantum computers are appealing: qubit count scales logarithmically with spatial resolution, and Coulomb operators…
Efficient Quantum Circuits for Non-Unitary and Unitary Diagonal Operators with Space-Time-Accuracy trade-offs
Julien Zylberman, Ugo Nzongani, Andrea Simonetto +1
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian…
Fast Laplace transforms on quantum computers
Julien Zylberman
While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this…