21 citations · 49 across the 12 of their papers we have counts for
13 papers
On the numerical limitations of dual Koopman von Neumann embeddings for solving conservative nonlinear ordinary differential equations on quantum computers
Thibault Fredon, Abhay K. Ram, Fabrice Debbasch +2
The simulation of nonlinear ordinary differential equations on quantum computers is inherently challenging, as quantum gates are linear operators on qubit states. In this paper, we…
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…
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…
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…
Polylogarithmic-depth controlled-NOT gates without ancilla qubits
Baptiste Claudon, Julien Zylberman, César Feniou +3
Controlled operations are fundamental building blocks of quantum algorithms. Decomposing -control-NOT gates () into arbitrary single-qubit and CNOT gates, is a crucial b…
Sparse Quantum State Preparation for Strongly Correlated Systems
C. Feniou, O. Adjoua, B. Claudon +3
Quantum Computing allows, in principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register, offering a promising solution…
Efficient Quantum State Preparation with Walsh Series
Julien Zylberman, Fabrice Debbasch
A new approximate Quantum State Preparation (QSP) method is introduced, called the Walsh Series Loader (WSL). The WSL approximates quantum states defined by real-valued functions o…
Quantum circuits for discrete-time quantum walks with position-dependent coin operator
Ugo Nzongani, Julien Zylberman, Carlo-Elia Doncecchi +3
The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is en…
Quantum spatial search with electric potential : long-time dynamics and robustness to noise
Thibault Fredon, Julien Zylberman, Pablo Arnault +1
We present various results on the scheme introduced , which is a quantum spatial-search algorithm on a two-dimensional (2D) square spatial grid, realized with a 2D Dirac discrete-t…
Hybrid Quantum-Classical Algorithm for Hydrodynamics
Julien Zylberman, Giuseppe Di Molfetta, Marc Brachet +2
A new model of nonlinear charged quantum relativistic fluids is presented. This model can be discretized into Discrete Time Quantum Walks (DTQWs), and a new hybrid (quantum-classic…