Related papers: A Simple Quantum Integro-Differential Solver (SQuI…
Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient…
Since a pure quantum system is incapable of faithfully simulating the solutions of the Schroedinger equation that actually pertains to itself, it is proposed that quantum computing technology (as opposed to cryptographic technology) not be…
Qubits are the basic building blocks of a quantum processor which require electromagnetic pulses in giga hertz frequency range and latency in nanoseconds for control and readout. In this paper, we address three main challenges associated…
Quantum computing is advancing rapidly in hardware and algorithms, but broad accessibility demands a comprehensive, efficient, unified software stack. Such a stack must flexibly span diverse hardware and evolving algorithms, expose usable…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
This document is an introduction to the Matlab package SDLS (Semi-Definite Least-Squares) for solving least-squares problems over convex symmetric cones. The package is shortly presented through the addressed problem, a sketch of the…
Quantum computers now show the promise of surpassing any possible classical machine. However, errors limit this ability and current machines do not have the ability to implement error correcting codes due to the limited number of qubits and…
In the evolving landscape of quantum computing, determining the most efficient parameters for Quantum Error Correction (QEC) is paramount. Various quantum computers possess varied types and amounts of physical noise. Traditionally,…
Recent advances in quantum error correction (QEC) codes for fault-tolerant quantum computing \cite{Terhal2015} and physical realizations of high-fidelity qubits in a broad range of platforms \cite{Kok2007, Brown2011, Barends2014,…
As quantum devices scale toward practical machine learning applications, the binary qubit paradigm faces expressivity and resource efficiency limitations. Multi-level quantum systems, or qudits, offer a promising alternative by harnessing a…
A novel scheme is proposed for realizing quantum entanglement, quantum information transfer and a set of universal quantum gates with superconducting-quantum-interference-device (SQUID) qubits in cavity QED. In the scheme, the two logical…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…
We introduce a hybrid oscillator-qubit formulation of linear combination of Hamiltonian simulation (LCHS) for solving linear ordinary differential equations. Instead of representing the quadrature rule with a discrete-variable (DV) ancilla…
We show that matrix $Q\times Q$ Self-dual type $S$-integrable Partial Differential Equations (PDEs) possess a family of lower-dimensional reductions represented by the matrix $ Q \times n_0 Q$ quasilinear first order PDEs solved in…
Quantum Physics-Informed Neural Networks (QPINNs) integrate quantum computing and machine learning to impose physical biases on the output of a quantum neural network, aiming to either solve or discover differential equations. The approach…
We present a method for preparing arbitrary pure states of spatial qudits, namely, D-dimensional (D > 2) quantum systems carrying information in the transverse momentum and position of single photons. For this purpose, a set of D slits with…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
Recent years have seen a rise in the popularity of quality diversity (QD) optimization, a branch of optimization that seeks to find a collection of diverse, high-performing solutions to a given problem. To grow further, we believe the QD…
Stochastic differential equations (SDEs), which models uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical…