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The numerical solution of partial differential equations by discretization techniques is ubiquitous in computational physics. In this work we benchmark this approach in the quantum realm by solving the heat equation for a square plate…
Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be…
Many quantum algorithms rely on a quality initial state for optimal performance. Preparing an initial state for specific applications can considerably reduce the cost of probabilistic algorithms such as the well studied quantum phase…
The general method for treating non-Gaussian wave functionals in the Hamiltonian formulation of a quantum field theory, which was previously proposed and developed for Yang--Mills theory in Coulomb gauge, is generalized to full QCD. For…
Quantum computers are expected to give major speed-ups for the simulation of quantum systems. In these conference proceedings, we discuss quantum algorithms for the simulation of perturbative Quantum Chromodynamics (QCD) processes. In…
Quantum chemistry is among the most promising applications of quantum computing, offering the potential to solve complex electronic structure problems more efficiently than classical approaches. A critical component of any quantum algorithm…
We develop a quantum algorithm for solving high-dimensional fractional Poisson equations. By applying the Caffarelli-Silvestre extension, the $d$-dimensional fractional equation is reformulated as a local partial differential equation in…
Accurate and scalable methods for computational quantum chemistry can accelerate research and development in many fields, ranging from drug discovery to advanced material design. Solving the electronic Schrodinger equation is the core…
Quantum chemistry calculations for small molecules on quantum hardware have been demonstrated to date only on universal-gate quantum computers, not quantum annealers. The latter devices are limited to finding the lowest eigenstate of the…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
We developed a general framework for hybrid quantum-classical computing of molecular and periodic embedding approaches based on an orbital space separation of the fragment and environment degrees of freedom. We demonstrate its potential by…
Quantum computational chemistry has emerged as an important application of quantum computing. Hybrid quantum-classical computing methods, such as variational quantum eigensolvers (VQE), have been designed as promising solutions to quantum…
This paper presents a quantum algorithm for efficiently decoding hypervectors, a crucial process in extracting atomic elements from hypervectors - an essential task in Hyperdimensional Computing (HDC) models for interpretable learning and…
Classical simulation of real-space quantum dynamics is challenging due to the exponential scaling of computational cost with system dimensions. Quantum computer offers the potential to simulate quantum dynamics with polynomial complexity;…
A solid-state implementation of a quantum computer composed entirely of silicon is proposed. Qubits are Si-29 nuclear spins arranged as chains in a Si-28 (spin-0) matrix with Larmor frequencies separated by a large magnetic field gradient.…
At large scales, quantum systems may become advantageous over their classical counterparts at performing certain tasks. Developing tools to analyse these systems at the relevant scales, in a manner consistent with quantum mechanics, is…
Density matrix electronic structure theory is used in many quantum chemistry methods to "alleviate" the computational cost that arises from directly using wave functions. Although density matrix based methods are computationally more…
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
Quantum algorithms based on classical processing of individual samples have recently emerged as the most effective and robust methods to approximate ground-state wave functions of many-body quantum systems on pre-fault-tolerant and…