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Quantum systems have entered a competitive regime where classical computers must make approximations to represent highly entangled quantum states. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and…
Quantum computing has the potential to solve many computational problems exponentially faster than classical computers. The high shares of renewables and the wide deployment of converter-interfaced resources require new tools that shall…
The quantum computation of electronic energies can break the curse of dimensionality that plagues many-particle quantum mechanics. It is for this reason that a universal quantum computer has the potential to fundamentally change…
Concordant computation is a circuit-based model of quantum computation for mixed states, that assumes that all correlations within the register are discord-free (i.e. the correlations are essentially classical) at every step of the…
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
Simulating thermal-equilibrium properties at finite temperature is crucial for studying quantum many-body systems. Quantum computers are expected to enable us to simulate large systems at finite temperatures, overcoming challenges faced by…
A measurement-based quantum computer could consist of a local-gapped Hamiltonian system, whose thermal states --at sufficiently low temperature-- are universal resources for the computation. Initialization of the computer would correspond…
In this paper, we present a quasi-polynomial time classical algorithm that estimates the partition function of quantum many-body systems at temperatures above the thermal phase transition point. It is known that in the worst case, the same…
In recent years, strong expectations have been raised for the possible power of quantum computing for solving difficult optimization problems, based on theoretical, asymptotic worst-case bounds. Can we expect this to have consequences for…
Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review…
While quantum computers are capable of simulating many quantum systems efficiently, the simulation algorithms must begin with the preparation of an appropriate initial state. We present a method for generating physically relevant quantum…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Quantum computing algorithms require that the quantum register be initially present in a superposition state. To achieve this, we consider the practical problem of creating a coherent superposition state of several qubits. Owing to…
Despite their importance as subfields of mathematics and engineering, signal and image processing have not received much attention in the field of quantum computation. Cross-correlations are instrumental to all the aforementioned fields. In…
The speed-up provided by quantum algorithms with respect to their classical counterparts is at the origin of scientific interest in quantum computation. However, the fundamental reasons for such a speed-up are not yet completely understood…
We study an open quantum system simulation on quantum hardware, which demonstrates robustness to hardware errors even with deep circuits containing up to two thousand entangling gates. We simulate two systems of electrons coupled to an…
We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a novel…
The partition function and free energy of a quantum many-body system determine its physical properties in thermal equilibrium. Here we study the computational complexity of approximating these quantities for $n$-qubit local Hamiltonians.…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
Quantum simulation is a potentially powerful application of quantum computing, holding the promise to be able to emulate interesting quantum systems beyond the reach of classical computing methods. Despite such promising applications, and…