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The analysis of multiparticle quantum states is a central problem in quantum information processing. This task poses several challenges for experimenters and theoreticians. We give an overview over current problems and possible solutions…
Quantum computing (QC) has experienced rapid growth in recent years with the advent of robust programming environments, readily accessible software simulators and cloud-based QC hardware platforms, and growing interest in learning how to…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
Some Open Problems Concerning Orthogonal Polynomials.
Quantum computing has been increasingly applied in nuclear physics. In this work, we combine quantum computing with the complex scaling method to address the resonance problem. Due to the non-Hermiticity introduced by complex scaling,…
An outstanding problem in quantum computing is the calculation of entanglement, for which no closed-form algorithm exists. Here we solve that problem, and demonstrate the utility of a quantum neural computer, by showing, in simulation, that…
We assess the potential of quantum computing to accelerate computation of central tasks in genomics, focusing on often-neglected theoretical limitations. We discuss state-of-the-art challenges of quantum search, optimization, and machine…
Scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite its ease of implementation of one-qubit gates. Two-qubit gates necessarily need a nonlinear…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
This paper, part of a Roadmap article, provides an account of the status and the current challenges in the area of nuclear quantum dynamics simulations, and presents advances in theory and computational techniques to address these…
We survey results on the hardness of approximating combinatorial optimization problems.
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
This paper reviews various engineering hurdles facing the field of quantum computing. Specifically, problems related to decoherence, state preparation, error correction, and implementability of gates are considered.
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…
We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.
On Tuesday 26th November 2024, four discussants participated in a moderated virtual panel titled Future of Quantum Computing as one session of the 8th International Conference on Quantum Techniques in Machine Learning hosted by the…