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The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…
Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which…
The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker-Plank-Smoluchowski equation models the time evolution of the…
In this paper, we investigate the use of variational quantum algorithms for simulating the thermodynamic properties of dinuclear metal complexes. Our study highlights the potential of quantum computing to transform advanced simulations and…
The quest for improved sampling methods to solve statistical mechanics problems of physical and chemical interest proceeds with renewed efforts since the invention of the Metropolis algorithm, in 1953. In particular, the understanding of…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
Efficiently simulating quantum circuits on classical computers is a fundamental challenge in quantum computing. This paper presents a novel theoretical approach that achieves substantial speedups over existing simulators for a wide class of…
Quantum cooling has demonstrated its potential in quantum computing, which can reduce the number of control channels needed for external signals. Recent progress also supports the possibility of maintaining quantum coherence in large-scale…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
We address the question of how a quantum computer can be used to simulate experiments on quantum systems in thermal equilibrium. We present two approaches for the preparation of the equilibrium state on a quantum computer. For both…
The quantum dynamics of many-qubit systems is an outstanding problem that has recently driven significant advances in both numerical methods and programmable quantum processing units. In this work, we employ a comprehensive toolbox of…
Simulation of time dynamical physical problems has been a challenge for classical computers due to their time-complexity. To demonstrate the dominance of quantum computers over classical computers in this regime, here we simulate a…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…
We extend the ability of unitary quantum circuits by interfacing it with classical autoregressive neural networks. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the…
Among the fundamental questions in computer science, at least two have a deep impact on mathematics. What can computation compute? How many steps does a computation require to solve an instance of the 3-SAT problem? Our work addresses the…
Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…
We consider whether trainable quantum unitaries can be used to discover quantum speed-ups for classical problems. Using methods recently developed for training quantum neural nets, we consider Simon's problem, for which there is a known…
We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal…
This thesis explores hybrid algorithms that combine classical and quantum computing to enhance the performance of classical algorithms. Two approaches are studied: a hybrid search and sample optimization algorithm and a classical algorithm…
A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum…