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In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial…
Quantum computers have the potential to simulate chemical systems beyond the capability of classical computers. Recent developments in hybrid quantum-classical approaches enable the determinations of the ground or low energy states of…
The well-known Turing machine is an example of a theoretical digital computer, and it was the logical basis of constructing real electronic computers. In the present paper we propose an alternative, namely, by formalising arithmetic…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…
In this paper we develop a quantum algorithm to realize finite temperature simulation on a quantum computer. As quantum computers use real-time evolution we did not use the imaginary time methods popular on classical algorithms. Instead, we…
We experimentally study the two-dimensional Fermi-Hubbard model using a Rydberg-based quantum processing unit in the analog mode. Our approach avoids encoding directly the original fermions into qubits and instead relies on reformulating…
Thermodynamic computing has emerged as a promising paradigm for accelerating computation by harnessing the thermalization properties of physical systems. This work introduces a novel approach to solving quadratic programming problems using…
Solving the Anderson impurity model typically involves a two-step process, where one first calculates the ground state of the Hamiltonian, and then computes its dynamical properties to obtain the Green's function. Here we propose a hybrid…
Solving finite-temperature properties of quantum many-body systems is generally challenging to classical computers due to their high computational complexities. In this article, we present experiments to demonstrate a hybrid…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
We present a new approach to study the thermodynamic properties of $d$-dimensional classical systems by reducing the problem to the computation of ground state properties of a $d$-dimensional quantum model. This classical-to-quantum mapping…
We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in…
Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamical properties can be computed from its grand canonical potential according to standard procedures. In general, there is no closed…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
Perturbation theory is an important technique for reducing computational cost and providing physical insights in simulating quantum systems with classical computers. Here, we provide a quantum algorithm to obtain perturbative energies on…