Related papers: A Probabilistic Imaginary Time Evolution Algorithm…
We present a method, which we shall call the probabilistic evolutionary process, based on the probabilistic nature of quantum theory to offer a possible solution to the problem of time in quantum cosmology. It offers an alternative for…
We present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…
Variational Quantum Imaginary Time Evolution (VQITE) is a leading technique for ground state preparation on quantum computers. A significant computational challenge of VQITE is the determination of the quantum geometric tensor. We show that…
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…
Simulations of scattering processes are essential in understanding the physics of our universe. Computing relevant scattering quantities from ab initio methods is extremely difficult on classical devices because of the substantial…
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this…
Efficiently preparing approximate ground-states of large, strongly correlated systems on quantum hardware is challenging and yet nature is innately adept at this. This has motivated the study of thermodynamically inspired approaches to…
We propose a numerical method for approximate calculations of the time evolution of point particle systems given only the system's Hamiltonian function and initial conditions. The method both generates and solves the equations of motion…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…
We present a code for solving the single-particle, time-independent Schr\"odinger equation in two dimensions. Our program utilizes the imaginary time propagation (ITP) algorithm, and it includes the most recent developments in the ITP…
Many physical and chemical processes in the condensed phase environment exhibit non-Markovian quantum dynamics. As such simulations are challenging on classical computers, we developed a variational quantum algorithm that is capable of…
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as…
We present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…
In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
Obtaining exact solutions to combinatorial optimization problems using classical computing is computationally expensive. The current tenet in the field is that quantum computers can address these problems more efficiently. While promising…
We propose a neural-network variational quantum algorithm to simulate the time evolution of quantum many-body systems. Based on a modified restricted Boltzmann machine (RBM) wavefunction ansatz, the proposed algorithm can be efficiently…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…