Related papers: Hamiltonian Encoding for Quantum Approximate Time …
Quantum imaginary time evolution (QITE) is a powerful method to derive the ground states of the systems. Only the damping of quantum states leads it; hence, reaching the ground state is guaranteed by nature without any external…
Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
We consider Hamiltonian simulation using the first order Lie-Trotter product formula under the assumption that the initial state has a high overlap with an energy eigenstate, or a collection of eigenstates in a narrow energy band. This…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
Solving combinatorial optimization problems using variational quantum algorithms (VQAs) has emerged as a promising research direction. Since the introduction of the Quantum Approximate Optimization Algorithm (QAOA), numerous variants have…
Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory, but offer higher accuracy. Accordingly, quantum computers have been…
Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results…
Hamiltonian simulation on quantum computers is strongly constrained by gate counts, motivating techniques to reduce circuit depths. While tensor networks are natural competitors to quantum computers, we instead leverage them to support…
We discuss a method to follow step-by-step time evolution of atomic and molecular systems based on QED (Quantum Electrodynamics). Our strategy includes expanding the electron field operator by localized wavepackets to define creation and…
We propose a method for constructing $\texttt{PREPARE}$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
In this work, we investigate the capability of known quantum-computing algorithms for fault-tolerant quantum computing to simulate the laser-driven electron dynamics in small molecules such as lithium hydride. These computations are…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
Quantum phase estimation (QPE) plays a pivotal role in many quantum algorithms, offering provable speedups in applications such as Shor's factoring algorithm. While fault-tolerant quantum algorithms for combinatorial and Hamiltonian…
Block-encodings have become one of the most common oracle assumptions in the circuit model. I present an algorithm that uses von Neumann's measurement procedure to measure a phase, using time evolution on a block-encoded Hamiltonian as a…
Simulating time evolution of quantum systems is one of the most promising applications of quantum computing and also appears as a subroutine in many applications such as Green's function methods. In the current era of NISQ machines we…
Imaginary-time evolution (ITE) on a quantum computer is a promising formalism for obtaining the ground state of a quantum system. As a kind of it, the probabilistic ITE (PITE) takes advantage of measurements to implement the nonunitary…
A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…
We introduce an approach for approximate real-time evolution of quantum systems using Tensor Renormalization Group (TRG) methods originally developed for imaginary time. We use Higher- Order TRG (HOTRG) to generate a coarse-grained time…