Related papers: Beyond Trotterization: Variational Product Formula…
Dynamical quantum simulation may be one of the first applications to see quantum advantage. However, the circuit depth of standard Trotterization methods can rapidly exceed the coherence time of noisy quantum computers. This has led to…
We present a unified theory of the variational Monte Carlo (VMC) and determinant quantum Monte Carlo (DQMC) methods using a novel density matrix formulation of VMC. We introduce an efficient algorithm for VMC to compute correlation…
Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks---generalised time evolution with…
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
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…
Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian…
Implementing time-evolution operators in shallow quantum circuits is important for quantum simulations. The standard method of Trotterization requires a large number of gates to achieve practical accuracy. Variational Quantum Simulation…
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…
Extending our previous work on time optimal quantum state evolution, we formulate a variational principle for the time optimal unitary operation, which has direct relevance to quantum computation. We demonstrate our method with three…
Trotter and linear-combination-of-unitary (LCU) are two popular Hamiltonian simulation methods. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates…
We propose an iterative variational quantum algorithm to simulate the time evolution of arbitrary initial states within a given subspace. The algorithm compresses the Trotter circuit into a shorter-depth parameterized circuit, which is…
Gradient-based optimization is a key ingredient of variational quantum algorithms, with applications ranging from quantum machine learning to quantum chemistry and simulation. The parameter-shift rule provides a hardware-friendly method for…
This work investigates variational compilation methods for simulating quantum systems with internal SU(2) symmetry. The central component of the research is the application of the Dynamic Mode Decomposition (DMD) method to extrapolate…
The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
We propose a method for finding approximate compilations of quantum unitary transformations, based on techniques from policy gradient reinforcement learning. The choice of a stochastic policy allows us to rephrase the optimization problem…
Randomized compilation protocols have recently attracted attention as alternatives to traditional deterministic Trotter-Suzuki methods, potentially reducing circuit depth and resource overhead. These protocols determine gate application…
As first proposed for the adiabatic quantum information processing by Wu, Byrd and Lidar [ Phys. Rev. Lett. 89, 057904 (2002)], the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the…
The extent to which quantum computers can simulate physical phenomena and solve the partial differential equations (PDEs) that govern them remains a central open question. In this work, one of the most fundamental PDEs is addressed: the…
Lie-Trotter-Suzuki decompositions are an efficient way to approximate operator exponentials $\exp(t H)$ when $H$ is a sum of $n$ (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution…