Related papers: First-Order Trotter Error from a Second-Order Pers…
Hamiltonian simulation is one of the most promising applications of quantum computers, and the product formula is one of the most important methods for this purpose. Previous related work has mainly focused on the worst$-$case or…
Operator scrambling, which governs the spread of quantum information in many-body systems, is a central concept in both condensed matter and high-energy physics. Accurately capturing the emergent properties of these systems remains a…
As noisy intermediate-scale quantum (NISQ) processors increase in size and complexity, their use as general purpose quantum simulators will rely on algorithms based on the Trotter-Suzuki expansion. We run quantum simulations on a small,…
One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved…
Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. This approach typically relies on deep circuits and is therefore hampered by the substantial…
The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of…
Quantum computation with Trotter product formulae is straightforward and requires little overhead in terms of logical qubits. The choice of the orbital basis significantly affects circuit depth, with localised orbitals yielding lowest…
Quantum computers can efficiently simulate many-body systems. As a widely used Hamiltonian simulation tool, the Trotter-Suzuki scheme splits the evolution into the number of Trotter steps $N$ and approximates the evolution of each step by a…
Efficiently simulating many-body quantum systems with Coulomb interactions is a fundamental question in quantum physics, quantum chemistry, and quantum computing, yet it presents unique challenges: the Hamiltonian is an unbounded operator…
Classical simulations of time-dependent quantum systems are widely used in quantum control research. In particular, these simulations are commonly used to host iterative optimal control algorithms. This is convenient for algorithms that are…
Trotter product formulas constitute a cornerstone quantum Hamiltonian simulation technique. However, the efficient implementation of Hamiltonian evolution of nested commutators remains an under explored area. In this work, we construct…
Quantum phase estimation requires simulating the evolution of the Hamiltonian, for which product formulas are attractive due to their smaller qubit cost and ease of implementation. However, the estimation of the error incurred by product…
Fault-tolerant quantum computing is a promising tool for simulating molecules and materials, but frequently-considered applications require substantial resources, and the gap between hardware capabilities and requirements remains…
We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from…
The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum…
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…
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized…
Computing the ground-state properties of quantum many-body systems is a promising application of near-term quantum hardware with a potential impact in many fields. The conventional algorithm quantum phase estimation uses deep circuits and…
We propose a hybrid approach to simulate quantum many body dynamics by combining Trotter based quantum algorithm with classical dynamic mode decomposition. The interest often lies in estimating observables rather than explicitly obtaining…
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…