Related papers: Symmetric Trotterization in digital quantum simula…
Simulating nonequilibirum dynamics of a quantum many-body system is one of the promising applications of quantum computing. We simulate the time evolution of one-dimensional ${\bf Z}_2$ lattice gauge theory on IBM's superconducting…
Compiling time-evolution operators of the form $U(t)=e^{-iHt}$ into hardware-native gate sequences is a central bottleneck for digital quantum simulation on noisy intermediate-scale quantum (NISQ) devices. Generic transpilation treats…
Toward scalable quantum computing, the control of quantum systems needs to be robust against both coherent errors induced by parametric uncertainties and incoherent errors induced by environmental decoherence. This poses significant…
We estimate the resource requirements for the quantum simulation of the ground state energy of the one dimensional quantum transverse Ising model (TIM), based on the surface code implementation of a fault tolerant quantum computer. The…
We present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system…
Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin-$\frac{1}{2}$ systems. Here, we instead consider…
Programmable quantum simulators such as superconducting quantum processors and ultracold atomic lattices represent rapidly developing emergent technology that may one day qualitatively outperform existing classical computers. Yet, apart…
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…
In analog and digital simulations of practically relevant quantum systems, the target dynamics can only be implemented approximately. The Trotter product formula is the most common approximation scheme as it is a generic method which allows…
Suzuki-Trotter decomposition is a well-known technique used to calculate the partition function of quantum spin systems, in which the imaginary-time dependence of the partition function occurs inevitably. Since it is very difficult to…
Product formulas for Trotter Suzuki simulation remain a practical route to Hamiltonian evolution on noisy intermediate scale quantum (NISQ) hardware, yet their accuracy hinges on three coupled choices: term grouping, product formula order,…
Quantum computers offer the potential to efficiently simulate the dynamics of quantum systems, a task whose difficulty scales exponentially with system size on classical devices. To assess the potential for near-term quantum computers to…
In this paper we provide a framework for combining multiple quantum simulation methods, such as Trotter-Suzuki formulas and QDrift into a single Composite channel that builds upon older coalescing ideas for reducing gate counts. The central…
Simulation of quantum many-body systems is a promising application of quantum computers. However, implementing the time-evolution operator as a quantum circuit efficiently on near-term devices with limited resources is challenging. Standard…
We discuss real time evolution for the quantum Ising model in one spatial dimension with $N_s$ sites. In the limit where the nearest neighbor interactions $J$ in the spatial directions are small, there is a simple physical picture where…
The quantum imaginary time evolution is a powerful algorithm for preparing the ground and thermal states on near-term quantum devices. However, algorithmic errors induced by Trotterization and local approximation severely hinder its…
Simulation of the Hubbard model is a leading candidate for the first useful applications of a fault-tolerant quantum computer. A recent study of quantum algorithms for early simulations of the Hubbard model [Kivlichan \textit{et al.}…
Using Suzuki-Trotter decompositions of exponential operators we describe new algorithms for the numerical integration of the equations of motion for classical spin systems. These techniques conserve spin length exactly and, in special…
The kicked top is one of the paradigmatic models in the study of quantum chaos~[F.~Haake et al., \emph{Quantum Signatures of Chaos (Springer Series in Synergetics vol 54)} (2018)]. Recently it has been shown that the onset of quantum chaos…
Simulated Quantum Annealing (SQA), that is emulating a Quantum Annealing (QA) dynamics on a classical computer by a Quantum Monte Carlo whose parameters are changed during the simulation, is a well established computational strategy to cope…