# Improved Hamiltonian simulation via a truncated Taylor series and corrections

@article{Novo2016ImprovedHS, title={Improved Hamiltonian simulation via a truncated Taylor series and corrections}, author={Leonardo Novo and Dominic W. Berry}, journal={Quantum Inf. Comput.}, year={2016}, volume={17}, pages={623-635} }

We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an operator that corrects the weightings of the Taylor series. This way, the desired accuracy is achieved with an improvement in the overall complexity of the algorithm. This quantum simulation method is applicable to a wide range of Hamiltonians of interestâ€¦Â

## 21 Citations

### A generalized circuit for the Hamiltonian dynamics through the truncated series

- PhysicsQuantum Inf. Process.
- 2018

A fixed-quantum circuit design for the simulation of the Hamiltonian dynamics, $${\mathcal {H}}(t)$$H(t), through the truncated Taylor series method described by Berry et al.

### Quantum Algorithm for Linear Differential Equations with Exponentially Improved Dependence on Precision

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This work presents a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients that produces a quantum state that is proportional to the solution at a desired final time using a Taylor series.

### Quantum Algorithm for Linear Differential Equations with Exponentially Improved Dependence on Precision

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This work presents a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients that produces a quantum state that is proportional to the solution at a desired final time using a Taylor series.

### Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries

- PhysicsQuantum
- 2022

It is shown that it is more efficient to apply LCU using a truncation that retains larger magnitude terms as determined by an iterative procedure, and it is found that the adaptive method can typically improve the simulation accuracy by an order of magnitude, for a given circuit depth.

### Hamiltonian Simulation in the Interaction Picture

- Physics
- 2018

We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians byâ€¦

### Low-Depth Quantum Simulation of Materials

- Computer Science
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Simulations of low-density jellium are identified as a promising first setting to explore quantum supremacy in electronic structure and a proposal to simulate the uniform electron gas using a low-depth variational ansatz realizable on near-term quantum devices is proposed.

### J un 2 01 9 Hamiltonian Simulation in the Interaction Picture

- Physics
- 2019

We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians byâ€¦

### A generalized circuit for the Hamiltonian dynamics through the truncated series

- Materials ScienceQuantum Information Processing
- 2018

In this paper, we present a method for Hamiltonian simulation in the context of eigenvalue estimation problems, which improves earlier results dealing with Hamiltonian simulation through theâ€¦

### Quantum computing for fusion energy science applications

- Computer SciencePhysics of Plasmas
- 2023

This work extends previous results on embedding nonlinear systems within linear systems by explicitly deriving the connection between the Koopman evolution operator, the Perronâ€“Frobenius evolutionoperator, and the Koopsmanâ€“von Neumann evolution (KvN) operator.

### Fourier series weight in quantum machine learning

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This work designed a quantum machine learning leveraged on the Hamiltonian encoding that performed the trigonometric interpolation, binary and multiclass classifier, and a quantum signal processing application and proposed a block diagram of determining approximately the Fourier coefficient.

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