# Quantum Algorithms for Quantum Field Theories

@article{Jordan2012QuantumAF, title={Quantum Algorithms for Quantum Field Theories}, author={Stephen P. Jordan and Keith S. M. Lee and John Preskill}, journal={Science}, year={2012}, volume={336}, pages={1130 - 1133} }

Quantum Leap? Quantum computers are expected to be able to solve some of the most difficult problems in mathematics and physics. It is not known, however, whether quantum field theories (QFTs) can be simulated efficiently with a quantum computer. QFTs are used in particle and condensed matter physics and have an infinite number of degrees of freedom; discretization is necessary to simulate them digitally. Jordan et al. (p. 1130; see the Perspective by Hauke et al.) present an algorithm for the…

## 311 Citations

BQP-completeness of Scattering in Scalar Quantum Field Theory

- Physics
- 2014

Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and…

Discretizing quantum field theories for quantum simulation

- Physics
- 2020

To date, all proposed quantum algorithms for simulating quantum field theory (QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone. Two overlooked issues are how large we can…

Faster quantum algorithm to simulate fermionic quantum field theory

- PhysicsPhysical Review A
- 2018

In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states…

Speeding Up Quantum Field Theories

- PhysicsScience
- 2012

On page 1130 of this issue, Jordan et al. (1) report on an efficient quantum algorithm that can solve the equations of quantum field theory (QFT), which reconcile quantum mechanics with special relativity and are crucial for studies of the interactions of fundamental particles.

Quantum simulation of quantum field theories as quantum chemistry

- PhysicsJournal of High Energy Physics
- 2020

Abstract
Conformal truncation is a powerful numerical method for solving generic strongly-coupled quantum field theories based on purely field-theoretic technics without introducing lattice…

Quantum simulation of quantum field theory using continuous variables

- Physics, Computer Science
- 2015

A new algorithm is presented which gives an exponential speedup over the best known classical methods for efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is known to be hard using a classical computer.

Quantum Simulation

- Physics
- 2013

Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum…

Scalar quantum field theories as a benchmark for near-term quantum computers

- Physics, Computer SciencePhysical Review A
- 2019

This work outlines and implements a hybrid algorithm to calculate the lowest energy levels of the paradigmatic 1+1--dimensional interacting scalar QFT, and shows that the accuracy of mass-renormalization calculations represents a useful metric with which near-term hardware may be benchmarked.

Simulating quantum field theory with a quantum computer

- PhysicsProceedings of The 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)
- 2019

Today's research can hasten the arrival of a new era in which quantum simulation fuels rapid progress in fundamental physics, and though the physics payoff may still be far away, it's worthwhile to get started now.

COMPLEXITY OF QUANTUM FIELD THEORIES

- Computer Science
- 2012

The recently-devised algorithm of Jordan, Lee, and Preskill is presented which gives an efficient simulation of φ4 theory in d = 1, 2, and 3 spatial dimensions with a non-relativistic quantum computer, allowing for the computation of scattering probabilities.

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