• DOI:10.1126/science.1217069
• Corpus ID: 6838713

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}
}

• S. Jordan, Keith S. M. Lee, J. Preskill
• Published 15 November 2011
• Physics
• Science

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 efficient simulation of a particular kind of QFT (with quartic interactions) and estimate the error caused by discretization. Even for the most difficult case of strong interactions, the run time of the algorithm was polynomial (rather than exponential) in parameters such as the number of particles, their energy, and the prescribed precision, making it much more efficient than the best classical algorithms. A quantum computer may be able to efficiently simulate theories used to describe particle scattering in accelerators. Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (ϕ4 theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.