Quantum Algorithms for Quantum Field Theories

By S. Jordan, Keith S. M. Lee, John Preskill. Science, 2011

561 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3dc2ed25682ef3d69f12e0d8e55b18954ab49745

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Citations in the corpus

Quantum computing and the entanglement frontier (2012, background): “35 Even in the case of quantum gravity, evolution may be governed by a local Hamiltonian, and therefore admit eﬃcient simulation by a quantum computer.”
Circuit complexity for free fermions (2018, methodology): “tion in the present paper but our result for a two-dimensional theory would be of order V, e.g., see explicit calculations for d= 2 in [37]. The latter is dramatically smaller than the bound found by [65] and hence it would be interesting to investigate if the present construction based on Nielsen’s”
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer (2016, background): “Our study should be understood as a first step in the effort to simulate increasingly complex dynamics, including quantum simulations of lattice gauge theories [5], that cannot be tackled by classical numerical methods.”
Observation of separated dynamics of charge and spin in the Fermi-Hubbard model (2020, background): “Our work paves the way toward simulating strongly correlated quantum systems [19, 22–32] on existing digital quantum computers.”
Toward the first quantum simulation with quantum speedup (2017, background): “Quantum computers can simulate a wide variety of quantum systems, including fermionic lattice models (9), quantum chemistry (10), and quantum ﬁeld theories (11).”
Quantum Simulation (2013, background): “Another proposal for the DQS of field theories was given in (Jordan et al., 2012).”
Quantum algorithms: an overview (2015, unknown): “Examples include work on increasing the accuracy of quantum simulation while retaining a fast runtime [14]; optimising the algorithm for particular applications such as quantum chemistry [48]; and exploring applications to new areas such as quantum (cid:12)eld theory [53].”