Quantum Algorithms for Quantum Field Theories

  title={Quantum Algorithms for Quantum Field Theories},
  author={Stephen P. Jordan and Keith S. M. Lee and John Preskill},
  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… 
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Discretizing quantum field theories for quantum simulation
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Speeding Up Quantum Field Theories
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
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
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
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Scalar quantum field theories as a benchmark for near-term quantum computers
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Simulating quantum field theory with a quantum computer
  • J. Preskill
  • Physics
    Proceedings 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.
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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  • Christof Zalka
  • Physics, Computer Science
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1998
It is shown that the time evolution of the wave function of a quantum–mechanical many–particle system can be simulated precisely and efficiently on a quantum computer, and that ultimately the simulation of quantum field theory might be possible on large quantum computers.
Simulating lattice gauge theories on a quantum computer (熱場の量子論とその応用)
We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation
An open-system quantum simulator with trapped ions
This work combines multi-qubit gates with optical pumping to implement coherent operations and dissipative processes and illustrates the ability to engineer the open-system dynamics through the dissipative preparation of entangled states, the simulation of coherent many-body spin interactions, and the quantum non-demolition measurement of multi- qubit observables.
Quantum simulations with cold trapped ions
The control of internal and motional quantum degrees of freedom of laser-cooled trapped ions has been subject to intense theoretical and experimental research for about three decades. In the realm of
Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation
We discuss real-space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We construct the Hamiltonian formalism which is appropriate for their solid-state physics
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In a recent experiment, Barreiro et al (2011 Nature 470 486) demonstrated the fundamental building blocks of an open-system quantum simulator with trapped ions. Using up to five ions, dynamics were
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Fast algorithms for simulating many body Fermi systems on a universal quantum computer are provided and a simulation of the Hubbard model is discussed in detail.
An optical-lattice-based quantum simulator for relativistic field theories and topological insulators
We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent