Quantum computation of scattering in scalar quantum field theories

  title={Quantum computation of scattering in scalar quantum field theories},
  author={Stephen P. Jordan and Keith S. M. Lee and John Preskill},
  journal={Quantum Inf. Comput.},
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to… 

Figures and Tables from this paper

Quantum Algorithms for Fermionic Quantum Field Theories
Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu
A pr 2 01 4 Quantum Algorithms for Fermionic Quantum Field Theories
Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive GrossNeveu
Systematically localizable operators for quantum simulations of quantum field theories
Correlations and measures of entanglement in ground state wavefunctions of relativistic quantum field theories are spatially localized over length scales set by the mass of the lightest particle. We
Digital quantum simulation of hadronization in Yang–Mills theory
A quantum algorithm of SU(N) Yang-Mills theory is formulated in terms of quantum circuits. It can nonperturbatively calculate the Dyson series and scattering amplitudes with polynomial complexity.
Sign Problems in Quantum Field Theory: Classical and Quantum Approaches
Monte Carlo calculations in the framework of lattice field theory provide non-perturbative access to the equilibrium physics of quantum fields. When applied to certain fermionic systems, or to the
Fixed-point quantum circuits for quantum field theories
Renormalization group ideas and effective operators are used to efficiently determine localized unitaries for preparing the ground states of non-interacting scalar field theories on digital quantum
Deeply inelastic scattering structure functions on a hybrid quantum computer
We outline a strategy to compute deeply inelastic scattering structure functions using a hybrid quantum computer. Our approach takes advantage of the representation of the fermion determinant in the
Calculation of Scattering Amplitudes in 4 Theory Using Quantum Computation
In this paper I will go over a method to calculate scattering amplitudes in scalar 4 theory using quantum circuits. I will rst go over formulas relevant to lattice 4 theory, then I will discuss the
3+1 Dimension Schwinger Pair Production with Quantum Computers
Real-time quantum simulation of quantum field theory in (3+1)D requires large quantum computing resources. With a few-qubit quantum computer, we develop a novel algorithm and experimentally study the
Quantum Computation of Scattering Amplitudes in Scalar Quantum Electrodynamics
The algorithm is based on continuous-variable quantum computing architecture resulting in expo- nential speedup over classical methods and derives a simple form of the Hamiltonian including interactions, and a straightforward implementation of the constraint due to gauge invariance.


Quantum Algorithms for Quantum Field Theories
A quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions in spacetime of four and fewer dimensions is developed and achieves exponential speedup over the fastest known classical algorithm.
Cold atom simulation of interacting relativistic quantum field theories.
It is demonstrated that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems, presenting an alternative to lattice gauge theory simulations.
Simulation of Topological Field Theories¶by Quantum Computers
Abstract: Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a
Quantum simulation of interacting fermion lattice models in trapped ions.
We propose a method of simulating efficiently many-body interacting fermion lattice models in trapped ions, including highly nonlinear interactions in arbitrary spatial dimensions and for arbitrarily
Quantum simulation of quantum field theories in trapped ions.
This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Dirac equation for cold atoms in artificial curved spacetimes
We argue that the Fermi–Hubbard Hamiltonian describing the physics of ultracold atoms on optical lattices in the presence of artificial non-Abelian gauge fields is exactly equivalent to the gauge
Adiabatic quantum computation is equivalent to standard quantum computation
The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown, so this result implies that the adiABatic computation model and the standard quantum circuit model are polynomially equivalent.
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
A new proof of the existence and nontriviality of the continuum ϕ24 and ϕ34 quantum field theories
We use Schwinger-Dyson equations combined with rigorous “perturbation-theoretic” correlation inequalities to give a new and extremely simple proof of the existence and nontriviality of the
Confinement and lattice quantum-electrodynamic electric flux tubes simulated with ultracold atoms.
A method for simulating (2+1)D compact lattice quantum-electrodynamics, using ultracold atoms in optical lattices, and shows that in the strong coupling limit this gives rise to "electric flux tubes" and to confinement.