Quantum simulation of quantum field theories as quantum chemistry
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Springer
Received: August 14, 2020 Accepted: October 19, 2020 Published: December 2, 2020
Quantum simulation of quantum field theories as quantum chemistry
a
Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, U.S.A. b Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, U.S.A. c Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, U.S.A. d Department of Physics, Yale University, New Haven, CT 06520, U.S.A.
E-mail: [email protected], [email protected] 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 regularization. We discuss possible speedups for performing those computations using quantum devices, with the help of near-term and future quantum algorithms. We show that this construction is very similar to quantum simulation problems appearing in quantum chemistry (which are widely investigated in quantum information science), and the renormalization group theory provides a field theory interpretation of conformal truncation simulation. Taking two-dimensional Quantum Chromodynamics (QCD) as an example, we give various explicit calculations of variational and digital quantum simulations in the level of theories, classical trials, or quantum simulators from IBM, including adiabatic state preparation, variational quantum eigensolver, imaginary time evolution, and quantum Lanczos algorithm. Our work shows that quantum computation could not only help us understand fundamental physics in the lattice approximation, but also simulate quantum field theory methods directly, which are widely used in particle and nuclear physics, sharpening the statement of the quantum Church-Turing Thesis. Keywords: Conformal Field Theory, Field Theories in Lower Dimensions, Lattice Quantum Field Theory ArXiv ePrint: 2004.13234
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP12(2020)011
JHEP12(2020)011
Junyu Liua,b and Yuan Xinc,d
Contents 1
2 Quantum field theory without lattice 2.1 Introduction to conformal truncation 2.2 Conformal truncation and quantum simulation 2.2.1 Quantum field theory without lattice 2.2.2 Digital quantum simulation and RG flows 2.2.3 Variational quantum simulation and RG flows 2.2.4 Features of conformal truncation problems and a natural variational ansatz
5 5 7 7 8 8 9
3 Digital quantum simulation 3.1 Adiabatic state preparation (ASP) 3.2 Oracle-based algorithms 3.3 Analysis in conformal truncation
10 10 11 14
4 Target: 2D QCD 4.1 Integrate out the gauge field 4.2 The UV CFT and the conformal basis 4.3 Compute the matrix element 4.4 Large Nc limit
15 15 17 18 19
5 Variational quantum simulation 5.1 Variational quantum eigensolver (VQE) 5.2 Encoding 5.3 Trial numerics 5.4 IBM Quantum Experience 5.4.1 Without noise 5.4.2 Noisy quantum circuit 5.4.3 Error mitigation
20 20 21 22 23 23 24 25
6 Othe
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