A Comparison of the Bravyi–Kitaev and Jordan–Wigner Transformations for the Quantum Simulation of Quantum Chemistry

Andrew Tranter; Peter J. Love; Florian Mintert; Peter V. Coveney

doi:10.1021/acs.jctc.8b00450

A Comparison of the Bravyi–Kitaev and Jordan–Wigner Transformations for the Quantum Simulation of Quantum Chemistry

Journal of Chemical Theory and Computation ◽

10.1021/acs.jctc.8b00450 ◽

2018 ◽

Vol 14 (11) ◽

pp. 5617-5630 ◽

Cited By ~ 11

Author(s):

Andrew Tranter ◽

Peter J. Love ◽

Florian Mintert ◽

Peter V. Coveney

Keyword(s):

Quantum Chemistry ◽

Quantum Simulation

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Experimental study of quantum simulation for quantum chemistry with a nuclear magnetic resonance simulator

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2011.0360 ◽

2012 ◽

Vol 370 (1976) ◽

pp. 4734-4747 ◽

Cited By ~ 1

Author(s):

Dawei Lu ◽

Nanyang Xu ◽

Boruo Xu ◽

Zhaokai Li ◽

Hongwei Chen ◽

...

Keyword(s):

Nuclear Magnetic Resonance ◽

Magnetic Resonance ◽

Quantum Chemistry ◽

Quantum Simulation ◽

Isomerization Reaction ◽

Quantum Computers ◽

One Dimensional ◽

Time Quantum ◽

Near Future ◽

Nuclear Magnetic

Quantum computers have been proved to be able to mimic quantum systems efficiently in polynomial time. Quantum chemistry problems, such as static molecular energy calculations and dynamical chemical reaction simulations, become very intractable on classical computers with scaling up of the system. Therefore, quantum simulation is a feasible and effective approach to tackle quantum chemistry problems. Proof-of-principle experiments have been implemented on the calculation of the hydrogen molecular energies and one-dimensional chemical isomerization reaction dynamics using nuclear magnetic resonance systems. We conclude that quantum simulation will surpass classical computers for quantum chemistry in the near future.

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Back to The Future: A Roadmap for Quantum Simulation From Vintage Quantum Chemistry

Advances in Chemical Physics - Quantum Information and Computation for Chemistry ◽

10.1002/9781118742631.ch02 ◽

2014 ◽

pp. 39-66 ◽

Cited By ~ 2

Author(s):

Peter J. Love

Keyword(s):

Quantum Chemistry ◽

Quantum Simulation ◽

The Future

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Improved Hamiltonian simulation via a truncated Taylor series and corrections

Quantum Information and Computation ◽

10.26421/qic17.7-8-5 ◽

2017 ◽

Vol 17 (7&8) ◽

pp. 623-635

Author(s):

Leonardo Novo ◽

Dominic Berry

Keyword(s):

Quantum Chemistry ◽

Taylor Series ◽

Evolution Operator ◽

Quantum Algorithm ◽

Simulation Method ◽

Quantum Simulation ◽

Wide Range ◽

Simulation Based ◽

Extra Step ◽

Hamiltonian Simulation

We describe an improved version of the quantum algorithm for Hamiltonian simulation based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an operator that corrects the weightings of the Taylor series. This way, the desired accuracy is achieved with an improvement in the overall complexity of the algorithm. This quantum simulation method is applicable to a wide range of Hamiltonians of interest, including to quantum chemistry problems.

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Quantum simulation of quantum field theories as quantum chemistry

Journal of High Energy Physics ◽

10.1007/jhep12(2020)011 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Junyu Liu ◽

Yuan Xin

Keyword(s):

Field Theory ◽

Quantum Chemistry ◽

Nuclear Physics ◽

Information Science ◽

Quantum Algorithms ◽

Quantum Simulation ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Lanczos Algorithm

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.

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