publication . Preprint . 2020

Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries

Meister, Richard; Benjamin, Simon C.; Campbell, Earl T.;
Open Access English
  • Published: 22 Jul 2020
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to approximate a Taylor series by truncating after some order. Here we present an adaptation of that method, optimized for Hamiltonians with terms of widely varying magnitude, as is commonly the case in electronic structure calculations. We show that it is more efficient to apply LCU using a truncation that retains larger magnitude terms as determined by an iterative procedure. We obtain bounds on the simulation error for this generalized...
free text keywords: Quantum Physics
Funded by
UKRI| Towards fault-tolerant quantum computing with minimal resources.
  • Funder: UK Research and Innovation (UKRI)
  • Project Code: EP/M024261/1
  • Funding stream: EPSRC
Download from
45 references, page 1 of 3

[4] G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme. Quantum algorithms for fermionic simulations. Physical Review A, 64(2), Jul 2001. doi 10.1103/PhysRevA.64.022319.

[5] A. Aspuru-Guzik. Simulated quantum computation of molecular energies. Science, 309(5741):1704-1707, Sep 2005. doi 10.1126/science.1113479.

[6] D. W. Berry, G. Ahokas, R. Cleve, and B. C. Sanders. Efficient quantum algorithms for simulating sparse Hamiltonians. Communications in Mathematical Physics, 270(2):359-371, Dec 2006. doi 10.1007/s00220-006-0150-x.

[7] H. Wang, S. Kais, A. Aspuru-Guzik, and M. R. Hoffmann. Quantum algorithm for obtaining the energy spectrum of molecular systems. Physical Chemistry Chemical Physics, 10(35):5388, 2008.

doi 10.1039/b804804e.

[8] J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik. Simulation of electronic structure Hamiltonians using quantum computers. Molecular Physics, 109(5):735- 750, 2011. doi 10.1080/00268976.2011.552441.

[9] E. Campbell. Random compiler for fast Hamiltonian simulation. Physical Review Letters, 123(7):070503, Aug 2019. doi 10.1103/physrevlett.123.070503.

[10] A. M. Childs and Y. Su. Nearly optimal lattice simulation by product formulas. Physical Review Letters, 123 (5):050503, Aug 2019. doi 10.1103/physrevlett.123.050503.

[11] A. M. Childs, A. Ostrander, and Y. Su. Faster quantum simulation by randomization. Quantum, 3:182, Sep 2019. doi 10.22331/q-2019-09-02-182. [OpenAIRE]

[12] Y. Ouyang, D. R. White, and E. T. Campbell. Compilation by stochastic Hamiltonian sparsification. Quantum, 4:235, Feb 2020. doi 10.22331/q-2020-02-27-235.

[13] H. F. Trotter. On the product of semi-groups of operators. Proceedings of the American Mathematical Society, 10(4):545-551, 1959. doi 10.2307/2033649.

[14] M. Suzuki. Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems. Communications in Mathematical Physics, 51(2):183- 190, 1976. doi 10.1007/BF01609348.

[15] D. Wecker, B. Bauer, B. K. Clark, M. B. Hastings, and M. Troyer. Gate-count estimates for performing quantum chemistry on small quantum computers. Physical Review A, 90:022305, Aug 2014. doi 10.1103/PhysRevA.90.022305.

[16] R. Babbush, J. McClean, D. Wecker, A. Aspuru-Guzik, and N. Wiebe. Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation. Physical Review A, 91(2), Feb 2015. doi 10.1103/PhysRevA.91.022311.

[17] M. B. Hastings, D. Wecker, B. Bauer, and M. Troyer. Improving quantum algorithms for quantum chemistry, 2014. arxiv 1403.1539.

45 references, page 1 of 3
Any information missing or wrong?Report an Issue