Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
Abstract
As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the fermionic swap network, we can simulate a Trotter step of the electronic structure Hamiltonian in exactly N depth and with N^2/2 two-qubit entangling gates, and prepare arbitrary Slater determinants in at most N/2 depth, all assuming only a minimal, linearly connected architecture. We conjecture that no explicit Trotter step of the electronic structure Hamiltonian is possible with fewer entangling gates, even with arbitrary connectivities. These results represent significant practical improvements on the cost of most Trotter-based algorithms for both variational and phase-estimation-based simulation of quantum chemistry.
Additional Information
© 2018 American Physical Society. Received 16 November 2017; revised manuscript received 20 January 2018; published 13 March 2018. We thank Zhang Jiang, Sergio Boixo, Eddie Farhi, James McClain, Kevin Sung, and Guang Hao Low for helpful discussions. I. D. K. acknowledges partial support from the National Sciences and Engineering Research Council of Canada. A. A.-G. acknowledges the Army Research Office under Grant No. W911NF-15-1-0256. We thank contributors to the open source library OpenFermion [51] which was used to verify some equations of this work.Attached Files
Published - PhysRevLett.120.110501.pdf
Submitted - 1711.04789.pdf
Supplemental Material - supp.pdf
Files
Additional details
- Eprint ID
- 83340
- Resolver ID
- CaltechAUTHORS:20171120-105229610
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Army Research Office (ARO)
- W911NF-15-1-0256
- Created
-
2017-11-20Created from EPrint's datestamp field
- Updated
-
2021-11-15Created from EPrint's last_modified field