The Bravyi-Kitaev transformation for quantum computation of electronic structure
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- 12 December 2012
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 137 (22), 224109
- https://doi.org/10.1063/1.4768229
Abstract
Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here, we develop an alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev [Ann. Phys. 298, 210 (2002); e-print arXiv:quant-ph/0003137v2], that reduces the simulation cost to O(log n) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chemical Hamiltonians, and give a detailed example for the simplest possible case of molecular hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equivalent circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for molecular hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure.Keywords
Funding Information
- National Science Foundation (CHE-1037992, PHY-0955518)
This publication has 26 references indexed in Scilit:
- Photonic quantum simulatorsNature Physics, 2012
- Quantum simulations with trapped ionsNature Physics, 2012
- Simulation of electronic structure Hamiltonians using quantum computersMolecular Physics, 2011
- Towards quantum chemistry on a quantum computerNature Chemistry, 2010
- Polynomial-time quantum algorithm for the simulation of chemical dynamicsProceedings of the National Academy of Sciences of the United States of America, 2008
- Fermions without Fermion FieldsPhysical Review Letters, 2005
- Fermionic Quantum ComputationAnnals of Physics, 2002
- Simulating physical phenomena by quantum networksPhysical Review A, 2002
- Quantum algorithms for fermionic simulationsPhysical Review A, 2001
- ber das Paulische quivalenzverbotThe European Physical Journal A, 1928