The Bravyi-Kitaev transformation for quantum computation of electronic structure.

By J. Seeley, Martin J. Richard, Peter J. Love. Journal of Chemical Physics, 2012

635 citations recorded by the source corpus.

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 H(2) 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/0f107c76b9cc834cf0c10eaea0e766c47fb664a1

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Citations in the corpus

Digitized adiabatic quantum computing with a superconducting circuit (2015, background): “In addition, long-range multibody interactions can be assembled to aid in quantum tunneling [20] or to encode the non-local terms required for fermionic simulations [21, 22], which is otherwise hampered by limited connectivity.”
Scalable Quantum Simulation of Molecular Energies (2015, methodology): “Until this work, important aspects of scalable chemistry simulation such as the Jordan-Wigner transformation [40] or the Bravyi-Kitaev transformation [41,42] had never been used to represent a molecule in an experiment; however, prior experiments such as Ref.”
Elucidating reaction mechanisms on quantum computers (2016, methodology): “[60] Jacob T Seeley, Martin J Richard, and Peter J Love, “The bravyi-kitaev transformation for quantum computation of electronic structure,” The Journal of chemical physics 137, 224109 (2012).”
Low-Depth Quantum Simulation of Materials (2017, methodology): “While past work has focused entirely on describing the FFFT under the Jordan-Wigner transformation [71,72], we generalize the approach to arbitrary mappings including Bravyi-Kitaev [24,25,46] and other modern approaches [26–28].”
Quantum algorithms to simulate many-body physics of correlated fermions. (2017, methodology): “The fermionic operators satisfying the anticommutation relations can be mapped to qubit operators using the JWT [25, 26], the Bravyi-Kitaev transformation (BKT) [40, 41], or the Ball-Verstraete-Cirac transformation (BVCT) [42–44].”
Tapering off qubits to simulate fermionic Hamiltonians (2017, methodology): “In the next two sections we discuss encodings based on the Jordan-Wigner transformation [10] and its recent generalizations [11, 13].”
Adiabatic Quantum Computing (2016, background): “…molecular energies can be formulated in terms of a second-quantized fermionic Hamiltonian that is mapped, via a generalized JordanWigner transformation (Bravyi and Kitaev, 2002; P. Jordan and E. Wigner, 1928), to a non-stoquastic qubit Hamiltonian (Aspuru-Guzik et al., 2005; Seeley et al., 2012).”