Estimating exact energies in quantum simulation without Toffoli gates

Physical Review A, vol. 101

Abstract

Qubitization is a modern approach to estimate Hamiltonian eigenvalues without simulating its time evolution. While in this way approximation errors are avoided, its resource and gate requirements are more extensive: qubitization requires additional qubits to store information about the Hamiltonian, and Toffoli gates to probe them throughout the routine. Recently, it was shown that storing the Hamiltonian in a unary representation can alleviate the need for such gates in one of the qubitization subroutines. Building on that principle, we develop an alternative decomposition of the entire algorithm: without Toffoli gates, we can encode the Hamiltonian into qubits within logarithmic depth.

Authors 2

1. Mark Steudtner Aachen Instituut-Lorentz

   Leiden University · QuTech · Delft University of Technology

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

   QuTech, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

2. Stephanie Wehner

   QuTech · Delft University of Technology

   Affiliation as printed

   QuTech, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands