A09.00007. Quantum simulation by qubitization without Toffoli gates

Presented by: Mark Steudtner


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 Hamitlonian in a unary representation can alleviate the need for such gates in one of the qubitization subroutines. Building on that principle, we develop an entirely new decomposition of the entire algorithm: without Toffoli gates, we can encode the Hamiltonian into qubits within logarithmic depth. *MS was supported by the Netherlands Organization for Scientific Research (NWO/OCW) and an ERC Synergy Grant. SW was supported by STW Netherlands, an NWO VIDI Grant and an ERC Starting Grant.


  • Mark Steudtner
  • Stephanie Wehner


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