Quantum simulation by qubitization without Toffoli gates

TL;DR

This paper introduces a novel qubitization method for quantum simulation that eliminates the need for Toffoli gates by encoding the Hamiltonian into qubits with logarithmic depth, reducing resource requirements.

Contribution

It presents a new decomposition of qubitization that encodes the Hamiltonian without Toffoli gates, improving efficiency in quantum simulation.

Findings

Eliminates Toffoli gates in qubitization routines.

Achieves logarithmic depth encoding of Hamiltonian.

Reduces resource and gate requirements for quantum simulation.

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 entirely new decomposition of the entire algorithm: without Toffoli gates, we can encode the Hamiltonian into qubits within logarithmic depth.