Fast universal quantum computation with railroad-switch local Hamiltonians

Abstract

We present two universal models of quantum computation with a time-independent, frustrationfree Hamiltonian. The first construction uses 3-local (qubit) projectors, and the second one requires only 2-local qubit-qutrit projectors. We build on Feynman's Hamiltonian computer idea [7] and use a railroad-switch type clock register. The resources required to simulate a quantum circuit with L gates in this model are O(L) small-dimensional quantum systems (qubits or qutrits), a timeindependent Hamiltonian composed of O(L) local, constant norm, projector terms, the possibility to prepare computational basis product states, a running time O(L log 2 L), and the possibility to measure a few qubits in the computational basis. Our models also give a simplified proof of the universality of 3-local Adiabatic Quantum Computation.

Noise-assisted quantum transport and computation

“…In order to restore the universality of the model Feynman introduced the Switch circuit [7], that implements the selection statement. For a recent review, see [19].…”

Time-dependent density-functional theory for open spin chains

“…In our choice of numerical examples, we have concentrated on themes motivated by our previous experience with Feynman's model of a quantum computer [13,17,18]. For instance, the numerical example of Fig.…”

Quantum 3-SAT Is QMA1-Complete

“…Our circuit-to-Hamiltonian mapping, presented in Sections IV and V exploits this feature (it is partly inspired by the railroad switch idea from [19]). Finally, we also exhibit 1-local (single-qubit) projectors C ≥i and C ≤i (6) for i = 1, .…”