Hamiltonian quantum computation

Hamiltonian quantum computation is a form of quantum computing.

Unlike methods of quantum computation such as the adiabatic, measurement-based and circuit model where eternal control is used to apply operations on a register of qubits, Hamiltonian quantum computers operate without external control.

[1] [2] [3] Hamiltonian quantum computation was the pioneering model of quantum computation, first proposed by Paul Benioff in 1980.

Benioff's motivation for building a quantum mechanical model of a computer was to have a quantum mechanical description of artificial intelligence and to create a computer that would dissipate the least amount of energy allowable by the laws of physics.

[1] However, his model was not time-independent and local.

[4] Richard Feynman, independent of Benioff, also wanted to provide a description of a computer based on the laws of quantum physics.

He solved the problem of a time-independent and local Hamiltonian by proposing a continuous-time quantum walk that could perform universal quantum computation.

[2] Superconducting qubits [5], Ultracold atoms and non-linear photonics[6] have been proposed as potential experimental implementations of Hamiltonian quantum computers.

Given a list of quantum gates described as unitaries

, define a hamiltonian

Evolving this Hamiltonian on a state

ϕ

ψ

composed of a clock register (

qubits and a data register (

ψ

ϕ

ϕ

, the state of the clock register can be

When that happens, the state of the data register will be

ψ

The computation is complete and

ϕ