Speed and entropy of an interacting continuous time quantum walk

Abstract

We present some dynamic and entropic considerations about the evolution of a continuous time quantum walk implementing the clock of an autonomous machine. On a simple model, we study in quite explicit terms the Lindblad evolution of the clocked subsystem, relating the evolution of its entropy to the spreading of the wave packet of the clock. We explore possible ways of reducing the generation of entropy in the clocked subsystem, as it amounts to a deficit in the probability of finding the target state of the computation. We are thus led to examine the benefits of abandoning some classical prejudice about how a clocking mechanism should operate.

Fast universal quantum computation with railroad-switch local Hamiltonians

“…leaving the work qubit q 2 untouched. Summing all the terms in (43)-(50) gives us the 2-local qubit-qutrit railroad switch Hamiltonian H (t) 23 . Similarly to what we did in Section III A, let us examine where the transitions in this Hamiltonian take the state |ψ t−1 = a |0 q1 |α q2,... where a |ϕ 0... + b |ϕ 1... is a general state of the work register and the active site of clock register is at the qubit c t−1 .…”

“…Omitting the connection to the region outside the gadget, this 12-dimensional subspace H (t) g23 is invariant under the transitions in H (t) 23 . It is convenient to analyze the dynamics of H (t) 23 using the basis just given. In this basis, the Hamiltonian within one gadget has a very simple form -the adjacency matrix of a line |ψ Figure 5.…”

“…|ϕ0... +b |1 q1 |β q2,... |ϕ1...⊗ |c t−1 c(51) The geometry of connections in H (t)23 restricted to the subspace H (t) g23 (within one gadget). The necklace graph depicting the connections in H23 in a particular basis.…”

An introduction to quantum annealing

“…We took an initial configuration having a single spin up and all the others down. The spin up plays the role of a quantum walker and, by a suitable choice of the initial conditions [17], it behaves as an excitation moving ballistically along the chain as in Figure 4. We introduce a simple potential/cost…”

Quantum annealing and the Schrödinger-Langevin-Kostin equation

“…, s} equipped with the set of edges E = {{i, j} : (i, j) ∈ Λ s × Λ s ∧ |i − j| = 1} . According to the general approach outlined in [4], this amounts to a search of the minimum of the function V defined on Λ s by means of an interacting continuous time quantum walk [21] on Λ s governed by a Hamiltonian of the form…”