Disorder-induced entropic potential in a flux qubit quantum annealer

In this manuscript we explore an experimentally observed statistical phenomenon by which domain walls on an Ising chain programmed onto a flux qubit quantum annealer tend toward a non-uniform distribution. We find that this distribution can be theoretically well described by a combination of control errors and thermal effects. Interestingly, the effect that produces this distribution is purely entropic, as it appears in cases where the average energy of all domain-wall locations is equal by definition. As well as being a counterintuitive statistical effect, we also show that our method can be applied to measure the strength of the noise on the device. The noise measured in this way is smaller than what is seen by other methods suggesting that the freeze time of a chain of coupled qubits on the device may be different than for isolated qubits with all couplings turned off, despite the fact that a qubit adjacent to a domain wall should effectively experience no coupling due to cancellation of the couplings one either side.