Realization of a classical counterpart of a scalable design for adiabatic quantum computation

Abstract

We implement a classical counterpart of a scalable design for adiabatic quantum computation.The key element of this design is a coupler providing controllable coupling between two bistable elements (in our case superconducting rings with a single Josephson junction playing the role of a classical counterpart of superconducting flux qubits). The coupler is also a superconducting ring with a single Josephson junction that operates in the nonhysteretic mode with a screening parameter of about 0.9. The flux-coupling between two bistable rings can be controlled by changing the magnetic flux through the coupler. Since the coupling amplitude is proportional to the derivative of the coupler's current-flux relation, the coupling can be tuned from ferromagnetic to anti-ferromagnetic. In between the coupling can also be switched off. PACS numbers: 85.25.DqThe magnetic properties of a single-junction interferometer (superconducting loop with one Josephson junction) depend on its normalized critical current β = 2πLI C /Φ 0 only. Here L is the loop inductance, I C the critical current of the junction and Φ 0 is the flux quantum. If β > 1 such an interferometer exhibits a double degenerated energy state if an external flux equal to half a flux quantum is applied (degeneracy point) 1 . Close to the degeneracy point, the single junction ring is a bistable element with two magnetic moments corresponding to the superconducting screening currents flowing clockwise and counterclockwise. These two states can be described in spin formalism by making use of Pauli matrices. In other words, a system of magnetically coupled interferometers is a realization of a two-dimensional Ising spin system. When the coupling between spins is randomly distributed the system represents a spin glass. The problem of finding the ground state of such a system is a nonpolynomial one, i.e., the amount of calculation resources needed grows exponentially with the number of elements. Mathematically this task is equivalent to solving the socalled MAXCUT problem. 2 Recently, the implementation of an adiabatic quantum algorithm 3 by making use of superconducting flux qubits has been proposed. 4,5 Schematically, the implementation is the same as for the 2D Ising model described above but instead of classical bits quantum bits (qubits) are used. It has been shown that such a quantum system could solve the problem discussed above in polynomial time. In this letter we present the realization of a scalable classical design implementing the 2D Ising model with a coupling which can be tuned from antiferromagnetic, through zero, to ferromagnetic.Theoretically several schemes of tunable coupling were proposed 6,7 and also some implemented. 8,9 In the design presented here we use the approach proposed by Maassen van den Brink et al. 10 Here a coupler, realized as a single-junction interferometer with β CO = 2πL CO I C /Φ 0 < 1, provides tunable coupling between two bistable elements. The coupling amplitude J can be varied by changing the magnetic flux through the coupler. Th...

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