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Journal of Applied Physics

Experimental analysis of phase-mode Josephson digital circuits

Kiyotaka Nakajima, H. Sugahara, Akira Fujimaki, Yasuji Sawada

Published Jul 15, 1989• 45 citations
Publisher

Abstract

We present experimental results on elementary phase-mode Josephson circuits whose combinations enable us to construct a total data processing system which is expected to be superior to the ordinary voltage-mode Josephson computer in several respects. In the phase-mode system a device depends for its operation on the existence of many stable states differing from one another by integer multiples of 2π in the phase plane. The total system is considered to be a prototype of quantum computer systems where physical quantum states are employed as logic states of information processing. By using the fabricated elementary circuits composed of SQUIDs and two types of branching points we have experimentally confirmed and, fan-out, fan-in operations, etc. We have also proposed an inhibit circuit, and presented the experimental results on the inhibit circuit.

DOI
10.1063/1.343524

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We present experimental results on elementary phase-mode Josephson circuits whose combinations enable us to construct a total data processing system which is expected to be superior to the ordinary voltage-mode Josephson computer in several respects. In the phase-mode system a device depends for its operation on the existence of many stable states differing from one another by integer multiples of 2π in the phase plane. The total system is considered to be a prototype of quantum computer systems where physical quantum states are employed as logic states of information processing. By using the fabricated elementary circuits composed of SQUIDs and two types of branching points we have experimentally confirmed and, fan-out, fan-in operations, etc. We have also proposed an inhibit circuit, and presented the experimental results on the inhibit circuit.
The transition to Josephson digital circuits with the representation of information in the form of phase jumps of the superconducting order parameter on heterostructures promises a radical increase in the degree of integration while maintaining high speed and energy efficiency. However, it is not yet possible to manufacture reproducible bistable Josephson junctions, which are necessary for the functioning of the previously proposed basic units of the phase logic. To solve this problem, the concept of phase logic based on π junctions is proposed and analyzed within the resistive model of Josephson heterostructures. The potential energy of such junctions has a single minimum, with a difference in the order parameters of the electrodes equal to π. It is demonstrated that the use of π junctions allows one to implement the entire set of logic devices necessary for the operation of digital computing devices based on phase logic.
Quantum computing holds the promise of a novel form of information processing in which data resides in quantum states. By exploiting superpositions and entanglement among these states, quantum logic operations are expected to far surpass conventional digital logic in certain classes of problems. To realize this prospect, we employ superconducting circuits at millikelvin temperatures. The nonlinearity of a Josephson tunnel junction enables a two-level quantum system, or qubit, with excitation energy in the microwave regime. Key recent advances in such devices are the demonstration of robust and simple multi-qubit gates, the integration of superconducting qubits into arrays of four or more, and gate fidelities reaching 99%. [1,2,3]
Quantum information processing systems can be used in a variety of applications. Among proposed realizations of quantum bits nano-electronic circuits appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. In one limit, two logic states of the quantum bit differ by a Cooper pair charge, 2e, on a superconducting island. In the other limit different magnetic fluxes penetrate a superconducting loop in two states. Single-qubit and two-qubit logic operations can be performed by means of voltage or current pulses. Weak coupling to the environment allows a series of these elementary steps before the phase coherence is lost. To read out the result of the computation a quantum measurement is needed. For charge qubits this can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. Monitoring the current in the transistor one can extract the information about the state of the qubit. We discuss recent experiments and present a suitable set of circuit parameters available with the present-day technology.
One of the most important features of the quantum computing circuits that distinguishes them from the traditional computational models is their full, physical and logical, reversibility at all stages of the calculations. This makes the large-scale architecture of potential quantum and classical reversible computers quite similar. The goal of this work is to analyze this similarity in the case of reversible superconducting logic circuits based on the recently suggested elementary gate, the nSQUID. Specifically, we present the results of numerical simulations and some limited measurements of a reversible 8-bit circular shift register fabricated at HYPRES, Inc., and working in the classical mode. The measured energy dissipation per bit operation per nSQUID is still about 20 times higher than the thermodynamic reversibility threshold of kBTIn 2 at T ap 4 K. We also discuss qualitatively operation of the reversible circuits of galvan- ically-coupled nSQUIDs in the quantum mode which provides the basis for implementation of "flying" superconducting qubits. Such qubits have several attractive features for Josephson-junction quantum logic devices beyond the single- or two-qubit circuits.
We have investigated the possibility of the phase mode operation, i.e. the mode to transfer the fluxoid, not to transfer the voltage pulse, of Josephson switching system by fabricating a resistively coupled D.C. SQUID's array and 4J-loop which are expected to be advantageous in miniaturization by using its large kinetic momentum effect. The threshold characteristics of these superconducting loops and its LIcdependence agreed with the theoretical predictions. The phase mode logic actions were verified to operate really in a resistively coupled D.C.SQUID's and a coupled D.C. SQUID with a 4J-loop. A computer simulation showed that a resistively coupled SQUID's array acts both on phase mode and voltage mode by changing the circuit parameters, but that the two modes are clearly separated in a parameter space. Finally we have shown a total system configuration of the phase mode operation. For the power loss and the information processing speed, the phase mode was verified to have an advantage over the ordinary voltage mode by two orders of magnitude.
Among the potential physical implementations of quantum bits (qubits) solid state devices appear most promising for large scale applications and integration in electronic circuits. Devices based on low-capacitance Josephson junctions exploit the coherence of the superconducting state, combined with the possibility to control individual charges by Coulomb blockade effects. The logical states in these systems differ by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. If, in addition, the strength of the Josephson coupling is controlled (e.g. by currents in SQUID loops) the system is ideal for quantum computation. Recent experiments by Nakamura et al. show the feasibility of this approach. In addition to the manipulations of qubits the resulting quantum state has to be read out. This quantum measurement process can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. We investigate the process by analyzing the time-evolution of the density matrix of the coupled system. The measurement process is characterized by three time scales: the dephasing time, which is fast when a dissipative current flows in the SET, a longer ‘measurement time’ needed to read out the signal, and a third, even longer ‘mixing time’, characterizing measurement induced transitions which destroy the information about the initial quantum state. The noise spectrum of the current in the SET displays these time scales and allows their direct observation.