Single flux quantum circuits for
special applications in novel devices

The class of Rapid Single Flux Quantum (RSFQ) logic circuits enables the processing of digital information presented by quantized voltage pulses corresponding to the transfer of single magnetic flux quanta across overdamped Josephson junctions [1]. During the last two decades the RSFQ technology had made significant progress in manufacturing complex circuits, using new superconducting materials, increasing the operation frequency etc. Recently, these circuits are considered as a promising solution for readout and control of the Josephson qubits, i.e. two-level quantum mechanical systems forming the basis for the superconducting quantum computer [2].

Figure 1: Example of an integrated RSFQ-qubit circuit [3]. The RSFQ circuit includes an SFQ-pulse generator (not shown), a Josephson Transmission Line (JTL), and a bistable Toggle Flip-flop (TFF) cell with a Josephson flux qubit of SQUID-in-SQUID configuration (proposed by the group of CNR-Rome [4]. The rectangular output pulses change the flux applied to the small two-junction SQUID and affect the height of the energy barrier in a two-well potential of the qubit.

The facts that both, a single-flux-quantum circuit and a Josephson qubit, are superconducting structures including Josephson junctions and, therefore, can be fabricated in one technological run, and both require low operation temperatures are encouraging to verifying on-chip integrated RSFQ-qubit devices. However, the parameters of traditional RSFQ circuits [5] do not allow straightforward integrating these circuits with Josephson qubits. In particular, typical values of the critical current (about 100 µA) of RSFQ circuits are too large for matching with critical current values of Josephson qubits (0.1-1 µA). Beyond, very high speeds of operation of RSFQ circuits (of the order of 100 GHz) can produce even disturbing effects of the qubit performance causing unwanted excitation of its high-energy states. Therefore, the property of "Rapid" operation is needless, so the circuits in question are eventually the SFQ circuits. Reducing of the critical currents implies a corresponding increase of inductances and, hence, re-designing of the circuit. Moreover, there is an even more important conflict between the concepts of the SFQ and qubit technologies. The SFQ-technology-concept assumes sufficient damping in the Josephson junctions ensuring reliable generation, reproduction and manipulation of the SFQ pulses; such damping is usually realized by means of shunting of the tunnel junctions by low-ohmic metallic resistors. The qubit-technology-concept, however, assumes a minimization of damping in Josephson junctions, because unavoidable thermal/quantum noise related to this damping may cause decoherence of the qubit. To some extent it is possible to minimize this effect by reducing the coupling between the SFQ circuit and the qubit (as, for example, shown in Figure 1, where a superconducting coupling transformer significantly reduces the amplitude of applied pulses). However, if large reduction of the signal is undesirable, an alternative solution must be found. One possible solution is the realization of a frequency-dependent damping in the Josephson junctions of the SFQ circuit [6].

The idea of such damping is based on the fact that the characteristic frequencies of the Josephson qubits (typically up to 15-20 GHz) are appreciably lower than the SFQ circuit frequencies even in the case of implementation of Josephson junctions with rather small critical currents (of the order of 10 µA). Therefore, for correct operation of the SFQ circuit it is sufficient to damp the junctions at frequencies higher than the qubit frequencies. The deficit of damping at the qubit frequencies does not disturb the operation of the SFQ circuit while it should allow to preserve a sufficiently long decoherence time. In practice, the frequency-dependent damping can be realized by various methods, either by the usage of tunnel junctions with sufficiently high density of critical current and rather small value of the energy gap (e.g., Al-junctions [7]), or by the application of non-linear shunting elements (e.g., Superconductor-Insulator-Normal metal junctions [8]), or by the application of linear frequency-dependent circuits (e.g., RC-chains).

Figure 2: (a) Fragment of an SFQ circuit with Josephson junctions having RC-line shunts (instead of traditional R-shunts shown in (b)) ensuring frequency-dependent damping. (c) Josephson junction shunted by an RC-line with open end.

In conclusion, the SFQ circuits under investigation by our group belong to a class of devices for very special applications in novel devices with focus on the integration and joint operation with superconducting circuits exhibiting quantum behavior. These circuits are very different from traditional RSFQ circuits in their design, physical parameters, magnitude of electrical signals, speed of operation, dissipated power, operation temperature, etc. Besides the integration of RSFQ circuits with Josephson qubits, a challenging task under consideration is the realization of integrated structures of these circuits with superconducting single Cooper pair circuits. Achieving this goal can open the way to an efficient quantum standard of current. In such a device the SFQ circuit could perform, for example, the function of a fast counter module for single Cooper pairs.

Figure 3: Characterization of the circuits in our measurement laboratory.

The staff of working group "Single-charge-flux circuits".