Design of an RSFQ control circuit to observe MQC on an rf-SQUID

Abstract

Abstract-We believe that the best chance to observe macroscopic quantum coherence (MQC) in an rf-SQUID qubit i s to use on-chip RSFQ digital circuits for preparing, evolving and reading out the qubit's quantum state. This approach allows experiments to be conducted on a very short time scale (sub-nanosecond) without the use of large bandwidth control lines that would couple environmental degrees of freedom to the qubit, thus contributing to its decoherence. In this paper we present our design of an RSFQ digital control circuit for demonstrating MQC in an rf-SQUID. We assess some of the key practical issues in the circuit design including the achievement of the necessary flux bias stability. We present an "active" isolation structure to be used to increase coherence times. The structure decouples the SQUID from external degrees of freedom, and then couples it to the output measurement circuitry when required, all under the active control of RSFQ circuits.Index Terms-superconducting qubit, macroscopic quantum coherence, RSFQ control.

Flux-based superconducting qubits for quantum computation

“…The picosecond time scales that SFQ circuits can achieve means that superconducting qubits can be controlled rapidly on a time scale over which the qubits remain phase coherent. Circuits that fully integrate SFQ circuits with quantum experiments have recently been proposed [29][30][31].…”

Adiabatic evolution of a coupled-qubit Hamiltonian

“…For the cases we present here the ratio of the dispersion to the expectation value was in the vicinity of 0.3. We find that the three different gray areas of Fig [2] and [3] have well defined tableaux as follows: Hence a sweep from the central region to the right region will produce the desired mapping of Eq [26]. Similarly sweeping from the right region to the center and from the left region to the central region and vice-versa can also serve as realizations, differing simply in the assignment of (0,1) for the bits or the names (1,2) for the SQUIDs.…”

“…One can proceed as follows: we first search for an initial Hamiltonian whose variable external parameters (φ for a final Hamiltonian where another set of (φ ext 1 , φ ext 2 ), gives the tableau on the right of Eq [26]. In this procedure we need only to study the stationary Schroedinger equation at first.…”

“…Realization of operations such as Eq [26] can be accomplished by using adiabatic processes, thanks to the "no level crossing" behavior of adiabatic evolution. The no-crossing property assures that a state initially in the first, or second, or third,.... energy level will end up in the first, or second, or third,... energy level after the adiabatic evolution, while at the same time the logical state associated with the level may be changing.…”

“…We obtain [23] the switching behavior according to Eq [26] by fixing the control bias φ occurs. This is a generalization of a NOT [16] on φ 1 .…”