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Journal of Physics A Mathematical and Theoretical

Dynamical qubit controlling via pseudo-supersymmetry of two-level systems

B. F. Samsonov, V. V. Shamshutdinova

Published Jun 3, 2008• 6 citations
Publisher

Abstract

For a flux qubit considered as a two-level system, for which a hidden polynomial pseudo-supersymmetry was previously discovered, we propose a special time-dependent external control field. We show that for a qubit placed in this field there exists a critical value of tunnel frequency. When the tunnel frequency is close enough to its critical value, the external field frequency may be tuned in a way to keep the probability to detect a definite direction of the current circulating in a Josephson-junction circuit above 1/2 during a desirable time interval. We also show that such a behavior is not much affected by a sufficiently small dissipation.

DOI
10.1088/1751-8113/41/24/244023

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For a flux qubit considered as a two-level system, for which a hidden polynomial pseudo-supersymmetry was previously discovered, we propose a special time-dependent external control field. We show that for a qubit placed in this field there exists a critical value of tunnel frequency. When the tunnel frequency is close enough to its critical value, the external field frequency may be tuned in a way to keep the probability to detect a definite direction of the current circulating in a Josephson-junction circuit above 1/2 during a desirable time interval. We also show that such a behavior is not much affected by a sufficiently small dissipation.
For a flux qubit described by a two-level system of equations we propose a special time dependent external control field. We show that for a qubit placed in this field there exists a critical value of tunnel frequency. When the tunnel frequency is close to its critical value, the probability value of a definite direction of the current circulating in a Josephson-junction circuit may be kept above 1/2 during a desirable time interval. We also show that such a behavior is not much affected by a sufficiently small dissipation.
We present a technique to control the quantum state of a rf-SQUID qubit. We propose to employ a stream of single flux quantum (SFQ) pulses magnetically coupled to the qubit junction to momentarily suppress its critical current. This effectively lowers the barrier in the double-well rf SQUID potential thereby increasing the tunneling oscillation frequency between the wells. By carefully choosing the time interval between SFQ pulses one may accelerate the interwell tunneling rate. Thus it is possible to place the qubit into a chosen superposition of flux states and then effectively to freeze the qubit state. We present both numerical simulations and analytical time-dependent perturbation theory calculations that demonstrate the technique. Using this strategy one may control the quantum state of the rf SQUID in a way analogous to the /spl pi/ pulses in other qubit schemes.
We present the design of a superconducting qubit that has circulating currents of opposite sign as its two states. The circuit consists of three nanoscale aluminum Josephson junctions connected in a superconducting loop and controlled by magnetic fields. The advantages of this qubit are that it can be made insensitive to background charges in the substrate, the flux in the two states can be detected with a superconducting quantum interference device, and the states can be manipulated with magnetic fields. Coupled systems of qubits are also discussed as well as sources of decoherence.
Supersymmetries in quantum mechanics offer a way to obtain degeneracies in the excitation spectrum which do not originate from selection rules. The mechanism behind the degeneracies is the same as the one that leads to the miraculous cancellations of divergences in supersymmetric field theories found in the high energy physics context. There is up to now no realistic proposal of nonintegrable systems that show level degeneracies due to a supersymmetric structure. Here, we propose an implementation of a quantum-mechanical supersymmetry in a Cooper-pair box shunted by a Josephson junction rhombus which is effectively $\ensuremath{\pi}$ periodic in the superconducting phase difference. For a characteristic ratio between the strength of the $2\ensuremath{\pi}$- and the $\ensuremath{\pi}$-periodic junction, we find a twofold degeneracy of all the energy levels all the way from the weak junction/charge qubit limit to the strong junction/transmon regime. We provide explicit experimental values for the parameters of the system and show that tuning in and out of the supersymmetric point is easily achieved by varying an external gate voltage. We furthermore discuss a microwave experiment to detect the supersymmetry and conclude that it can indeed be implemented with currently existing Josephson junction technology.
I studied the Josephson junction system in the context of its usability for quan-tum computation. The zero-voltage state of a Josephson junction biased with constant current has a set of metastable quantum energy levels. In principle, it should be possible to use the two lowest states as a qubit for a quantum computer, provided both the dissipation time and coherence time of this qubit can be made long enough. I describe two methods for isolating a Josephson junction to increase its dissipation time. The rst is a resistive isolation scheme, for which I fabricated and measured a prototype system. I discuss the results of these measurements and show that the constraints of heating in conjunction with high-frequency design require-ments make it unlikely that this isolation method will lead to the coherence times required for quantum computation. I then discuss a resonant isolation method that I used to successfully increase the dissipation time of a Josephson junction qubit. I performed spectroscopic mea-surements at low temperatures to nd the coherence time of resonantly isolated 100 m2 Al/AlOx/Al and Nb/AlOx/Nb junctions with critical currents of roughly 10 A. The results of these measurements reveal two mechanisms beyond spontaneous emission for decoherence: low-frequency current noise and tunneling to the voltage state. To explain these results on decoherence, I present a model based on the Bloch equations. Going beyond a single qubit, I designed a capacitively coupled two-qubit system. Using spectroscopy, I showed that the energy level spacings between the ground state and the excited entangled states of the system agree with those calculated from the Schrodinger equation.
Quasiparticle tunneling across a Josephson junction sets a limit for the lifetime of a superconducting qubit state. We develop a general theory of the corresponding decay rate in a qubit controlled by a magnetic flux. The flux affects quasiparticles tunneling amplitudes, thus making the decay rate flux-dependent. The theory is applicable for an arbitrary quasiparticle distribution. It provides estimates for the rates in practically important quantum circuits and also offers a new way of measuring the phase-dependent admittance of a Josephson junction.