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arXiv:quant-ph/0102090 · IEEE Transactions on Applied Superconductivity

A tipping pulse scheme for a rf-SQUID qubit

Xingxiang Zhou, Jonathan L. Habif, Andrea M. Herr, M. J. Feldman, Mark F. Bocko

Published Mar 1, 2001• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/77.919522

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A tipping pulse scheme for an rf-SQUID qubit

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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.
At low temperature and low damping, the magnetic flux of a rf Superconducting QUantum Interference Device (SQUID) acts as a macroscopic quantum variable whose dynamic is described by a double well potential. A rf SQUID consists of a superconducting loop interrupted by a thin insulating barrier, known as a Josephson junction. The modified rf SQUID design discussed in this thesis has independent, in situ, controls that allow varying the barrier height between the potential wells and their relative tilt. This high level of control of the potential together with the capability to implement an experimental setup optimized to reduce coupling to external sources of noise, made this system ideal not only for tests of quantum transition at a macroscopic level, but also as a scalable solid state device for quantum computation. A variety of measurements of quantum phenomena are reported in this thesis, including microwave level spectroscopy, coherent oscillations, and macroscopic resonant tunneling (MRT). These measurements are compared with theoretical models to study the possible sources of decoherence in a rf SQUID qubit. The analysis confirmed that the main source of decoherence is not due to coupling to the external environment, but it can be linked to intrinsic low frequency flux noise. Work from many groups over the last several years has shown that the performance of a superconductive qubit is limited by coupling to spurious defects in the materials used for the device fabrication. In this work we analyze the possibility of using the MRT as a tool for future studies of effects of materials and fabrication process in the realization of improved qubits, and we also explore the feasibility for measurements of quantum phenomena that involve fast pulsing of the potential barrier height.
We report on development of a set-up for measuring intrawell dynamics in a Nb-based rf-SQUID qubit described by a double well potential, by rapidly tilting the potential, allowing escape to the adjacent well with high probability for an excited state but low probability for the ground state. The rapid tilt of the double well potential is accomplished via a readout flux pulse inductively coupled to the qubit from a microstrip transmission line on a separate chip suspended above the qubit chip. The readout pulse is analogous to the current bias pulse used to readout phase qubits and hysteretic dc-SQUID magnetometers. The coupling between the transmission line and the qubit is carefully controlled via a window in the ground plane between the signal conductor of the microstrip and the qubit loop. Since the high frequency transmission lines are on a separate chip, they can be independently characterized and reused for different qubit samples. Clean flux pulses as short as 5 ns with rise times of 0.5 ns have been coupled to the qubit to measure escape rates higher than 10 8 s −1 , the lifetime of the excited state, and coherent oscillations between the ground and excited states within the same well.
We report on the development and test of an integrated system composed of a flux qubit and a rapid single-flux quantum (RSFQ) circuit that allows qubit manipulation. The goal is to demonstrate the feasibility of control electronics integrated on the same chip as the qubit, in view of the application in quantum computation with superconducting devices. RSFQ logic relies on the storage and transmission of magnetic flux quanta and can be profitably used with superconducting qubits because of the speed, scalability, compatibility with the qubit fabrication process and low temperature environment. While standard RSFQ circuitry is well assessed, the application to quantum computing requires a complete rescaling of parameter values, in order to preserve the qubit coherence and reduce the power dissipation. In the system presented in this paper, the qubit role is played by a superconducting loop interrupted by a small dc SQUID, usually called a double SQUID, which behaves as a tunable rf-SQUID. Its energy potential has the shape of a double well, with the barrier between the wells controlled by magnetic flux applied to the inner dc SQUID. Here for the first time we report measurements at a base temperature of 370 mK in which flux control pulses with desired characteristics were supplied by a RSFQ circuit fabricated using non-standard parameters in the same chip as the qubit.
Single-flux-quantum (SFQ) circuits have great potential in building cryogenic quantum-classical interfaces for scaling up superconducting quantum processors. SFQ-based quantum gates have been designed and realized. However, current control schemes are difficult to tune the driving strength to qubits, which restricts the gate length and usually induces leakage to unwanted levels. In this study, we design the scheme and corresponding pulse generator circuit to continuously adjust the driving strength by coupling SFQ pulses with variable intervals. This scheme not only provides a way to adjust the SFQ-based gate length, but also proposes the possibility to tune the driving strength envelope. Simulations show that our scheme can suppress leakage to unwanted levels and reduce the error of SFQ-based Clifford gates by more than an order of magnitude.
We experimentally demonstrate the observation of macroscopic resonant tunneling (MRT) phenomenon of the macroscopic distinct flux states in a radio frequency superconducting quantum interference device (rf-SQUID) under a single-cycle sinusoidal driving. The population of the qubit exhibits interference patterns corresponding to resonant tunneling peaks between states in the adjacent potential wells. The dynamics of the qubit depends significantly on the amplitude, frequency, and initial phase of the driving signal. We do the numerical simulations considering the intra-well and inter-well relaxation mechanism, which agree well with the experimental results. This approach provides an effective way to manipulate the qubit population by adjusting the parameters of the external driving field.