IOP PUBLISHING
SUPERCONDUCTOR SCIENCE AND TECHNOLOGY
Supercond. Sci. Technol. 20 (2007) S450–S454
doi:10.1088/0953-2048/20/11/S29
Design of a ballistic fluxon qubit readout Anna Herr (Kidiyarova-Shevchenko)1, Arkady Fedorov2 , Alexander Shnirman2,3 , Evgeny Il’ichev4 and Gerd Sch¨on2 1 Microtechnology and Nanoscience Department, Chalmers University of Technology, 41296 Gothenburg, Sweden 2 Institut f¨ur Theoretische Festk¨orperphysik, Universit¨at Karlsruhe, D-76128 Karlsruhe, Germany 3 Institut f¨ur Theoretische Physik, Universit¨at Innsbruck, A-6020 Innsbruck, Austria 4 IPHT, 07745 Jena, Germany
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Received 14 June 2007, in final form 21 August 2007 Published 18 October 2007 Online at stacks.iop.org/SUST/20/S450 Abstract A detailed design is given for a flux qubit readout using ballistic fluxons. In this scheme, fluxons propagate through an underdamped Josephson transmission line (JTL) coupled to the qubit, whose state affects the fluxon propagation time. For strong qubit–JTL coupling, and far from the symmetry point, a qubit can be measured with fidelity greater than 99% and measurement time of 4 ns. The readout circuit requires additional rapid single flux quantum (RSFQ) interface circuitry to launch and receive the delayed flux solitons. The parameters of this driver and receiver have been optimized to produce low fluxon speed at launch and impedance matching at the receiver. The delayed solitons are compared to a reference line using a detector with time resolution of better than 16 ps. Both the JTL and RSFQ interface were designed for the Nb 30 A cm−2 process developed at VTT, Finland, with postdeposition of the Al qubit at IPHT, Germany. (Some figures in this article are in colour only in the electronic version)
1. Introduction Application of a long Josephson junction for manipulation with a superconducting flux qubit was first introduced in connection with the realization of an RSFQ/qubit classical interface [1]. One of the advantages of such a scheme is that long Josephson junctions act as good high-pass filters, providing up to −100 dB noise attenuation below the plasma frequency [2]. This would eliminate the noise attributed to the resistively shunted junctions used in RSFQ circuits. Another, probably the most important, aspect of the proposed scheme is that the propagation dynamics of fluxons in the long Josephson junctions is quite sensitive to the external field induced by the qubit. Recent work has theoretically developed the principles of the qubit readout when the information about the state of a qubit is contained either in the fluxon transmission probability or propagation time delay [3]. It was shown that, under certain ideal conditions, the measurement time is equal to the backaction dephasing time, which correspond to the criteria of an ideal quantum detector. The fluxon-based readout was further developed in [4]. This paper investigates the efficiency of the delay time 0953-2048/07/110450+05$30.00
detection mode for experimentally accessible parameters, taking into account various sources of measurement errors. It was found that for optimized fluxon velocity and number of fluxons used in experiment, the qubit can be measured with accuracy reaching 99% far from the symmetry point and above 90% at the symmetry point for strong qubit–JTL coupling. The optimum number of fluxons for both cases is 5, which corresponds to the measurement time of approximately 4 ns. In this paper we present a design of a flux qubit readout using ballistic fluxons that follows up the theoretical analysis in [4]. A block diagram of the designed circuit is shown in figure 1. The fluxons propagate through two underdamped Josephson transmission lines (JTLs) that are discrete analogs of long Josephson junctions. A JTL consists of a number of identical underdamped Josephson junctions connected in parallel by inductances. The inductance between junctions is small, so the length of the JTL unit cell a is equal to half of the Josephson penetration depth λJ = (0 /(2π L Ic ))1/2 . The fluxons are injected into the lines using an RSFQ driver that is, either electrically or magnetically, coupled to the first cell of the line. One of the lines is coupled to the qubit, whose state affects the fluxon propagation time. The delayed fluxons
© 2007 IOP Publishing Ltd Printed in the UK
S450
Design of a ballistic fluxon qubit readout
a)
b)
Figure 1. Flux qubit readout scheme using fluxons propagating through an underdamped Josephson transmission line: block diagram (a) and schematic (b).
are compared to reference fluxons at the RSFQ receiver. The following sections describe in detail the designs of the ballistic JTL and RSFQ circuitry.
2. Fabrication process and design parameters Both the JTL and the RSFQ interface were designed for the Nb 30 A cm−2 process at VTT, Finland [5]. The junctions have a NbAlOx Nb trilayer with Pd shunt resistors. Typical measured parameters of the unshunted junctions are Ic = 2 μA, Ic RN = 2.4 mV, RN /Rg = 0.1 (4.2 K). These parameters result in a plasma frequency of the junctions of about 28 GHz and dissipation parameter α = ωp /ωc = 0.02 at 4.2 K. At low (
