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IEEE Transactions on Applied Superconductivity

Development and Testing of a Persistent Flux Bias for Qubits

Luigi Longobardi, Shawn Pottorf, Vijay Patel, James E. Lukens

Published Jun 1, 2007• 6 citations
Publisher

Abstract

We have realized an on-chip persistent flux bias for our flux based qubit by adding a switchable aluminum shunt to the niobium flux bias coils. This inductive shunt can create a persistent current loop by trapping the bias flux at the superconducting transition of the Al. When the Al is superconducting, the noise spectral density from the flux bias and the damping due to the flux bias should both be reduced by a factor of 100, since the inductance ratio,Lsh/Lp, is 0.1. This reduces one of the sources of decoherence for the qubit. To permit changes to the persistent current in the superconducting loops at mK temperatures, a local heater has been coupled to the Al shunt. This makes it possible to briefly drive the shunt to its normal state to change to flux without heating the entire device.

DOI
10.1109/tasc.2007.897413

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We have realized an on-chip persistent flux bias for our flux based qubit by adding a switchable aluminum shunt to the niobium flux bias coils. This inductive shunt can create a persistent current loop by trapping the bias flux at the superconducting transition of the Al. When the Al is superconducting, the noise spectral density from the flux bias and the damping due to the flux bias should both be reduced by a factor of 100, since the inductance ratio,Lsh/Lp, is 0.1. This reduces one of the sources of decoherence for the qubit. To permit changes to the persistent current in the superconducting loops at mK temperatures, a local heater has been coupled to the Al shunt. This makes it possible to briefly drive the shunt to its normal state to change to flux without heating the entire device.
Qubits based on the magnetic flux degree of freedom require a flux bias, whose stability and precision strongly affect the qubit performance, up to a point of forbidding the qubit operation. Moreover, in the perspective of multiqubit systems, it must be possible to flux-bias each qubit independently, hence avoiding the traditional use of externally generated magnetic fields in favour of on-chip techniques that minimize cross-couplings. The solution discussed in this paper exploits a persistent current, trapped in a superconducting circuit integrated on chip that can be inductively coupled with an individual qubit. The circuit does not make use of resistive elements that can be detrimental for the qubit coherence. The trapping procedure allows to control and change stepwise the amount of stored current; after that, the circuit can be completely disconnected from the external sources. We show in a practical case how this works and how to drive the bias circuit at the required value.
We report the development of flux memory for use with superconducting circuits. This technology stores persistent currents in superconducting loops on-chip to be used to provide flux biasing for superconducting circuits, like qubits. We developed three types of flux memory and draw comparisons among them for circuit design. We demonstrate the utility of flux memory by using an in-situ flux detector and characterize each approach and further demonstrate that once flux is set in a memory cell, benchtop DC control sources can be powered off, leaving the on-chip flux bias in place. We propose that flux memory can be arranged in a two-dimensional configuration to multiplex control signals and reduce how line counts scale (N^2 devices -> 2N control lines), and our experimental results pave the path to the proposed scalability. We demonstrate the use of flux memory to flux bias a transmon qubit and show the tunability of the qubit state to a target frequency which remained stable on-chip for 20 hours.
A rf--superconducting quantum interference device (SQUID) flux qubit that is robust against fabrication variations in Josephson-junction critical currents and device inductance has been implemented. Measurements of the persistent current and of the tunneling energy between the two lowest-lying states, both in the coherent and incoherent regimes, are presented. These experimental results are shown to be in agreement with predictions of a quantum-mechanical Hamiltonian whose parameters were independently calibrated, thus justifying the identification of this device as a flux qubit. In addition, measurements of the flux and critical current noise spectral densities are presented that indicate that these devices with Nb wiring are comparable to the best Al wiring rf SQUIDs reported in the literature thus far, with a 1/f1/f1/f flux noise spectral density at 1 Hz of ${1.3}_{\ensuremath{-}0.5}^{+0.7}\text{ }\ensuremath{\mu}{\ensuremath{\Phi}}_{0}/\sqrt{\text{Hz}}$. An explicit formula for converting the observed flux noise spectral density into a free-induction-decay time for a flux qubit biased to its optimal point and operated in the energy eigenbasis is presented.
While quantum computation has the potential to revolutionize the scientific community, to date no architecture has been developed which offers the necessary combination of high coherence times and massive scalability. Superconducting flux qubits satisfy the second requirement well but to date useful devices are limited to coherence times of typically only a few &mus. In this dissertation we examine the possibilities of improving the coherence performance of the flux qubit to the levels required for fault-tolerant quantum computation. We find that coherence times for many devices are limited by photon-induced quasiparticles and mitigation of these quasiparticles increases coherence times by more than a factor of two. Beyond this, however, we find little improvement in flux qubit performance compared to prior results. Despite improved fabrication techniques and varied device designs we find flux qubit coherence times are still typically below 5 &mus. Furthermore, wide device-to-device variations are observed which prevent effective scaling of the flux qubit to quantum information circuits.Based on the proposal by You, et al. we develop of a capacitively-shunted version of the flux qubit called the C-shunt flux qubit. With the addition of a capacitive shunt across the small junction of the flux qubit we are able to reduce the amplitude sensitivity to both charge and flux noise by more than a factor of three. The result is a predicted ten-fold enhancement in the coherence times compared to the unshunted flux qubit. At the same time we preserve much of the anharmonicity of the flux qubit resulting in a device with coherence times comparable to modern transmons but with a factor of four better anharmonicity and more flexible coupling configurations.By using a high-quality MBE aluminum shunt process on an annealed sapphire substrate coupled with a more conventional electron-beam-evaporated aluminum Josephson junction process we fabricate hybrid C-shunt flux qubits. We also incorporate a new bridgeless junction technique which offers more robust and repeatable fabrication processing. This technique enables improved accuracy of the junction sizing, a trait which will become essential as we move to multi-qubit experiments. T1 and T2 times for these C-shunt devices reach in excess of 40 &mus at degeneracy, achieving the predicted ten-fold improvement based on the reduced noise sensitivity. At the same time we see decreased device-to-device variation with typical T1 times exceeding 20&ndash25 &mus at all bias points. Combined with the high anharmonicity and standard planar fabrication techniques these coherence times make the C-shunt flux qubit a competitive candidate for fault-tolerant quantum computation.
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.