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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Control of a superconducting qubit in the presence of a nonlinear backreaction

Jason F. Ralph, Terrence D. Clark, M. J. Everitt, Peter Steiffell, Robert J. Prance, Helen Prance

Published Jul 31, 2002• 0 citations
Publisher

Abstract

There are a number of systems that are currently being considered as candidates for the construction of qubits, quantum logic gates and quantum computers. Some of the systems, notably atoms in magnetic traps and nuclear magnetic resonance (NMR) systems, have had some success in performing the elementary operations that would be required in large-scale quantum computer. However, these systems are not necessarily seen as viable technologies for quantum computing in the longer term. The recent demonstration of macroscopic coherence in a superconducting ring (consisting of a thick superconducting ring containing one or more Josephson weak link devices) has added significant weight to the idea of using superconducting persistent current devices (SQUIDs) in quantum logic systems. In this paper, we consider one aspect of the quantum mechanical SQUID, the nonlinear effect of SQUID on the classical control parameters, and we discuss how it may influence the construction and design of quantum logic gates based on SQUID devices. In particular, we look at problems associated with fixing the classical magnetic flux bias for a quantum mechanical SQUID at, or near, a quantum mechanical transition or resonance.

DOI
10.1117/12.477421

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There are a number of systems that are currently being considered as candidates for the construction of qubits, quantum logic gates and quantum computers. Some of the systems, notably atoms in magnetic traps and nuclear magnetic resonance (NMR) systems, have had some success in performing the elementary operations that would be required in large-scale quantum computer. However, these systems are not necessarily seen as viable technologies for quantum computing in the longer term. The recent demonstration of macroscopic coherence in a superconducting ring (consisting of a thick superconducting ring containing one or more Josephson weak link devices) has added significant weight to the idea of using superconducting persistent current devices (SQUIDs) in quantum logic systems. In this paper, we consider one aspect of the quantum mechanical SQUID, the nonlinear effect of SQUID on the classical control parameters, and we discuss how it may influence the construction and design of quantum logic gates based on SQUID devices. In particular, we look at problems associated with fixing the classical magnetic flux bias for a quantum mechanical SQUID at, or near, a quantum mechanical transition or resonance.
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.
Two classes of superconducting devices have been proposed as quantum bits (qubits) for realizing quantum logic operations. The flux qubits based on a superconducting quantum interference device (SQUID) appear to be particularly promising owing to the macroscopic nature of the qubit and potential integration with high-speed control circuitry in the form of rapid single-flux quantum electronics. Recent progress is discussed and near-term challenges mentioned. The radio frequency SQUID-based qubit offers a prospect for a reliably manufacturable scalable approach.
Hybrid quantum systems play an essential role in efforts towards the advancements of quantum information technology and quantum sensing by bridging distinct technological platforms. In particular, hybrid systems comprising superconducting microwave circuits are being pursued intensely in light of existing achievements in superconducting qubits and precise quantum control in microwave circuits. Their realization relies on the design of superconducting resonators capable of coupling to an oscillatory mode of a second quantum system, facilitating the probing and manipulation of one via the other. In order to accommodate the coupled system, its particular constraints and requirements must be respected, which may be quite extreme from the perspective of established superconducting circuit design and operation. Overcoming this challenge has proved to be a substantial obstacle for the attainment of strongly coupled hybrid systems, despite spectacular advances in superconducting microwave circuits individually. In this work, we examine two approaches tackling this issue for different hybrid quantum systems, focusing on the optimization and characterization of the superconducting circuits. The first device aims at a superconductor-atom hybrid system through the coupling to Rydberg-Rydberg transitions in ultra-cold Rb-87 atoms trapped near the superconducting chip. Using simulations in conjunction with theoretical considerations, we demonstrate a comprehensive geometry parameter optimization procedure for maximum coupling rate. Presenting an experimental implementation of the resulting circuit, we validate its suitability for use under the intended operation conditions, including the option of tuning the electronic transition frequencies using a dc voltage. Secondly, we investigate a device designed for applications in large magnetic in-plane fields used to mediate coupling to integrated micromechanical oscillators; more specifically it is a flux-tunable SQUID resonator comprising Josephson nano-constrictions as nonlinear inductive components. Performing a thorough characterization of its frequency and Kerr anharmonicity tuning behavior at fields up to several hundred mT, we discover a pronounced asymmetry in its flux response at large fields. We show this asymmetry to be caused by the nano-constrictions turning into Josephson diodes, develop an intuitive macroscopic model for its field-induced emergence and reconstruct the diode current-phase relation from the flux tuning data. Several figures of merit informing the suitability of the SQUID resonators for optomechanical systems as well as other applications are improved by the diode effect, highlighting the potential of Josephson diodes in superconducting microwave circuits. Our results provide a promising stepping stone for the advancement of hybrid systems involving superconducting microwave circuits, putting new and exciting operation and coupling regimes within reach.
This paper considers the behavior of a model persistent current qubit in the presence of a time-dependent electromagnetic field. A semi-classical approximation for the electromagnetic field is used to solve the time- dependent Schrodinger equation (TDSE) for the qubit, which is treated as a macroscopic quantum object. The qubit is describe3d by a Hamiltonian involving the enclosed magnetic flux (Phi) and the electric displacement flux Q, which obey the quantum mechanical commutation relation. The paper includes a brief summary of recent work on quantum mechanical coherence in persistent current circuits, and the solution of the TDSE in superconducting rings. Of particular interest is the emergence of strongly non-perturbative behavior that corresponds to transitions between the energy levels of the qubit. These transitions are due to the strong coupling between the electromagnetic fields and the superconducting condensate and can appear at frequencies predicted by conventional methods based on perturbations around the energy eigenstate of the time-independent system. The relevance of these non-perturbative processes to the operation of quantum logic gates based on superconducting circuits and the effect of the resultant non linearities on the environmental degrees of freedom coupled to the qubit are considered.
The recovery of classical nonlinear and chaotic dynamics from quantum systems has long been a subject of interest.Furthermore, recent work indicates that quantum chaos may well be significant in quantum information processing.In this paper, we discuss the quantum to classical crossover of a superconducting quantum interference device (SQUID) ring.Such devices comprise a thick superconducting loop enclosing a Josephson weak link and are currently strong candidates for many applications in quantum technologies.The weak link brings with it a nonlinearity such that semiclassical models of this system can exhibit nonlinear and chaotic dynamics.For many similar systems an application of the correspondence principle together with the inclusion of environmental degrees of freedom through a quantum trajectories approach can be used to effectively recover classical dynamics.Here we show (i) that the standard expression of the correspondence principle is incompatible with the ring Hamiltonian and we present a more pragmatic and general expression which finds application here and (ii) that practical limitations to circuit parameters of the SQUID ring prevent arbitrarily accurate recovery of classical nonlinear dynamics.