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Josephson Junction Triangular Prism Qubits Coupled to a Resonant LC Bus: Qubits and Gates for a Holonomic Quantum Computer

Stanford P. Yukon

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

We investigate the properties of Josephson junction triangular prism qubits coupled by mutual inductance to a resonant LC bus. We show how the symmetries of the qubit potential may be used to implement the Duan Cirac Zoller scheme for holonomic quantum computation.

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This work concerns the study of Josephson junction circuits in the context of their usability for quantum computing. The zero-voltage state of a current-biased Josephson junction has a set of metastable quantum energy levels. If a junction is well isolated from its environment, it will be possible to use the two lowest states as a qubit in a quantum computer. I first examine the meaning of isolation theoretically. Using a master equation, I analyzed the effect of dissipation on escape rates and suggested a simple method, population depletion technique, to measure the relaxation time. Using a stochastic Bloch equation to analyze microwave resonance shapes, I found a relation between current noise induced decoherence and the noise spectrum. I then analyze and test a few qubit isolation schemes, including resistive isolation, inductor-capacitor (LC) isolation, and inductor-junction (LJ) isolation. I found the resistive isolation scheme has a severe heating problem. Macroscopic quantum tunneling and energy level quantization were observed in the LC isolated junction qubits at 25 mK. Relaxation times of 4-12 ns and spectroscopic coherence times of 1-3 ns were obtained for these LC isolated qubits. I measured a relaxation time of 50 ns and a spectroscopic coherence time of 5-8 ns for the LJ isolated junction qubit. Both times are much longer than those of the LC isolated qubits. Rabi oscillations were also observed on this sample with a decay time of around 10 ns. Using microwave spectroscopy techniques, I probed quantum phenomena in a coupled macroscopic three-qubit system that is comprised of two Nb/AlOx/Nb Josephson junctions and an LC resonator. The measured spectrum at 25 mK in the frequency range 4-15 GHz agrees well with quantum mechanical calculations, consistent with the existence of entangled states between the three degrees of freedom. These entangled states and a first-order strong coupling between two junction qubits open the possibility of using a resonator as a data bus for information storage and manipulation in a multi-qubit system. The measurements also demonstrate spectroscopy is a powerful tool and can be used to study a composite system with many qubits.
Josephson junction-based qubits have been shown to be promising components for a future quantum computer. A network of these superconducting qubits will require quantum information to be stored in and transferred among them. Resonators made of superconducting metal strips are useful elements for this purpose because they have long coherence times and can dispersively couple qubits. We explore the use of multiple resonators with different resonant frequencies to couple qubits. We find that an array of resonators with different frequencies can be individually addressed to store and retrieve information, while coupling qubits dispersively. We show that a control qubit can be used to effectively isolate an active qubit from an array of resonators so that it can function within the same frequency range used by the resonators.
The implementation of holonomic quantum computation in superconducting quantum circuits is challenging due to the general requirement of controllable complicated coupling between multi-level systems. In this Letter, we solve this problem by proposing a scalable circuit QED lattice with simple realization of the universal set of non-adiabatic holonomic quantum computation. Compared with existed proposals, here we can achieve both the single- and two- logical qubit gates in an unprecedented tunable and all-resonant way through a hybrid transmon-transmission-line encoding of the logical qubits in the decoherence-free subspaces. This distinct advantage thus leads to quantum gates with very fast speeds and consequently very high fidelities. Our scheme therefore paves a promising way towards the realization of high fidelity universal holonomic quantum computation.
Josephson qubits without direct interaction can be effectively coupled by sequentially connecting them to an information bus: a current-biased large Josephson junction treated as an oscillator with adjustable frequency. The coupling between any qubit and the bus can be controlled by modulating the magnetic flux applied to that qubit. This tunable and selective coupling provides two-qubit entangled states for implementing elementary quantum logic operations, and for experimentally testing Bell's inequality.