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TEION KOGAKU (Journal of Cryogenics and Superconductivity Society of Japan)

Experimental Findings on the Superconducting Quantum Annealing Circuit and those Applications to a Gate-Type Quantum Computer

Daisuke Saida

Published Jul 19, 2024• 0 citations
Publisher

Abstract

The superconducting quantum annealing circuit is constructed with four Nb layers and Josephson junctions with a critical current density of 1 μA/μm2. Three key points exist to perform the quantum annealing in experiments. First, the shape of the energy potential of the qubit should be accurately designed. Second, the current pulses for modulation of the shape of the energy potential must propagate to the qubit accurately. Third is the suppression of noise in the environment where the qubit is placed. Furthermore, calibration of the measurement data is necessary with consideration of the experimental environment. In this paper, I will present a mechanism for realizing quantum annealing from two perspectives: a theoretical model and an experiment. Experimental findings on quantum annealing will contribute to study of the surrounding circuit of a gate-type quantum computer.

DOI
10.2221/jcsj.59.228

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The superconducting quantum annealing circuit is constructed with four Nb layers and Josephson junctions with a critical current density of 1 μA/μm2. Three key points exist to perform the quantum annealing in experiments. First, the shape of the energy potential of the qubit should be accurately designed. Second, the current pulses for modulation of the shape of the energy potential must propagate to the qubit accurately. Third is the suppression of noise in the environment where the qubit is placed. Furthermore, calibration of the measurement data is necessary with consideration of the experimental environment. In this paper, I will present a mechanism for realizing quantum annealing from two perspectives: a theoretical model and an experiment. Experimental findings on quantum annealing will contribute to study of the surrounding circuit of a gate-type quantum computer.
A circuit consisting of a network of coupled compound Josephson junction rf-SQUID flux qubits has been used to implement an adiabatic quantum optimization algorithm. It is shown that detailed knowledge of the magnitude of the persistent current as a function of annealing parameters is key to implementation of the algorithm on this particular type of hardware. Experimental results contrasting two annealing protocols, one with and one without active compensation for the growth of the qubit persistent current during annealing, are presented in order to illustrate this point.
Although quantum annealing has received considerable interest as a potential computing paradigm, it has not met the key criterion of improved scaling over classical methods. Qubit coherence is currently a major limitation. Starting from a detailed theoretical understanding of the system, the authors demonstrate tunably coupled flux qubits with a circuit geometry similar to those used in existing annealers, but with coherence times that are roughly two orders of magnitude longer. Their design concepts are not limited to superconducting qubits, and could be generalized to other types being considered for quantum annealing.
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The applicability of quantum annealing to various problems can be improved by expressing the Hamiltonian using a circuit satisfiability problem. We investigate the detailed characteristics of the NOR/NAND functions of a superconducting quantum circuit, which are the basic building blocks to implementing various types of problem Hamiltonians. The circuit is composed of superconducting flux qubits with all-to-all connectivity, where direct magnetic couplers are utilized instead of the variable couplers in the conventional superconducting quantum circuit. This configuration provides efficient scalability because the problem Hamiltonian is implemented using fewer qubits. We present an experiment with a complete logic operation of NOR/NAND, in which the circuit produces results with a high probability of success for arbitrary combinations of inputs. The features of the quantum circuit agree qualitatively with the theory, especially the mechanism for an operation under external flux modulation. Moreover, by calibrating the bias conditions to compensate for the offset flux from the surrounding circuit, the quantum circuit quantitatively agrees with the theory. To achieve true quantum annealing, we discuss the effects of the reduction in electric noise in quantum annealing.
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.
In superconducting quantum circuits, Josephson junctions are a key component to provide nonlinearity and enable superconducting qubits. Fabricating junctions with precise critical currents is crucial to defining qubit frequency. Here we suppress the critical current variation of Josephson junctions by varying the critical current density Jc and junction areas. The relative standard deviation of the critical current Ic is controlled to be below 0.8%. This uniform fabrication is promising for realizing scalable superconducting quantum computation.