Yulin Wu

Solving Systems of Linear Equations with a Superconducting Quantum Processor

Superconducting quantum circuits are a promising candidate for building scalable quantum computers. Here, we use a four-qubit superconducting quantum processor to solve a two-dimensional system of linear equations based on a quantum algorithm proposed by Harrow, Hassidim, and Lloyd [Phys. Rev. Lett. 103, 150502 (2009)PRLTAO0031-900710.1103/PhysRevLett.103.150502], which promises an exponential speedup over classical algorithms under certain circumstances. We benchmark the solver with quantum inputs and outputs, and characterize it by nontrace-preserving quantum process tomography, which yields a process fidelity of 0.837±0.006. Our results highlight the potential of superconducting quantum circuits for applications in solving large-scale linear systems, a ubiquitous task in science and engineering.

The Effect of Low Frequency External Field Disturbance on the SQUID Based Ultra-Low Field NMR Measurements

We have carried out NMR experiments in the microtesla range using a high-Tc DC-SQUID sensor. The measurements were carried out in a simple magnetically shielded room. Resonance spectra of 1H nuclei from tap water and other substance samples were obtained in the field range 7-70 μT. The effect of frequency, strength, direction and phase of a low frequency external disturbance field on the NMR spectra was investigated. A sinusoidal field was applied along or perpendicular to the measurement field to simulate the external disturbance. The results were compared with the numerical calculations based on the Bloch equation and good agreement was obtained. In all cases, the field disturbance less than a few Hz are proved to influence the NMR spectra more severely, suppressing the resonance peak and driving it into split bands. On the other hand, the influence of the disturbance field at the frequency range around 50 Hz on the resonance peak position and profile is small, even though some additional small peaks appear in the spectra due to frequency mixing. The effect is more significant when the disturbance field is along the direction of the measurement field. The phase difference between the disturbance field and the free-induction-decay signal could change the NMR peak position and profile drastically.

Fabrication of Al/AlOx/Al Josephson junctions and superconducting quantum circuits by shadow evaporation and a dynamic oxidation process

Besides serving as promising candidates for realizing quantum computing, superconducting quantum circuits are one of a few macroscopic physical systems in which fundamental quantum phenomena can be directly demonstrated and tested, giving rise to a vast field of intensive research work both theoretically and experimentally. In this paper we report our work on the fabrication of superconducting quantum circuits, starting from its building blocks: Al/AlOx/Al Josephson junctions. By using electron beam lithography patterning and shadow evaporation, we have fabricated aluminum Josephson junctions with a controllable critical current density (jc) and wide range of junction sizes from 0.01 μm2 up to 1 μm2. We have carried out systematical studies on the oxidation process in fabricating Al/AlOx/Al Josephson junctions suitable for superconducting flux qubits. Furthermore, we have also fabricated superconducting quantum circuits such as superconducting flux qubits and charge-flux qubits.

Flux qubit with a large loop size and tunable Josephson junctions

We present the design of a superconducting flux qubit with a large loop inductance. The large loop inductance is desirable for coupling between qubits. The loop is configured into a gradiometer form that could reduce the interference from environmental magnetic noise. A combined Josephson junction, i.e., a DC-SQUID is used to replace the small Josephson junction in the usual 3-JJ (Josephaon junction) flux qubit, leading to a tunable energy gap by using an independent external flux line. We perform numerical calculations to investigate the dependence of the energy gap on qubit parameters such as junction capacitance, critical current, loop inductance, and the ratio of junction energy between small and large junctions in the flux qubit. We suggest a range of values for the parameters.

Fabrication and characterization of ultra-low noise narrow and wide band Josephson parametric amplifiers*

We have fabricated two types of lumped-element Josephson parameter amplifiers (JPAs) by using a multilayer micro-fabrication process involving wet etching of Al films. The first type is a narrow band JPA which shows typical gain above 14 dB in a bandwidth around 35 MHz. The second type is a wideband JPA which is coupled to an input 50 Ω transmission line via an impedance transformer that changes the impedance from about 15 Ω on the non-linear resonator side to 50 Ω on the input transmission line side. The wideband JPA could operate in a 200 MHz range with a gain higher than 14 dB. The amplifiers were used for superconducting qubit readout. The results showed that the signal to noise ratio and hence the readout fidelity were improved significantly.

Design of a gap tunable flux qubit with FastHenry

In the preparations of superconducting qubits, circuit design is a vital process because the parameters and layout of the circuit not only determine the way we address the qubits, but also strongly affect the qubit coherence properties. One of the most important circuit parameters, which needs to be carefully designed, is the mutual inductance among different parts of a superconducting circuit. In this paper we demonstrate how to design a gap-tunable flux qubit by layout design and inductance extraction using a fast field solver FastHenry. The energy spectrum of the gap-tunable flux qubit shows that the measured parameters are close to the design values.

Working Point Adjustable DC-SQUID for the Readout of Gap Tunable Flux Qubit

In flux qubits, qubit states are commonly read out by a dc superconducting quantum interference device (SQUID), which is inductively coupled to the qubit and works as a persistent current detector. However, neither the bottom nor the top regions of the critical current modulation curve of the SQUID can be used for the readout. In this paper, we show that a flux-trap loop inserted to the readout SQUID provides the ability to adjust the working point, which helps to avoid this constraint. This improvement is useful for some complicated flux qubit experiments.

Ultra-Low-Field MRI and Spin-Lattice Relaxation Time of

We have carried out ultra-low-field nuclear magnetic resonance (NMR) and magnetic resonance imaging experiments in microtesla magnetic fields using a high-Tc dc-SQUID sensor. The measurements were carried out in a home-made magnetically shielded room. NMR spectra of 1H from tap water and other substance samples were obtained in the field range from 10-200 μT. By adapting a transformer coupled detection system, the signal-to-noise ratio of NMR peak in a single-shot measurement for 10 ml tap water was increased significantly as compared with our previously used direct detection method. The improvement was attributed to the increased coupling efficiency and reduced SQUID noise. By applying magnetic field gradient in three directions, one- and two-dimensional imaging results were obtained from water phantom samples. Furthermore, the effect of Fe3O4 magnetic nanoparticles on the spin-lattice relaxation time T1 was studied.

^{1}\hbox{H}

Measurements of three-junction flux qubits, both single flux qubits and coupled flux qubits, using a coupled direct current superconducting quantum interference device (dc-SQUID) for readout are reported. The measurement procedure is described in detail. We performed spectroscopy measurements and coherent manipulations of the qubit states on a single flux qubit, demonstrating quantum energy levels and Rabi oscillations, with Rabi oscillation decay time TRabi = 78 ns and energy relaxation time T1 = 315 ns. We found that the value of TRabi depends strongly on the mutual inductance between the qubit and the magnetic coil. We also performed spectroscopy measurements on inductively coupled flux qubits.

in the Presence of

We study two flux qubits with a parameter coupling scenario. Under the rotating wave approximation, we truncate the 4-dimensional Hilbert space of a coupling flux qubits system to a 2-dimensional subspace spanned by two dressed states vertical bar 01 > and vertical bar 10 >. In this subspace, we illustrate how to generate an Aharnov-Anandan phase, based on which, we can construct a NOT gate (as effective as a C-NOT gate) in this coupling flux qubits system. Finally, the fidelity of the NOT gate is also calculated in the presence of the simulated classical noise.