Xmon Qubit Research Articles

Locating Two-Level Systems in a Superconducting Xmon Qubit

One significant source of decoherence in superconducting circuits is known as two-level systems (TLSs), found in amorphous oxide layers. These circuits can, however, also be utilized as spectral and temporal TLS probes. Comprehensive investigations on the physics of TLSs are now possible thanks to recent advancements in superconducting qubits. Here, we simultaneously measure the tunable Xmon qubit decoherence time as well as the resonance frequency for more than 3 days to investigate stochastic fluctuations. Time-domain Allan deviation and frequency-domain power spectral density analysis indicate that two TLSs in near resonance with the qubit are responsible for the fluctuations. From the extracted oscillation in T1 decay, we locate the two TLSs near the junctions.

Frequency Adjustable Resonator as a Tunable Coupler for Xmon Qubits

We propose a scheme of tunable coupler based on a frequency adjustable resonator for scalable quantum integrated circuits. One side of the T-shape quarter-wave resonator is short to the ground through a DC SQUID, which is used to tune the frequency of the resonator coupler. In the other side with two open ends, either end capacitively couples to a different Xmon qubit, which determines the effective coupling between the two qubits. The fundamental mode of the tunable resonator dominates the interaction with the qubits and functions as a tunable coupler to switch off/on the qubit–qubit interaction. The required external magnetic flux for the tunable coupler’s switching off frequency is affected by the asymmetry degree of the DC SQUID, which can help to choose a better noise environment (of the qubits) induced by the resonator coupler. The T-shape tunable resonator can help to reduce the direct interaction between two qubits, which should be an important way to suppress the ZZ crosstalk and realize high-fidelity quantum gates. The DC SQUID is several millimeters away from the Xmon qubits, which in principle creates less flux noises compared with the transmon-type coupler.

Experimental realization of nonadiabatic geometric gates with a superconducting Xmon qubit

Geometric phases are only dependent on evolution paths but independent of evolution details so that they possess some intrinsic noise-resilience features. Based on different geometric phases, various quantum gates have been proposed, such as nonadiabatic geometric gates based on nonadiabatic Abelian geometric phases and nonadiabatic holonomic gates based on nonadiabatic non-Abelian geometric phases. Up to now, nonadiabatic holonomic one-qubit gates have been experimentally demonstrated with superconducting transmons, where the three lowest levels are all utilized in operation. However, the second excited state of transmons has a relatively short coherence time, which results in a decreased fidelity of quantum gates. Here, we experimentally realize Abelian-geometric-phase-based nonadiabatic geometric one-qubit gates with a superconducting Xmon qubit. The realization is performed on the two lowest levels of an Xmon qubit and thus avoids the influence from the short coherence time of the second excited state. The experimental result indicates that the average fidelities of single-qubit gates can be up to 99.6% and 99.7% characterized by quantum process tomography and randomized benchmarking.

Simplified Josephson-junction fabrication process for reproducibly high-performance superconducting qubits

We introduce a simplified fabrication technique for Josephson junctions and demonstrate superconducting Xmon qubits with T1 relaxation times averaging above 50 μs (Q>1.5×106). Current shadow-evaporation techniques for aluminum-based Josephson junctions require a separate lithography step to deposit a patch that makes a galvanic, superconducting connection between the junction electrodes and the circuit wiring layer. The patch connection eliminates parasitic junctions, which otherwise contribute significantly to dielectric loss. In our patch-integrated cross-type junction technique, we use one lithography step and one vacuum cycle to evaporate both the junction electrodes and the patch. This eliminates a key bottleneck in manufacturing superconducting qubits by reducing the fabrication time and cost. In a study of more than 3600 junctions, we show an average resistance variation of 3.7% on a wafer that contains forty 0.5×0.5-cm2 chips, with junction areas ranging between 0.01 and 0.16 μm2. The average on-chip spread in resistance is 2.7%, with 20 chips varying between 1.4% and 2%. For the junction sizes used for transmon qubits, we deduce a wafer-level transition-frequency variation of 1.7%–2.5%. We show that 60%–70% of this variation is attributed to junction-area fluctuations, while the rest is caused by tunnel-junction inhomogeneity. Such high frequency predictability is a requirement for scaling-up the number of qubits in a quantum computer.

A wideband cryogenic microwave low-noise amplifier.

A broadband low-noise four-stage high-electron-mobility transistor amplifier was designed and characterized in a cryogen-free dilution refrigerator at the 3.8 K temperature stage. The obtained power dissipation of the amplifier is below 20 mW. In the frequency range from 6 to 12 GHz its gain exceeds 30 dB. The equivalent noise temperature of the amplifier is below 6 K for the presented frequency range. The amplifier is applicable for any type of cryogenic microwave measurements. As an example we demonstrate here the characterization of the superconducting X-mon qubit coupled to an on-chip coplanar waveguide resonator.

Simultaneous Feedback and Feedforward Control and Its Application to Realize a Random Walk on the Bloch Sphere in an Xmon-Superconducting-Qubit System

Measurement-based feedback control is central in quantum computing and precise quantum control. Here we realize a fast and flexible field-programmable-gate-array-based feedback control in a superconducting Xmon qubit system. The latency of room-temperature electronics is custom optimized to be as short as 140 ns. Projective measurement of a signal qubit produces a feedback tag to actuate a conditional pulse gate to the qubit. In a feed-forward process, the measurement-based feedback tag is brought to a different target qubit for a conditional control. In a two-qubit experiment, the feedback and feed-forward controls are simultaneously actuated in consecutive steps. A quantum number is then generated by the signal qubit, and a random walk of the target qubit is correspondingly triggered and realized on the Bloch sphere. Our experiment provides a conceptually simple and intuitive benchmark for the feedback control in a multi-qubit system. The feedback system can be further scaled up for more complex feedback control experiments.

Landau–Zener–Stückelberg Interference in Nonlinear Regime**Supported by the National Natural Science Foundation of China under Grant No 11874065, the Key R&D Program of Guangdong Province under Grant No 2018B030326001, the Guangdong Innovative and Entrepreneurial Research Team Program under Grant No 2016ZT06D348, the Natural Science Foundation of Guangdong Province under Grant No 2017B030308003, the Natural Science Foundation of Hunan Province under Grant

Landau–Zener–Stückelberg (LZS) interference has drawn renewed attention to quantum information processing research because it is not only an effective tool for characterizing two-level quantum systems but also a powerful approach to manipulate quantum states. Superconducting quantum circuits, due to their versatile tunability and degrees of control, are ideal platforms for studying LZS interference phenomena. We use a superconducting Xmon qubit to study LZS interference by parametrically modulating the qubit transition frequency nonlinearly. For dc flux biasing of the qubit slightly far away from the optimal flux point, the qubit excited state population shows an interference pattern that is very similar to the standard LZS interference in linear regime, except that all bands shift towards lower frequencies when increasing the rf modulation amplitude. For dc flux biasing close to the optimal flux point, the negative sidebands and the positive sidebands behave differently, resulting in an asymmetric interference pattern. The experimental results are also in good agreement with our analytical and numerical simulations.

Tunable coupling between Xmon qubit and coplanar waveguide resonator**Project supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0304300 and 2016YFA0300600), the National Natural Science Foundation of China (Grant Nos. 11725419 and 11434008), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000).

Realization of a flexible and tunable coupling scheme among qubits is critical for scalable quantum information processing. Here, we design and characterize a tunable coupling element based on Josephson junction, which can be adapted to an all-to-all connected circuit architecture where multiple Xmon qubits couple to a common coplanar waveguide resonator. The coupling strength is experimentally verified to be adjustable from 0 MHz to about 40 MHz, and the qubit lifetime can still be up to in the presence of the coupling element.

Topology-dependent quantum dynamics and entanglement-dependent topological pumping in superconducting qubit chains

We propose a protocol using a tunable Xmon qubit chain to construct generalized Su-Schrieffer-Heeger (SSH) models that support various topological phases. We study the time evolution of a single-excitation quantum state in a SSH-type qubit chain and find that such dynamics is linked to topological winding number. We also investigate the adiabatic transfer of a single-excitation quantum state in a generalized SSH-type qubit chain and show that this process can be connected with topological Chern number and be used to generate a novel entanglement-dependent topological pumping. All results have been demonstrated to be robust against qubit coupling imperfections and can be observed in a short Xmon qubit chain. Our study provides a simple method to directly measure topological invariants rooted in momentum space using quantum dynamics in real space.

Experimental demonstration of work fluctuations along a shortcut to adiabaticity with a superconducting Xmon qubit

In a ‘shortcut to adiabaticity’ (STA) protocol, the counter-diabatic Hamiltonian, which suppresses the non-adiabatic transition of a reference ‘adiabatic’ trajectory, induces a quantum uncertainty of the work cost in the framework of quantum thermodynamics. Following a theory derived recently (Funo et al 2017 Phys. Rev. Lett. 118 100602), we perform an experimental measurement of the STA work statistics in a high-quality superconducting Xmon qubit. Through the frozen-Hamiltonian and frozen-population techniques, we experimentally realize the two-point measurement of the work distribution for given initial eigenstates. Our experimental statistics verify (i) the conservation of the average STA work and (ii) the equality between the STA excess of work fluctuations and the quantum geometric tensor.

Robust quantum state transfer via topological edge states in superconducting qubit chains

Robust quantum state transfer (QST) is an indispensable ingredient in scalable quantum information processing. Here we present an experimentally feasible mechanism for realizing robust QST via topologically protected edge states in superconducting qubit chains. Using superconducting Xmon qubits with tunable couplings, we construct generalized Su-Schrieffer-Heeger models and analytically derive the wave functions of topological edge states. We find that such edge states can be employed as a quantum channel to realize robust QST between remote qubits. With a numerical simulation, we show that both single-qubit states and two-qubit entangled states can be robustly transferred in the presence of sizable imperfections in the qubit couplings. The transfer fidelity demonstrates a wide plateau at the value of unity in the imperfection magnitude. This approach is general and can be implemented in a variety of quantum computing platforms.

Cavity-induced ATS effect on a superconducting Xmon qubit**Project supported by the Science Funds from the Ministry of Science and Technology of China (Grant Nos. 2014CB921401, 2017YFA0304300, 2014CB921202, and 2016YFA0300601), the National Natural Science Foundation of China (Grant No. 11674376), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB07010300).

We couple a ladder-type three-level superconducting artificial atom to a cavity. Adjusting the artificial atom to make the cavity be resonant with the two upper levels, we then probe the lower two levels of the artificial atom. When driving the cavity to a coherent state, the probe spectrum shows energy level splitting induced by the quantized electromagnetic field in the cavity. This splitting size is related to the coupling strength between the cavity and the artificial atom and, thus, is fixed after the sample is fabricated. This is in contrast to the classical Autler–Townes splitting of a three-level system in which the splitting is proportional to the driving amplitude, which can be continuously changed. Our experiment results show the difference between the classical microwave driving field and the quantum field of the cavity.

Modulation of energy spectrum and control of coherent microwave transmission at single-photon level by longitudinal field in a superconducting quantum circuit**Project supported by the Ministry of Science and Technology of China (Grant Nos. 2014CB921401, 2017YFA0304300, 2014CB921202, and 2016YFA0300601), the National Natural Science Foundation of China (Grant No. 11674376), and the Strategic Priority Research Program of the Chinese Academy of Sciences

We study the effect of longitudinally applied field modulation on a two-level system using superconducting quantum circuits. The presence of the modulation results in additional transitions and changes the magnitude of the resonance peak in the energy spectrum of the qubit. In particular, when the amplitude λz and the frequency ωl of the modulation field meet certain conditions, the resonance peak of the qubit disappears. Using this effect, we further demonstrate that the longitudinal field modulation of the Xmon qubit coupled to a one-dimensional transmission line could be used to dynamically control the transmission of single-photon level coherent resonance microwave.

The experimental realization of high-fidelity ‘shortcut-to-adiabaticity’ quantum gates in a superconducting Xmon qubit

Based on a ‘shortcut-to-adiabaticity’ (STA) scheme, we theoretically design and experimentally realize a set of high-fidelity single-qubit quantum gates in a superconducting Xmon qubit system. Through a precise microwave control, the qubit is driven to follow a fast ‘adiabatic’ trajectory with the assistance of a counter-diabatic field and the correction of derivative removal by adiabatic gates. The experimental measurements of quantum process tomography and interleaved randomized benchmarking show that the process fidelities of our STA quantum gates are higher than 94.9% and the gate fidelities are higher than 99.8%, very close to the state-of-art gate fidelity of 99.9%. An alternate of high-fidelity quantum gates is successfully achieved under the STA protocol.

Novel superconducting qubits and quantum physics

In the past years, superconducting quantum computation has received much attention and significant progress of the device design and fabrication has been made, which leads qubit coherence times to be improved greatly. Recently, we have successfully designed, fabricated, and tested the superconducting qubits based on the negative-inductance superconducting quantum interference devices (nSQUIDs), which are expected to have the advantages for the fast quantum information transfer and macroscopic quantum phenomenon study with a two-dimensional potential landscape. Their quantum coherence and basic physical properties have been demonstrated and systematically investigated. On the other hand, a new type of superconducting qubit, called transmon and Xmon qubit, has been developed in the meantime by the international community, whose coherence time has been gradually increased to the present scale of tens of microseconds. These devices are demonstrated to have many advantages in the sample design and fabrication, and multi-qubit coupling and manipulation. We have also studied this type of superconducting qubit. In collaboration with Zhejiang University and the University of Science and Technology of China, we have successfully fabricated various types of the coupled Xmon devices having the qubit numbers ranging from 4 to 10. Quantum entanglement, quantum algorithm of solving coupled linear equations, and quantum simulation of the many-body localization problem in solid-state physics have been demonstrated by using these devices. Also, we have made significant achievements in the studies of the macroscopic quantum phenomena, quantum dissipation, quantum microwave lasing, and some other quantum optics problems. In particular, Autler-Townes splitting under strong microwave drive, electromagnetically induced transparency, stimulated Raman adiabatic passage, microwave mixing, correlated emission lasing, and microwave frequency up-and-down conversion have been successfully studied, both experimentally and theoretically.

Characterization and reduction of capacitive loss induced by sub-micron Josephson junction fabrication in superconducting qubits

Josephson junctions form the essential non-linearity for almost all superconducting qubits. The junction is formed when two superconducting electrodes come within ∼1 nm of each other. Although the capacitance of these electrodes is a small fraction of the total qubit capacitance, the nearby electric fields are more concentrated in dielectric surfaces and can contribute substantially to the total dissipation. We have developed a technique to experimentally investigate the effect of these electrodes on the quality of superconducting devices. We use λ/4 coplanar waveguide resonators to emulate lumped qubit capacitors. We add a variable number of these electrodes to the capacitive end of these resonators and measure how the additional loss scales with the number of electrodes. We then reduce this loss with fabrication techniques that limit the amount of lossy dielectrics. We then use these techniques for the fabrication of Xmon qubits on a silicon substrate to improve their energy relaxation times by a factor of 5.

Robust surface code topology against sparse fabrication defects in a superconducting-qubit array

Superconducting qubits arrays have become one of the most promising architectures for the practical implementation of universal quantum computing with quantum error correction codes. Here we propose a defect-tolerant surface code topology which is resistant to sparse fabrication defects. The topology is equivalent to a disk folded into $N$ layers. A physically defective qubit can be replaced with a working physical qubit within the same unit cell from a different layer. Thereby sparse fabrication errors can be collected into one sacrificial layer and isolated from the working layers by turning off their controllable couplers. We propose two schemes to realize this robust topology. One is to use flux qubits, and the other is based on Xmon qubits. A modified quantum circuit for the stabilization cycle of the Xmon qubits scheme is developed. We calculate and compare the per-operation error thresholds for these two schemes and find that the error threshold for the modified quantum circuit is close to that for the original stabilization cycle. A possible way to implement the intersecting connections between different Xmon qubits on the circuit level is also provided.

Quantum theory of a bandpass Purcell filter for qubit readout

The readout fidelity of superconducting transmon and Xmon qubits is partially limited by the qubit energy relaxation through the resonator into the transmission line, which is also known as the Purcell effect. One way to suppress this energy relaxation is to employ a filter which impedes microwave propagation at the qubit frequency. We present semiclassical and quantum analyses for the bandpass Purcell filter realized by E.\ Jeffrey \textit{et al}.\ [Phys.\ Rev.\ Lett.\ 112, 190504 (2014)]. For typical experimental parameters, the bandpass filter suppresses the qubit relaxation rate by up to two orders of magnitude while maintaining the same measurement rate. We also show that in the presence of a microwave drive the qubit relaxation rate further decreases with increasing drive strength.

Tunable coupler for superconducting Xmon qubits: Perturbative nonlinear model

We study a recently demonstrated design for a high-performance tunable coupler suitable for superconducting Xmon and planar transmon qubits [Y. Chen et al., Phys. Rev. Lett. 113, 220502 (2014)]. The coupler circuit uses a single flux-biased Josephson junction and acts as a tunable current divider. We calculate the effective qubit-qubit interaction Hamiltonian by treating the nonlinearity of the qubit and coupler junctions perturbatively. We find that the qubit nonlinearity has two principal effects: The first is to suppress the magnitude of the transverse ${\ensuremath{\sigma}}^{x}\ensuremath{\bigotimes}{\ensuremath{\sigma}}^{x}$ coupling from that obtained in the harmonic approximation by about 15%, assuming typical qubit parameters. The second is to induce a small diagonal ${\ensuremath{\sigma}}^{z}\ensuremath{\bigotimes}{\ensuremath{\sigma}}^{z}$ coupling. The effects of the coupler junction nonlinearity are negligible in the parameter regime considered. The approach used here can be applied to other complex nonlinear circuits arising in the design of superconducting hardware for quantum information processing.

Compressed sensing quantum process tomography for superconducting quantum gates

We apply the method of compressed sensing (CS) quantum process tomography (QPT) to characterize quantum gates based on superconducting Xmon and phase qubits. Using experimental data for a two-qubit controlled-Z gate, we obtain an estimate for the process matrix $\chi$ with reasonably high fidelity compared to full QPT, but using a significantly reduced set of initial states and measurement configurations. We show that the CS method still works when the amount of used data is so small that the standard QPT would have an underdetermined system of equations. We also apply the CS method to the analysis of the three-qubit Toffoli gate with numerically added noise, and similarly show that the method works well for a substantially reduced set of data. For the CS calculations we use two different bases in which the process matrix $\chi$ is approximately sparse, and show that the resulting estimates of the process matrices match each ther with reasonably high fidelity. For both two-qubit and three-qubit gates, we characterize the quantum process by not only its process matrix and fidelity, but also by the corresponding standard deviation, defined via variation of the state fidelity for different initial states.