Flux Qubit Research Articles

Capacitive coupling of coherent quantum phase slip qubits to a resonator

We demonstrate capacitive coupling of coherent quantum phase slip (CQPS) flux qubits to a resonator patterned on a highly disordered TiN film. We are able to detect and characterise CQPS flux qubits with linewidths down to on several resonator modes, and show that, unlike inductive coupling, here the coupling strength does not depend on the qubit’s energy. Since the qubit is galvanically decoupled from the resonator, our approach provides flexibility in material, design and fabrication choices for CQPS-based devices. Our results are two-fold: we report CQPS in TiN and demonstrate, to our knowledge for the first time, capacitive coupling of a CQPS flux qubit.

Efficient scheme for implementing a hybrid Toffoli gate with two NV ensembles simultaneously controlling a single superconducting qubit

The Toffoli gate is a three-qubit controlled-controlled-NOT gate, which plays a central role in quantum information processing and quantum computing. Recently, hybrid systems and hybrid quantum gates have attracted much attention. We propose an efficient scheme to implement a hybrid Toffoli gate with two nitrogen-vacancy center ensembles (NV ensembles) as the control qubits and a single superconducting flux qubit as the target qubit. This hybrid Toffoli gate is realized by employing two NV ensembles coupled to a superconducting qutrit. The hybrid Toffoli gate is constructed by a controlled-controlled-phase (CCPHASE) gate sandwiched between two Hadamard gates applied on the target qubit. Since the CCPHASE gate is realized using only a single-step operation and no conventional gate decomposition protocol is applied, the Toffoli-gate implementation is greatly simplified. Because the higher energy level of the flux qutrit is not populated, the decoherence of this level is greatly suppressed. In addition, our hybrid Toffoli gate can be used to generate a hybrid Greenberger–Horne–Zeilinger entangled state of a flux qubit and two NV ensembles. Numerical simulations demonstrate that high-fidelity implementation of a hybrid Toffoli gate is feasible within current experimental technology. This proposal is universal and can be applied to accomplish the same task in a wide range of physical systems.

Dynamics of Dispersive Measurements of Flux-Qubit States: Energy-Level Splitting Connected to Quantum Wave Mechanics.

Superconducting flux qubits have many advantages as a storage of quantum information, such as broad range tunability of frequency, small-size fabricability, and high controllability. In the flux qubit-oscillator, qubits are connected to SQUID resonators for the purpose of performing dispersive non-destructive readouts of qubit signals with high fidelity. In this work, we propose a theoretical model for analyzing quantum characteristics of a flux qubit-oscillator on the basis of quantum solutions obtained using a unitary transformation approach. The energy levels of the combined system (qubit + resonator) are analyzed in detail. Equally spaced each energy level of the resonator splits into two parts depending on qubit states. Besides, coupling of the qubit to the resonator brings about an additional modification in the split energy levels. So long as the coupling strength and the tunnel splitting are not zero but finite values, the energy-level splitting of the resonator does not disappear. We conclude that quantum nondemolition dispersive measurements of the qubit states are possible by inducing bifurcation of the resonator states through the coupling.

High Dimensional Quantum Machine Learning With Small Quantum Computers

Quantum computers hold great promise to enhance machine learning, but their current qubit counts restrict the realisation of this promise. To deal with this limitation the community has produced a set of techniques for evaluating large quantum circuits on smaller quantum devices. These techniques work by evaluating many smaller circuits on the smaller machine, that are then combined in a polynomial to replicate the output of the larger machine. This scheme requires more circuit evaluations than are practical for general circuits. However, we investigate the possibility that for certain applications many of these subcircuits are superfluous, and that a much smaller sum is sufficient to estimate the full circuit. We construct a machine learning model that may be capable of approximating the outputs of the larger circuit with much fewer circuit evaluations. We successfully apply our model to the task of digit recognition, using simulated quantum computers much smaller than the data dimension. The model is also applied to the task of approximating a random 10 qubit PQC with simulated access to a 5 qubit computer, even with only relatively modest number of circuits our model provides an accurate approximation of the 10 qubit PQCs output, superior to a neural network attempt. The developed method might be useful for implementing quantum models on larger data throughout the NISQ era.

Coherent Quantum Network of Superconducting Qubits as a Highly Sensitive Detector of Microwave Photons for Searching of Galactic Axions

We propose a novel approach to detect a low power microwave signal with a frequency of the order of several GHz based on a coherent collective response of quantum states occurring in a superconducting qubits network (SQN). An SQN composes of a large number of superconducting qubits embedded in a low-dissipative superconducting resonator. Our theory predicts that an SQN interacting with the off-resonance microwave radiation, demonstrates the collective alternating current Stark effect that can be measured even in the limit of single photon counting. A design of the layout of three terminals SQN detectors containing 10 flux qubits weakly coupled to a low-dissipative R-resonator and T-transmission line was developed. The samples were fabricated by Al-based technology with Nb resonator. The SQN detector was tested in terms of microwave measurements of scattering parameters and two-tone spectroscopy. A substantial shift of the frequency position of the transmission coefficient drop induced by a second tone pump signal was observed, and this effect clearly manifests a nonlinear multiphoton interaction between the second-tone microwave pump signal and an array of qubits.

Probing the symmetry breaking of a light–matter system by an ancillary qubit

Hybrid quantum systems in the ultrastrong, and even more in the deep-strong, coupling regimes can exhibit exotic physical phenomena and promise new applications in quantum technologies. In these nonperturbative regimes, a qubit–resonator system has an entangled quantum vacuum with a nonzero average photon number in the resonator, where the photons are virtual and cannot be directly detected. The vacuum field, however, is able to induce the symmetry breaking of a dispersively coupled probe qubit. We experimentally observe the parity symmetry breaking of an ancillary Xmon artificial atom induced by the field of a lumped-element superconducting resonator deep-strongly coupled with a flux qubit. This result opens a way to experimentally explore the novel quantum-vacuum effects emerging in the deep-strong coupling regime.

Extremely large Lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator

We report experimental and theoretical results on the extremely large Lamb shift in a multimode circuit quantum electrodynamics (QED) system in the deep-strong coupling (DSC) regime, where the qubit-resonator coupling strength is comparable to or larger than the qubit and resonator frequencies. The system comprises a superconducting flux qubit (FQ) and a quarter-wavelength coplanar waveguide resonator (lambda /4 CPWR) that are coupled inductively through a shared edge that contains a Josephson junction to achieve the DSC regime. Spectroscopy is performed around the frequency of the fundamental mode of the CPWR, and the spectrum is fitted by the single-mode quantum Rabi Hamiltonian to obtain the system parameters. Since the qubit is also coupled to a large number of higher modes in the resonator, the single-mode fitting does not provide the bare qubit energy but a value that incorporates the renormalization from all the other modes. We derive theoretical formulas for the Lamb shift in the multimode resonator system. As shown in previous studies, there is a cut-off frequency omega _{textrm{cutoff}} for the coupling between the FQ and the modes in the CPWR, where the coupling grows as sqrt{omega _n} for omega _n/omega _{textrm{cutoff}}ll 1 and decreases as 1/sqrt{omega _n} for omega _n/omega _{textrm{cutoff}}gg 1. Here omega _n is the frequency of the nth mode. The cut-off effect occurs because the qubit acts as an obstacle for the current in the resonator, which suppresses the current of the modes above omega _{textrm{cutoff}} at the location of the qubit and results in a reduced coupling strength. Using our observed spectrum and theoretical formulas, we estimate that the Lamb shift from the fundamental mode is 82.3% and the total Lamb shift from all the modes is 96.5%. This result illustrates that the coupling to the large number of modes in a CPWR yields an extremely large Lamb shift but does not suppress the qubit energy to zero, which would happen in the absence of a high-frequency cut-off.

Two-qubit quantum nonlocality dynamics induced by interacting of two coupled superconducting flux qubits with a resonator under intrinsic decoherence

This paper explores the dynamics of two spatially separated superconducting flux qubits, initially in a maximally correlated state, without mutual interaction. The system is modeled using the master intrinsic decoherence equation with the flux-qubits-resonator interaction Hamiltonian. The effects of initial state, detuning, and decoherence on the generated oscillatory correlation dynamics and the sudden death-birth phenomenon of the two flux-qubits entanglement are examined. The results demonstrate that qubit-resonator-qubit interactions have a high ability to generate quantum interferometric power and local quantum uncertainty correlations beyond that of concurrence entanglement.

Semiconductor spin qubits

Spin qubits, employing the fundamental quantum property of intrinsic angular momentum of individual electrons and nuclei, continue to develop and evolve. Lithographically patterned semiconductor chips play host to spin-qubit systems in which long coherence times, high-fidelity quantum gates, and single-shot quantum measurement are now routine. This review summarizes progress in four current qubit types: single spin qubits, donor spin qubits, singlet triplet spin qubits, and exchange-only spin qubits. All have been boosted by advances in mesoscopic physics. On the other hand, all systems still need to address challenges to further progress, such as the mitigation of noise and the establishment of long-distance quantum entanglement.

Evolution of 1/f Flux Noise in Superconducting Qubits with Weak Magnetic Fields.

The microscopic description of 1/f magnetic flux noise in superconducting circuits has remained an open question for several decades despite extensive experimental and theoretical investigation. Recent progress in superconducting devices for quantum information has highlighted the need to mitigate sources of qubit decoherence, driving a renewed interest in understanding the underlying noise mechanism(s). Though a consensus has emerged attributing flux noise to surface spins, their identity and interaction mechanisms remain unclear, prompting further study. Here, we apply weak in-plane magnetic fields to a capacitively shunted flux qubit (where the Zeeman splitting of surface spins lies below the device temperature) and study the flux-noise-limited qubit dephasing, revealing previously unexplored trends that may shed light on the dynamics behind the emergent 1/f noise. Notably, we observe an enhancement (suppression) of the spin-echo (Ramsey) pure-dephasing time in fields up to B=100 G. With direct noise spectroscopy, we further observe a transition from a 1/f to approximately Lorentzian frequency dependence below 10Hz and a reduction of the noise above 1MHz with increasing magnetic field. We suggest that these trends are qualitatively consistent with an increase of spin cluster sizes with magnetic field. These results should help to inform a complete microscopic theory of 1/f flux noise in superconducting circuits.

Signatures of Dissipation Driven Quantum Phase Transition in Rabi Model.

By using the worldline MonteCarlo technique, matrix product state, and a variational approach àla Feynman, we investigate the equilibrium properties and relaxation features of the dissipative quantum Rabi model, where a two level system is coupled to a linear harmonic oscillator embedded in a viscous fluid. We show that, in the Ohmic regime, a Beretzinski-Kosterlitz-Thouless quantum phase transition occurs by varying the coupling strength between the two level system and the oscillator. This is a nonperturbative result, occurring even for extremely low dissipation magnitude. By using state-of-the-art theoretical methods, we unveil the features of the relaxation towards the thermodynamic equilibrium, pointing out the signatures of quantum phase transition both in the time and frequency domains. We prove that, for low and moderate values of the dissipation, the quantum phase transition occurs in the deep strong coupling regime. We propose to realize this model by coupling a flux qubit and a damped LC oscillator.

Classical analogous quantum coherent superposition through the Hertz-type nonlinearity of elastic granules

The theory of quantum superposition of states is one of the fundamental concepts related to quantum information science and technology (QIST). Two or more pure quantum states can be superposed to get a distinct quantum state, and one of the examples is the quantum bit, or qubit, state. But decoherence makes it easy for the current qubits, the most critical part of QIST platforms, to lose their superposition of states. Therefore, we theoretically propose and experimentally realize a classical analogous to the coherent superposition of energy states through the Hertz-type nonlinearity of elastic granules driven externally. The granules’ nonlinear vibrations depend mutually through phase and form a coherent superposition when projected into linear modes of vibration. We demonstrate how the state vector components can emerge from the amplitudes of coherent states, spanning to the two-dimensional time-dependent parametric Hilbert space. These amplitudes represent an actual amplitude rather than a probability amplitude, which opens the possibility of exploring two-state quantum-like computations through the superposition of states without decoherence and wave function collapse. These characteristics make it possible to understand the material-based quantum analogous information technology through experimentation of elastic bit.

Tunable Superconducting Flux Qubits with Long Coherence Times

In this work, we study a series of tunable flux qubits inductively coupled to a coplanar waveguide resonator fabricated on a sapphire substrate. Each qubit includes an asymmetric superconducting quantum interference device which is controlled by the application of an external magnetic field and acts as a tunable Josephson junction. The tunability of the qubits is typically $\pm 3.5$ GHz around their central gap frequency. The measured relaxation times are limited by dielectric losses in the substrate and can attain $T_{1}\sim 8 \mu s$. The echo dephasing times are limited by flux noise even at optimal points and reach $T_{2E}\sim 4 \mu s$, almost an order of magnitude longer than state of the art for tunable flux qubits.

Probing flux and charge noise with macroscopic resonant tunneling

We report on measurements of flux and charge noise in an rf-SQUID flux qubit using macroscopic resonant tunneling (MRT). We measure rates of incoherent tunneling from the lowest energy state in the initial well to the ground and first excited states in the target well. The result of the measurement consists of two peaks. The first peak corresponds to tunneling to the ground state of the target well, and is dominated by flux noise. The second peak is due to tunneling to the excited state and is wider due to an intrawell relaxation process dominated by charge noise. We develop a theoretical model that allows us to extract information about flux and charge noise within one experimental setup. The model agrees very well with experimental data over a wide dynamic range and provides parameters that characterize charge and flux noise.

Magnetometry of neurons using a superconducting qubit

Iron plays important physiological and pathological roles in the human body. However, microscopic analysis including redox status by a conventional electron spin resonance (ESR) spectrometer is difficult due to limited spatial resolution and sensitivity. Here we demonstrate magnetometry of cultured neurons on a polymeric film using a superconducting flux qubit that works as a sensitive magnetometer in a microscale area towards realizing ESR spectroscopy. By changing temperature (12.5–200 mK) and a magnetic field (2.5–12.5 mT), we observe a clear magnetization signal from the neurons that is well above the control magnetometry of the polymeric film itself. From ESR spectrum measured at 10 K, the magnetization signal is identified to originate from electron spins of iron ions in neurons. This technique to detect a bio-spin system can be extended to achieve ESR spectroscopy at the single-cell level, which will give the spectroscopic fingerprint of cells.

Spin-wave-based tunable coupler between superconducting flux qubits

Quantum computing and simulation based on superconducting qubits have achieved significant progress and entered the noisy intermediate-scale quantum (NISQ) era recently. Using a third qubit or object as a tunable coupler between qubits is an important step in this process. In this article, we propose a hybrid system made of superconducting qubit and a yttrium iron garnet (YIG) system as an alternative way to realize this. YIG thin films have spin wave (magnon) modes with low dissipation and reliable control for quantum information processing. Here, we propose a scheme to achieve strong coherent coupling between superconducting (SC) flux qubits and magnon modes in YIG thin film. Unlike the direct $\sqrt{N}$ enhancement factor in coupling to the Kittel mode and other spin ensembles, with $N$ the total number of spins, an additional spatial-dependent phase factor needs to be considered when the qubits are magnetically coupled with the magnon modes of finite wavelength. To avoid undesirable cancellation of coupling caused by the symmetrical boundary condition, a CoFeB thin layer is added to one side of the YIG thin film to break the symmetry. Our numerical simulation demonstrates avoided crossing and coherent transfer of quantum information between the flux qubit and the standing spin waves in YIG thin films. We show that the YIG thin film can be used as a tunable coupler between two flux qubits, which have a modified shape with small direct inductive coupling between them. Our results manifest that by cancellation of direct inductive coupling and indirect spin-wave couple of flux qubits we can turn on and off the net coupling between qubits. This bring magnonic YIG thin film into the field of quantum information processing.

An RF SQUID readout for a flux qubit-based microwave single photon counter

An analysis of the measurement of the magnetic flux in superconducting qubits based on RF SQUIDs was carried out with an 800 MHz bandwidth low-power-consumption cryogenic high-electron-mobility transistor amplifier. The preliminary experimental results obtained at temperatures 2 K and 4 K for RF SQUIDs in hysteretic, and in two non-hysteretic, regimes with a pump frequency of about 30 MHz are discussed. Parameters of RF SQUIDs in the hysteretic and non-hysteretic modes are analyzed within the framework of the resistively and capacitively shunted junction model for Josephson junctions. Its sensitivity at a temperature of 30 mK and frequency band (speed) are calculated and optimized to read the states of a flux qubit used as a single microwave photon counter. It is shown that an RF SQUID, operated in an adiabatic non-hysteretic mode for qubit readout, allows us to minimize its back-action effect and the dark count rate. This is due to the absence of Josephson generation, the small amplitude of the resonator electromagnetic field, and the selection of the pump frequency that does not coincide with the characteristic frequencies of the flux qubit.

P T symmetry in a superconducting hybrid quantum system with longitudinal coupling.

We propose a scheme consisting of coupled nanomechanical cantilever resonators and superconducting flux qubits to engineer a parity-time- (P T-) symmetric phononic system formed by active and passive modes. The effective gain (loss) of the phonon mode is achieved by the longitudinal coupling of the resonator and the fast dissipative superconducting qubit with a blue-sideband driving (red-sideband driving). A P T-symmetric to broken-P T-symmetric phase transition can be observed in both balanced gain-to-loss and unbalanced gain-to-loss cases. Applying a resonant weak probe field to the dissipative resonator, we find that (i) for balanced gain and loss, the acoustic signal absorption to amplification can be tuned by changing the coupling strength between resonators; (ii) for unbalanced gain and loss, both acoustically induced transparency and anomalous dispersion can be observed around Δ = 0, where the maximum group delay is also located at this point. Our work provides an experimentally feasible scheme to design P T-symmetric phononic systems and a powerful platform for controllable acoustic signal transmission in a hybrid quantum system.

Submicrometer-scale temperature sensing using quantum coherence of a superconducting qubit

Interest is growing in the development of quantum sensing based on the principles of quantum mechanics, such as discrete energy levels, quantum superposition, and quantum entanglement. Superconducting flux qubits are quantum two-level systems whose energy is sensitive to a magnetic field. Therefore, they can be used as high-sensitivity magnetic field sensors that detect the magnetization of a spin ensemble. Since the magnetization depends on temperature and the magnetic field, the temperature can be determined by measuring the magnetization using the flux qubit. In this study, we demonstrated highly sensitive temperature sensing with high spatial resolution as an application of a magnetic field sensor using the quantum coherence of a superconducting flux qubit. By using a superconducting flux qubit to detect the temperature dependence of the polarization ratio of electron spins in nano-diamond particles, we succeeded in measuring the temperature with a sensitivity of 1.3 µKµ at T = 9.1 mK in the submicrometer range.

Topological phase transitions and topological quantum states modulated by the counter-rotating wave terms in a one-dimensional superconducting microwave cavity lattice

We propose a one-dimensional lattice theory scheme based on superconducting microwave cavities, which includes two different types of microwave cavity unit cells. The coupling between unit cells is controlled by flux qubits to simulate and study their topological insulator characteristics. Specifically, a one-dimensional superconducting microwave cavity lattice scheme with a p-wave superconducting pairing term is achieved by mapping the counter-rotating wave terms to the p-wave superconducting pairing term. We found that the p-wave superconducting pairing term can modulate the topological quantum state of the system, allowing for the creation of topological quantum information transmission channels with four edge states. In addition, when the p-wave superconducting pairing term and the nearest-neighbor interaction exist, we find that the energy band undergoes fluctuations, inducing the generation of new energy bands, but the degeneracy of the edge states remains stable, which can achieve multiple topological quantum state transmission paths. However, when its regulatory value exceeds the threshold, the energy gap of the system will close, causing the edge states to annihilate in new energy bands. Furthermore, when considering the existence of defects in the system, we found that when the strength of the defects are small, the edge state produces small fluctuations, but it can be clearly distinguished, indicating its robustness. When the strength of the defect exceeds the threshold, the edge state and energy band cause irregular fluctuations, allowing the edge state to integrate into the energy band. Our research results have important theoretical value and practical significance, and can be applied in quantum optics and quantum information processing in the future.