We analyze a two-level quantum system, describing the phase qubit, during a single-pulse readout process by a numerical solution of the time-dependent Schroedinger equation. It has been demonstrated that the readout error has a minimum for certain values of the system`s basic parameters. In particular, the optimization of the qubit capacitance and the readout pulse shape leads to significant reduction of the readout error. It is shown that in an ideal case the fidelity can be increased to almost 97% for 2 ns pulse duration and to 96% for 1 ns pulse duration.
An important desired ingredient of superconducting quantum circuits is a readout scheme whose complexity does not increase with the number of qubits involved in the measurement. Here, we present a readout scheme employing a single microwave line, which enables simultaneous readout of multiple qubits. Consequently, scaling up superconducting qubit circuits is no longer limited by the readout apparatus. Parallel readout of 6 flux qubits using a frequency division multiplexing technique is demonstrated, as well as simultaneous manipulation and time resolved measurement of 3 qubits. We discuss how…
We introduce a frequency-multiplexed readout scheme for superconducting phase qubits. Using a quantum circuit with four phase qubits, we couple each qubit to a separate lumped-element superconducting readout resonator, with the readout resonators connected in parallel to a single measurement line. The readout resonators and control electronics are designed so that all four qubits can be read out simultaneously using frequency multiplexing on the one measurement line. This technology provides a highly efficient and compact means for reading out multiple qubits, a significant advantage for scali…
We report single-shot readout of a superconducting flux qubit by using a flux-driven Josephson parametric amplifier (JPA). After optimizing the readout power, gain of the JPA and timing of the data acquisition, we observe the Rabi oscillations with a contrast of 74% which is mainly limited by the bandwidth of the JPA and the energy relaxation of the qubit. The observation of quantum jumps between the qubit eigenstates under continuous monitoring indicates the nondestructiveness of the readout scheme.
We present a new readout method for a superconducting flux qubit, based on the measurement of the Josephson inductance of a superconducting quantum interference device that is inductively coupled to the qubit. The intrinsic flux detection efficiency and back-action are suitable for a fast and nondestructive determination of the quantum state of the qubit, as needed for readout of multiple qubits in a quantum computer. We performed spectroscopy of a flux qubit and we measured relaxation times of the order of 80 $μs$.
We present a method for measuring the internal state of a superconducting qubit inside an on-chip microwave resonator. We show that one qubit state can be associated with the generation of an increasingly large cavity coherent field, while the other remains associated with the vacuum. By measuring the outgoing resonator field with conventional devices, an efficient single-shot QND-like qubit readout can be achieved, enabling a high-fidelity measurement in the spirit of the electron-shelving technique for trapped ions. We expect that the proposed ideas can be adapted to different superconductin…
We analyze a readout scheme for Majorana qubits based on dispersive coupling to a resonator. We consider two variants of Majorana qubits: the Majorana transmon and the Majorana box qubit. In both cases, the qubit-resonator interaction can produce sizeable dispersive shifts in the MHz range for reasonable system parameters, allowing for submicrosecond readout with high fidelity. For Majorana transmons, the light-matter interaction used for readout manifestly conserves Majorana parity, which leads to a notion of quantum nondemolition (QND) readout that is stronger than for conventional charge qu…
Developing fast and accurate control and readout techniques is an important challenge in quantum information processing with semiconductor qubits. Here, we study the dynamics and the coherence properties of a GaAs/AlGaAs double quantum dot (DQD) charge qubit strongly coupled to a high-impedance SQUID array resonator. We drive qubit transitions with synthesized microwave pulses and perform qubit readout through the state dependent frequency shift imparted by the qubit on the dispersively coupled resonator. We perform Rabi oscillation, Ramsey fringe, energy relaxation and Hahn-echo measurements …
We propose a quantum non-demolition Majorana qubit readout protocol based on parametricmodulation of a longitudinal interaction between a pair of Majorana bound states and a resonator. The interaction can be modulated through microwave frequency gate-voltage or flux control of a tunable tunnel barrier. The qubit-resonator coupling is quantum non-demolition to exponential accuracy, a property inherited from the topological nature of the Majorana zero modes. The same mechanism as used for single-qubit readout can also be extended to perform multi-qubit measurements and be used to enact long rang…
We study a readout scheme of superconducting flux qubit state with a Cooper pair box as a transmon. The qubit states consist of the superpositions of two degenerate states where the charge and phase degrees of freedom are entangled. Owing to the robustness of transmon against external fluctuations, our readout scheme enables the quantum non-demolition and single-shot measurement of flux qubit states. The qubit state readout can be performed by using the non-linear Josephson amplifiers after a $π/2$-rotation driven by an ac-electric field.
Solid-state qubits incorporating quantum dots can be read out by gate reflectometry. Here, we theoretically describe physical mechanisms that render such reflectometry-based readout schemes imperfect. We discuss charge qubits, singlet-triplet spin qubits, and Majorana qubits. In our model, we account for readout errors due to slow charge noise, and due to overdriving, when a too strong probe is causing errors. A key result is that for charge and spin qubits, the readout fidelity saturates at large probe strengths, whereas for Majorana qubits, there is an optimal probe strength which provides a…
The parametric phase-locked oscillator (PPLO), also known as a parametron, is a resonant circuit in which one of the reactances is periodically modulated. It can detect, amplify, and store binary digital signals in the form of two distinct phases of self-oscillation. Indeed, digital computers using PPLOs based on a magnetic ferrite ring or a varactor diode as its fundamental logic element were successfully operated in 1950s and 1960s. More recently, basic bit operations have been demonstrated in an electromechanical resonator, and an Ising machine based on optical PPLOs has been proposed. Here…
We show how to realize high-fidelity quantum non-demolition qubit readout using longitudinal qubit-oscillator interaction. This is realized by modulating the longitudinal coupling at the cavity frequency. The qubit-oscillator interaction then acts as a qubit-state dependent drive on the cavity, a situation that is fundamentally different from the standard dispersive case. Single-mode squeezing can be exploited to exponentially increase the signal-to-noise ratio of this readout protocol. We present an implementation of this idea in circuit quantum electrodynamics and a possible multi-qubit arch…
Single-shot qubit readout typically combines high readout contrast with long-lived readout signals, leading to large signal-to-noise ratios and high readout fidelities. In recent years, it has been demonstrated that both readout contrast and readout signal lifetime, and thus the signal-to-noise ratio, can be enhanced by forcing the qubit state to transition through intermediate states. In this work, we demonstrate that the sub-Poissonian relaxation statistics introduced by intermediate states can reduce the single-shot readout error rate by orders of magnitude even when there is no increase in…
Determination of qubit initialisation and measurement fidelity is important for the overall performance of a quantum computer. However, the method by which it is calculated in semiconductor qubits varies between experiments. In this paper we present a full theoretical analysis of electronic single-shot readout and describe critical parameters to achieve high fidelity readout. In particular, we derive a model for energy selective state readout based on a charge detector response and examine how to optimise the fidelity by choosing correct experimental parameters. Although we focus on single ele…
Accurate and precise detection of multi-qubit entanglement is key for the experimental development of quantum computation. Traditionally, non-classical correlations between entangled qubits are measured by counting coincidences between single-shot readouts of individual qubits. We report entanglement metrology using a single detection channel with direct access to ensemble-averaged correlations between two superconducting qubits. Following validation and calibration of this joint readout, we demonstrate full quantum tomography on both separable and highly-entangled two-qubit states produced on…
We propose and demonstrate a frequency-multiplexed readout scheme in 3D cQED architecture. We use four transmon qubits coupled to individual rectangular cavities which are aperture-coupled to a common rectangular waveguide feedline. A coaxial to waveguide transformer at the other end of the feedline allows one to launch and collect the multiplexed signal. The reflected readout signal is amplified by an impedance engineered broadband parametric amplifier with 380 MHz of bandwidth. This provides us high fidelity single-shot readout of multiple qubits using compact microwave circuitry, an efficie…
In a Rabi oscillation experiment with a superconducting qubit we show that a visibility in the qubit excited state population of more than 90 % can be attained. We perform a dispersive measurement of the qubit state by coupling the qubit non-resonantly to a transmission line resonator and probing the resonator transmission spectrum. The measurement process is well characterized and quantitatively understood. The qubit coherence time is determined to be larger than 500 ns in a measurement of Ramsey fringes.
In dispersive readout schemes, qubit-induced nonlinearity typically limits the measurement fidelity by reducing the signal-to-noise ratio (SNR) when the measurement power is increased. Contrary to seeing the nonlinearity as a problem, here we propose to use it to our advantage in a regime where it can increase the SNR. We show analytically that such a regime exists if the qubit has a many-level structure. We also show how this physics can account for the high-fidelity avalanchelike measurement recently reported by Reed {\it et al.} [arXiv:1004.4323v1].
We observe measurement-induced qubit state mixing in a transmon qubit dispersively coupled to a planar readout cavity. Our results indicate that dephasing noise at the qubit-readout detuning frequency is up-converted by readout photons to cause spurious qubit state transitions, thus limiting the nondemolition character of the readout. Furthermore, we use the qubit transition rate as a tool to extract an equivalent flux noise spectral density at f ~ 1 GHz and find agreement with values extrapolated from a $1/f^α$ fit to the measured flux noise spectral density below 1 Hz.
We analyze the dispersive readout of superconducting charge and flux qubits as a quantum measurement process. The measurement oscillator frequency is considered much lower than the qubit frequency. This regime is interesting because large detuning allows for strong coupling between the measurement oscillator and the signal transmission line, thus allowing for fast readout. Due to the large detuning we may not use the rotating wave approximation in the oscillator-qubit coupling. Instead we start from an approximation where the qubit follows the oscillator adiabatically, and show that non-adiaba…
Quantum systems must be prepared, controlled, and measured with high fidelity in order to perform complex quantum algorithms. Control fidelities have greatly improved in silicon spin qubits, but state preparation and readout fidelities have generally been poor. By operating with low electron temperatures and employing high-bandwidth cryogenic amplifiers, we demonstrate single qubit readout visibilities >99%, exceeding the threshold for quantum error correction. In the same device, we achieve average single qubit control fidelities >99.95%. Our results show that silicon spin qubits can be opera…
We have detected coherent quantum oscillations between Josephson phase qubits and microscopic critical-current fluctuators by implementing a new state readout technique that is an order of magnitude faster than previous methods. The period of the oscillations is consistent with the spectroscopic splittings observed in the qubit's resonant frequency. The results point to a possible mechanism for decoherence and reduced measurement fidelity in superconducting qubits and demonstrate the means to measure two-qubit interactions in the time domain.
The charge-phase Josephson qubit based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-frequency driven tank circuit enabling the readout of the qubit states by measuring the effective Josephson inductance of the transistor. The effect of qubit dephasing and relaxation due to electric and magnetic control lines as well as the measuring system is evaluated. Recommendations for operation of the qubit in magic points producing minimum decoherence are given.
We present the realization of a cavity quantum electrodynamics setup in which photons of strongly different lifetimes are engineered in different harmonic modes of the same cavity. We achieve this in a superconducting transmission line resonator with superconducting qubits coupled to the different modes. One cavity mode is strongly coupled to a detection line for qubit state readout, while a second long lifetime mode is used for photon storage and coherent quantum operations. We demonstrate sideband based measurement of photon coherence, generation of n photon Fock states and the scaling of th…
A primary method of reading out a quantum dot hybrid qubit involves projection of the logical basis onto distinct charge states that are readily detected by an integrated charge sensing dot. However, in the simplest configuration, the excited charge state decays rapidly, making single-shot readout challenging. Here, we demonstrate a readout procedure where the qubit excited state is latched to a metastable charge configuration whose lifetime is tunnel rate limited, persisting here as long as 2.5 ms. Additionally, we show that working in the (4,1)-(3,2) charge configuration enables a latched re…
We study bifurcation measurement of a multi-level superconducting qubit using a nonlinear resonator biased in the straddling regime, where the resonator frequency sits between two qubit transition frequencies. We find that high-fidelity bifurcation measurements are possible because of the enhanced qubit-state-dependent pull of the resonator frequency, the behavior of qubit-induced nonlinearities and the reduced Purcell decay rate of the qubit that can be realized in this regime. Numerical simulations find up to a threefold improvement in qubit readout fidelity when operating in, rather than ou…
We study qubit decoherence under generalized dispersive readout, i.e., we investigate a qubit coupled to a resonantly driven dissipative harmonic oscillator. We provide a complete picture by allowing for arbitrarily large qubit-oscillator detuning and by considering also a coupling to the square of the oscillator coordinate, which is relevant for flux qubits. Analytical results for the decoherence time are obtained by a transformation of the qubit-oscillator Hamiltonian to the dispersive frame and a subsequent master equation treatment beyond the Markov limit. We predict a crossover from Marko…
Qubit readout is commonly performed by thresholding a collection of analog detector signals to obtain a sequence of single-shot bit values. The intrinsic irreversibility of the mapping from analog to digital signals discards soft information associated with an \emph{a posteriori} confidence that can be assigned to each bit value when a detector is well characterized. Accounting for soft information, we show significant improvements in enhanced state detection with the quantum repetition code as well as quantum state or parameter estimation. These advantages persist in spite of non-Gaussian fea…
We have developed a cryogenic platform for the control and readout of spin qubits that comprises a high density of dc and radio frequency sample interconnects based on a set of coupled printed circuit boards. The modular setup incorporates 24 filtered dc lines, 14 control and readout lines with bandwidth from dc to above 6 GHz, and 2 microwave connections for excitation to 40 GHz. We report the performance of this platform, including signal integrity and crosstalk measurements and discuss design criteria for constructing sample interconnect technology needed for multi-qubit devices.
A better understanding of the noise causing qubit decoherence is crucial for improving qubit performance. The noise spectrum affecting the qubit may be extracted by measuring dephasing under the application of pulse sequences but requires accurate qubit control and sufficiently long relaxation times, which are not always available. Here, we describe an alternative method to extract the spectrum from correlations of single-shot measurement outcomes of successive free induction decays. This method only requires qubit initialization and readout with a moderate fidelity and also allows independent…
A superconducting flux qubit is inductively coupled to a Superconducting QUantum Interference Device (SQUID) magnetometer, capacitively shunted to form a 1.294-GHz resonator. The qubit-state-dependent resonator frequency is weakly probed with a microwave signal and detected with a Microstrip SQUID Amplifier. At a mean resonator occupation $\bar{n}$ = 1.5 photons, the readout visibility is increased by a factor of 4.5 over that using a cryogenic semiconductor amplifier. As $\bar{n}$ is increased from 0.008 to 0.1, no reduction in $T_1$ is observed, potentially enabling continuous monitoring of …
We present a superconducting device that realizes the sequential measurement of a transmon qubit. The device disables common limitations of dispersive readout such as Purcell effect or transients in the cavity mode by turning on and off the coupling to the measurement channel on demand. The qubit measurement begins by loading a readout resonator that is coupled to the qubit. After an optimal interaction time with negligible loss, a microwave pump releases the content of the readout mode by upconversion into a measurement line in a characteristic time as low as 10~ns, which is 400 times shorter…
We introduce and analyze a dispersive qubit readout scheme where two-mode squeezing is generated directly in the measurement cavities. The resulting suppression of noise enables fast, high- fidelity readout of naturally weakly coupled qubits, and the possibility to protect strongly coupled qubits from decoherence by weakening their coupling. Unlike other approaches exploiting squeezing, our setup avoids the difficult task of transporting and injecting with high fidelity an externally-generated squeezed state. Our setup is also surprisingly robust against unwanted non-QND backaction effects, as…
The dispersive coupling between a qubit and a cavity mode is widely used for performing non-destructive readout of the qubit state. In this approach, it is typically required that the dispersive strong coupling regime is achieved. Here we show that the use of an auxiliary cavity mode reduces by orders of magnitude the required value of the dispersive coupling, for a given decay rate of the cavity mode. The analysis is performed within the input-output formalism, in terms of the photon scattering matrix elements and of the signal-to-noise ratio. We derive simple analytical expressions for the o…
We study the time-dependent effect of Markovian readout processes on Majorana qubits whose parity degrees of freedom are converted into the charge of a tunnel-coupled quantum dot. By applying a recently established effective Lindbladian approximation [1-3], we obtain a completely positive and trace preserving Lindblad master equation for the combined dot-qubit dynamics, describing relaxation and decoherence processes beyond the rotating-wave approximation. This approach is applicable to a wide range of weakly coupled environments representing experimentally relevant readout devices. We study i…
We analyzed the Josephson bifurcation amplifier (JBA) readout process of a superconducting qubit quantum mechanically. This was achieved by employing numerical analyses of the dynamics of the density operator of a driven nonlinear oscillator and a qubit coupled system during the measurement process. In purely quantum cases, the wavefunction of the JBA is trapped in a quasienergy-state, and bifurcation is impossible. Introducing decoherence enables us to reproduce the bifurcation with a finite hysteresis. Moreover, we discuss in detail the dynamics involved when a qubit is initially in a superp…
We discuss the current situation concerning measurement and readout of Josephson-junction based qubits. In particular we focus attention of dispersive low-dissipation techniques involving reflection of radiation from an oscillator circuit coupled to a qubit, allowing single-shot determination of the state of the qubit. In particular we develop a formalism describing a charge qubit read out by measuring its effective (quantum) capacitance. To exemplify, we also give explicit formulas for the readout time.
Visibility of singlet-triplet qubit readout is reduced to almost zero in large magnetic field gradients due to relaxation processes. Here we present a new readout technique that is robust against relaxation and allows for measurement when previously studied methods fail. This technique maps the qubit onto spin states that are immune to relaxation using a spin dependent electron tunneling process between the qubit and the lead. We probe this readout's performance as a function of magnetic field gradient and applied magnetic field, and optimize the pulse applied to the qubit through experiment a…
Machine Learning finds application in the quantum control and readout of qubits. In this work we apply Artificial Neural Networks to assist the manipulation and the readout of a prototypical molecular spin qubit - an Oxovanadium(IV) moiety - in two experiments designed to test the amplitude and the phase recognition, respectively. We first successfully use an artificial network to analyze the output of a Storage/Retrieval protocol with four input pulses to recognize the echo positions and, with further post selection on the results, to infer the initial input pulse sequence. We then apply an A…
We demonstrate a low loss, chip-level frequency multiplexing scheme for readout of scaled-up spin qubit devices. By integrating separate bias tees and resonator circuits on-chip for each readout channel, we realize dispersive gate-sensing in combination with charge detection based on two rf quantum point contacts (rf-QPCs). We apply this approach to perform multiplexed readout of a double quantum dot in the few-electron regime, and further demonstrate operation of a 10-channel multiplexing device. Limitations for scaling spin qubit readout to large numbers of multiplexed channels is discussed.
We propose a scheme for entangled state measurement at flux qubits (quantum bits) depending on the sensitivity measurement of a DC-SQUID (Superconducting QUantum Interference Device). The DC-SQUID is used as a flux qubit readout device. The switching current distribution of a DC-SQUID is sufficiently narrow to distinguish between two ground states of three Josephson junction qubits with a large mutual inductance between a qubit and the DC-SQUID. But discrimination between two ground states becomes difficult with the smaller mutual inductance that is preferable as regards of qubit coherence. Ho…
Schemes for topological quantum computation with Majorana bound states rely heavily on the ability to measure products of Majorana operators projectively. Here, we employ Markovian quantum measurement theory, including the readout device, to analyze such measurements. Specifically, we focus on the readout of Majorana qubits via continuous charge sensing of a tunnel-coupled quantum dot by a quantum point contact. We show that projective measurements of Majorana products $\prod_i\hatγ_i$ can be implemented by continuous charge sensing under quite general circumstances. Essential requirements are…
Using single-shot charge detection in a GaAs double quantum dot, we investigate spin relaxation time T_1 and readout visibility of a two-electron singlet-triplet qubit following single-electron dynamic nuclear polarization (DNP). For magnetic fields up to 2 T, the DNP cycle is in all cases found to increase Overhauser field gradients, which in turn decrease T_1 and consequently reduce readout visibility. This effect was previously attributed to a suppression of singlet-triplet dephasing under a similar DNP cycle. A model describing relaxation after singlet-triplet mixing agrees well with exper…
We study the dynamics of a charge qubit that is capacitively coupled to an open double quantum dot. Depending on the qubit state, the transport through the open quantum dot may be resonant or off-resonant, such that the qubit affects the current through the open double dot. We relate the initial qubit state to the magnitude of an emerging transient current peak. The relation between these quantities enables the readout of not only the charge but also the phase of the qubit.
For solid-state spin qubits, single-gate RF readout can help minimise the number of gates required for scale-up to many qubits since the readout sensor can integrate into the existing gates required to manipulate the qubits (Veldhorst 2017, Pakkiam 2018). However, a key requirement for a scalable quantum computer is that we must be capable of resolving the qubit state within single-shot, that is, a single measurement (DiVincenzo 2000). Here we demonstrate single-gate, single-shot readout of a singlet-triplet spin state in silicon, with an average readout fidelity of $82.9\%$ at a $3.3~\text{kH…
Silicon spin qubits have emerged as a promising path to large-scale quantum processors. In this prospect, the development of scalable qubit readout schemes involving a minimal device overhead is a compelling step. Here we report the implementation of gate-coupled rf reflectometry for the dispersive readout of a fully functional spin qubit device. We use a p-type double-gate transistor made using industry-standard silicon technology. The first gate confines a hole quantum dot encoding the spin qubit, the second one a helper dot enabling readout. The qubit state is measured through the phase res…
Quantum state transfer into a memory, state shuttling over long distances via a quantum bus, and high-fidelity readout are important tasks for quantum technology. Realizing these tasks is challenging in the presence of realistic couplings to an environment. Here, we introduce and assess protocols that can be used in cavity QED to perform high-fidelity quantum state transfer and fast quantum nondemolition qubit readout through Hamiltonian engineering. We show that high-fidelity state transfer between a cavity and a single qubit can be performed, even in the limit of strong dephasing due to inho…
Readout sweet spots for spin qubits with strong spin-orbit interaction
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；IBM Research Europe – Zurich（IBM 欧洲苏黎世研究中心）；ELTE Eötvös Loránd University（厄特沃什·罗兰大学）；Moth Quantum AG（蛾量子股份公司）；University of Basel（巴塞尔大学）；Delft University of Technology（代尔夫特理工大学）
Many promising approaches to fault-tolerant quantum computation require repeated quantum nondemolition (QND) readout of binary observables such as quantum bits (qubits). A commonly used figure of merit for readout performance is the error rate for binary assignment in a single repetition. However, it is known that this figure of merit is insufficient. Indeed, real-world readout outcomes are typically analog instead of binary. Binary assignment therefore discards important information on the level of confidence in the analog outcomes. Here, a generalized figure of merit that fully captures the …
