For some cavity-quantum-electrodynamics systems, such as a single electron spin coupled to a passive cavity, it is challenging to reach the strong-coupling regime. In such a weak-coupling regime, the conventional dispersive readout technique cannot be used to resolve the quantum states of the spin. Here we propose an improved dispersive readout method to measure the quantum states of a weakly coupled qubit by harnessing either one or two auxiliary cavities linearly coupled to the passive cavity containing the qubit. With appropriate parameters in both cases, the system excluding the qubit can exhibit a parity-time-symmetric phase transition at the exceptional point (EP). Because the EP can amplify the perturbation induced by the qubit and the parity-time symmetry can narrow the linewidths of the peaks in the transmission spectrum of the passive cavity, we can measure the quantum states of the weakly coupled qubit via this transmission spectrum. Owing to the weak coupling between the qubit and the passive cavity, the backaction due to the measurement of the qubit can also be reduced in comparison with the conventional dispersive readout technique in the strong-coupling regime.
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…
We propose a quantum state readout mechanism of a weakly coupled qubit in dispersive regime. The hybrid system consists of ferromagnetic insulator and a superconducting qubit in a microwave cavity. The enhancement of the measurement sensitivity is achieved by exerting torque on the ferromagnetic insulator magnetization, which compensates the damping of the system leading to an exceptional point. The proposed machanism allows to measure the qubit state either via the transmission of the cavity or the FMR signal of the magnetic material.
We report the dispersive charge-state readout of a double quantum dot in the few-electron regime using the in situ gate electrodes as sensitive detectors. We benchmark this gate-sensing technique against the well established quantum point contact (QPC) charge detector and find comparable performance with a bandwidth of 10 MHz and an equivalent charge sensitivity of 6.3 x 10-3 e/ \sqrt Hz. Dispersive gate-sensing alleviates the burden of separate charge detectors for quantum dot systems and promises to enable readout of qubits in scaled-up arrays.
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…
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 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…
Quantum computers require interfaces with classical electronics for efficient qubit control, measurement and fast data processing. Fabricating the qubit and the classical control layer using the same technology is appealing because it will facilitate the integration process, improving feedback speeds and offer potential solutions to wiring and layout challenges. Integrating classical and quantum devices monolithically, using complementary metal-oxide-transistor (CMOS) processes, enables the processor to profit from the most mature industrial technology for the fabrication of large scale circui…
We present and demonstrate a general three-step method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. We use active depletion of post-measurement photons and optimal integration weight functions on two quadratures to maximize the signal-to-noise ratio of the non-steady-state homodyne measurement. We derive analytically and demonstrate experimentally that the method robustly extracts the quantum efficiency for arbitrary readout conditions in the linear regime. We use the proven method to optimally bias a Josephson traveling-wave parametric amplifier and to qua…
We demonstrate dispersive readout of the spin of an ensemble of Nitrogen-Vacancy centers in a high-quality dielectric microwave resonator at room temperature. The spin state is inferred from the reflection phase of a microwave signal probing the resonator. Time-dependent tracking of the spin state is demonstrated, and is employed to measure the T1 relaxation time of the spin ensemble. Dispersive readout provides a microwave interface to solid state spins, translating a spin signal into a microwave phase shift. We estimate that its sensitivity can outperform optical readout schemes, owing to th…
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 develop a time-dependent Schrieffer-Wolff-Lindblad perturbation theory to study effective interactions for driven open quantum systems. The starting point of our analysis is a given Lindblad equation, based on which we obtain an effective (averaged) map that describes the renormalization of both the Hamiltonian and collapse operators due to the drive. As a case study, we apply this method to the dispersive readout of a transmon qubit and derive an effective disperive map that describes measurement-induced dephasing and Stark shift for the transmon. The effective map we derive is completely …
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.
Spectral properties of a quantum circuit are efficiently read out by monitoring the resonance frequency shift it induces in a microwave resonator coupled to it. When the two systems are strongly detuned, theory attributes the shift to an effective resonator capacitance or inductance that depends on the quantum circuit state. At small detuning, the shift arises from the exchange of virtual photons, as described by the Jaynes-Cummings model. Here we present a theory bridging these two limits and illustrate, with several examples, its necessity for a general description of quantum circuits readou…
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…
The speed of quantum gates and measurements is a decisive factor for the overall fidelity of quantum protocols when performed on physical qubits with finite coherence time. Reducing the time required to distinguish qubit states with high fidelity is therefore a critical goal in quantum information science. The state-of-the-art readout of superconducting qubits is based on the dispersive interaction with a readout resonator. Here, we bring this technique to its current limit and demonstrate how the careful design of system parameters leads to fast and high-fidelity measurements without affectin…
We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement, and crucially, is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities, and making use of a symmetry in the dynamics of joint cavity quadratures (a so-called quantum-mechanics-free subsystem). We discuss the basic scaling of the scheme and its robustness against imperfections, as well as a realistic implementation in circui…
We present experimental results on a dispersive scheme for reading out a Josephson phase qubit. A capacitively shunted dc-SQUID is used as a nonlinear resonator which is inductively coupled to the qubit. We detect the flux state of the qubit by measuring the amplitude and phase of a microwave pulse reflected from the SQUID resonator. By this low-dissipative method, we reduce the qubit state measurement time down to 25 microseconds, which is much faster than using the conventional readout performed by switching the SQUID to its non-zero dc voltage state. The demonstrated readout scheme allows f…
Dispersive sensing is a powerful technique that enables scalable and high-fidelity readout of solid-state quantum bits. In particular, gate-based dispersive sensing has been proposed as the readout mechanism for future topological qubits, which can be measured by single electrons tunneling through zero-energy modes. The development of such a readout requires resolving the coherent charge tunneling amplitude from a quantum dot in a Majorana-zero-mode host system faithfully on short time scales. Here, we demonstrate rapid single-shot detection of a coherent single-electron tunneling amplitude be…
We demonstrate high-contrast state detection of a superconducting flux qubit. Detection is realized by probing the microwave transmission of a nonlinear resonator, based on a SQUID. Depending on the driving strength of the resonator, the detector can be operated in the monostable or the bistable mode. The bistable operation combines high-sensitivity with intrinsic latching. The measured contrast of Rabi oscillations is as high as 87 %; of the missing 13 %, only 3 % is unaccounted for. Experiments involving two consecutive detection pulses are consistent with preparation of the qubit state by t…
We study the physics of a magnetic molecule described by a "giant" spin with multiple ($d > 2$) spin states interacting with the quantized cavity field produced by a superconducting resonator. By means of the input-output formalism, we derive an expression for the output modes in the dispersive regime of operation. It includes the effect of magnetic anisotropy, which makes different spin transitions addressable. We find that the measurement of the cavity transmission allows to uniquely determine the spin state of the qudits. We discuss, from an effective Hamiltonian perspective, the conditions…
Strong coupling of semiconductor spin qubits to superconducting microwave resonators was recently demonstrated. These breakthroughs pave the way for quantum information processing that combines the long coherence times of solid-state spin qubits with the long-distance connectivity, fast control, and fast high-fidelity quantum-non-demolition readout of existing superconducting qubit implementations. Here, we theoretically analyze and optimize the dispersive readout of a single spin in a semiconductor double quantum dot (DQD) coupled to a microwave resonator via its electric dipole moment. The s…
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…
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…
High-fidelity qubit measurements play a crucial role in quantum computation, communication, and metrology. In recent experiments, it has been shown that readout fidelity may be improved by performing repeated quantum non-demolition (QND) readouts of a qubit's state through an ancilla. For a qubit encoded in a two-level system, the fidelity of such schemes is limited by the fact that a single error can destroy the information in the qubit. On the other hand, if a bosonic system is used, this fundamental limit could be overcome by utilizing higher levels such that a single error still leaves sta…
Dark state as a measurable state by a dispersive readout without a Purcell limit
National Chung Hsing University（中兴大学）；Feng Chia University（逢甲大学）；Research Center for Critical Issues, Academia Sinica（中央研究院关键问题研究中心）；National Changhua University of Education（国立彰化师范大学）
We study the dispersive readout of a qubit in the ultimate limit of a single-photon probe. The use of a single-photon probe avoids the errors due to nonorthogonality of coherent states. A photodetector is used in the scheme we consider. The dynamics of the system is studied using the Heisenberg-Langevin equations. We treat the counter-rotating terms in the Hamiltonian perturbatively, which leads to the Bloch-Siegert shift in the resonator frequency. It is shown how this can improve the readout. The theory of photon transport through the qubit and the resonator it couples to is provided while t…
A three-dimensional multimode lumped-element resonator for collective spin manipulation and dispersive readout
Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China（中国科学技术大学物理科学学院、合肥微尺度物质科学国家研究中心）；Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学、上海量子科学研究与探索中心、中国科学院量子信息与量子物理学前沿卓越创新中心）
Reading out the state of superconducting artificial atoms typically relies on dispersive coupling to a readout resonator. For a given system noise temperature, increasing the circulating photon number $\bar{n}$ in the resonator enables a shorter measurement time and is therefore expected to reduce readout errors caused by spontaneous atom transitions. However, increasing $\bar{n}$ is generally observed to also increase these transition rates. Here we present a fluxonium artificial atom in which we measure an overall flat dependence of the transition rates between its first two states as a func…
Squeezing for dispersive readout of NV magnetometer
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理工程技术学院）；P.N.Lebedev Physical Institute of the Russian Academy of Science（俄罗斯科学院列别杰夫物理研究所）；LLC Sensor Spin Technologies（传感器自旋技术有限责任公司）
We determine the optimal parameters for a simple and efficient scheme of dispersive readout of a qubit. Depending on the qubit state (ground or excited), the resonance of a cavity is shifted either to the red or to the blue side. Qubit state is inferred by detecting the photon number transmitted through the cavity. It turns out that this kind of detection provides better measurement fidelity than the detection of the presence or absence of photons only. We show that radiating the cavity on either of the frequencies it shifts to results in a suboptimal measurement. The optimal frequency of the …
Parity measurement is a key step in many entanglement generation and quantum error correction schemes. We propose a protocol for non-destructive parity measurement of two remote qubits, i.e., macroscopically separated qubits with no direct interaction. The qubits are instead dispersively coupled to separate resonators that radiate to shared photodetectors. The scheme is deterministic in the sense that there is no fundamental bound on the success probability. Compared to previous proposals, our protocol addresses the scenario where number resolving photodetectors are available but the qubit-res…
A striking characteristic of superconducting circuits is that their eigenspectra and intermode coupling strengths are well predicted by simple Hamiltonians representing combinations of quantum circuit elements. Of particular interest is the Cooper-pair-box Hamiltonian used to describe the eigenspectra of transmon qubits, which can depend strongly on the offset-charge difference across the Josephson element. Notably, this offset-charge dependence can also be observed in the dispersive coupling between an ancillary readout mode and a transmon fabricated in the offset-charge-sensitive (OCS) regim…
We theoretically examine a scheme for projectively reading out the parity state of a pair of Majorana bound states (MBS) using a tunnel coupled quantum dot. The dot is coupled to one end of the topological wire but isolated from any reservoir, and is capacitively coupled to a charge sensor for measurement. The combined parity of the MBS-dot system is conserved and charge transfer between the MBS and dot only occurs through resonant tunnelling. Resonance is controlled by the dot potential through a local gate and by the MBS energy splitting due to the overlap of the MBS pair wavefunctions. The …
We establish a testbed system for the development of high-sensitivity Electron Spin Resonance (ESR) techniques for small samples at cryogenic temperatures. Our system consists of a Niobium Nitride thin-film planar superconducting microresonator designed to have a concentrated mode volume to couple to a small amount of paramagnetic material, and to be resilient to magnetic fields of up to 400 mT. At 65 mK we measure high-cooperativity coupling ($C \approx 19$) to an organic radical microcrystal containing $10^{12}$ spins in a pico-litre volume. We detect the spin-lattice decoherence rate via th…
Open quantum systems can undergo dissipative phase transitions, and their critical behavior can be exploited in sensing applications. For example, it can be used to enhance the fidelity of superconducting qubit readout measurements, a central problem toward the creation of reliable quantum hardware. A recently introduced measurement protocol, named ``critical parametric quantum sensing'', uses the parametric (two-photon driven) Kerr resonator's driven-dissipative phase transition to reach single-qubit detection fidelity of 99.9\% [arXiv:2107.04503]. In this work, we improve upon the previous p…
Reading out Majorana bound states (MBSs) is essential both to verify their non-Abelian property and to realize topological quantum computation. Here, we construct a protocol to measure the parity of two MBSs in a Majorana island coupled to double quantum dot (DQD). The parity information is mapped to the charge state of the DQD through Landau-Zener transition. The operation needed is sweeping the bias of the DQD, which is followed by charge sensing. In the case without fine-tuning, a single run of sweep-and-detection implement a weak measurement of the parity. We find that in general a sequenc…
