In superconducting circuit architectures for quantum computing, microwave resonators are often used both to isolate qubits from the electromagnetic environment and to facilitate qubit state readout. We analyze the full counting statistics of photons emitted from such driven readout resonators both in and beyond the dispersive approximation. We calculate the overlap between emitted-photon distributions for the two qubit states and explore strategies for its minimization with the purpose of increasing fidelity of intensity-sensitive readout techniques. In the dispersive approximation and at negligible qubit relaxation, both distributions are Poissonian, and the overlap between them can be easily made arbitrarily small. Nondispersive terms of the Hamiltonian generate squeezing and the Purcell decay with the latter effect giving the dominant contribution to the overlap between two distributions.
In superconducting circuit architectures for quantum computing, microwave resonators are often used both to isolate qubits from the electromagnetic environment and to facilitate qubit state readout. We analyze the full counting statistics of photons emitted from such driven readout resonators both in and beyond the dispersive approximation. We calculate the overlap between emitted-photon distributions for the two qubit states and explore strategies for its minimization with the purpose of increasing fidelity of intensity-sensitive readout techniques. In the dispersive approximation and at negligible qubit relaxation, both distributions are Poissonian, and the overlap between them can be easily made arbitrarily small. Nondispersive terms of the Hamiltonian generate squeezing and the Purcell decay with the latter effect giving the dominant contribution to the overlap between two distributions.
Physical implementations of qubits can be extremely sensitive to environmental coupling, which can result in decoherence. While efforts are made for protection, coupling to the environment is necessary to measure and manipulate the state of the qubit. As such, the goal of having long qubit energy relaxation times is in competition with that of achieving high-fidelity qubit control and measurement. Here, we propose a method that integrates filtering techniques for preserving superconducting qubit lifetimes together with the dispersive coupling of the qubit to a microwave resonator for control and measurement. The result is a compact circuit that protects qubits from spontaneous loss to the environment, while also retaining the ability to perform fast, high-fidelity readout. Importantly, we show the device operates in a regime that is attainable with current experimental parameters and provide a specific example for superconducting qubits in circuit quantum electrodynamics.
Strong coupling of semiconductor spin qubits to superconducting microwave resonators was recently demonstrated [X. Mi et al., Nature 555, 599 (2018); A. J. Landig et al., Nature 560, 179 (2018); N. Samkharadze et al., Science 359, 1123 (2018); T. Cubaynes et al., NPJ Quant. Inf. 5, 47 (2019)]. 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 strong spin-photon coupling arises from the motion of the electron spin in a local magnetic field gradient. We calculate the signal-to-noise ratio (SNR) of the readout accounting for both Purcell spin relaxation and spin relaxation arising from intrinsic electric noise within the semiconductor. We express the maximum achievable SNR in terms of the cooperativity associated with these two dissipation processes. We find that while the cooperativity increases with the strength of the dipole coupling between the DQD and the resonator, it does not depend on the strength of the magnetic field gradient. We then optimize the SNR as a function of experimentally tunable DQD parameters. We identify wide regions of parameter space where the unwanted backaction of the resonator photons on the qubit is small. Moreover, we find that the coupling of the resonator to other DQD transitions can enhance the SNR by at least a factor of two, a ``straddling'' effect [J. Koch et al., Phys. Rev. A 76, 042319 (2007)] that occurs only at nonzero energy detuning of the DQD double-well potential. We estimate that with current technology, single-shot readout fidelities in the range 82--95% can be achieved within a few $\ensuremath{\mu}\mathrm{s}$ of readout time without requiring the use of Purcell filters.
PhD Thesis: Superconducting circuit quantum electrodynamics (QED) has developed into a powerful platform for studying the interaction between matter and different states of light. In this context, superconducting quantum bits (qubits) act as artificial atoms interacting with quantized modes of the electromagnetic field. The field can be trapped in superconducting microwave resonators or propagating in transmission lines. In this thesis, we particularly study circuit QED systems where microwave fields are coupled with superconducting flux and transmon qubits. We optimize the coherence properties of the resonators, by analyzing loss mechanisms at excitation powers of approximately one photon on average. We find that two-level fluctuators associated with oxide layers at substrate and metal surfaces and metal-metal interfaces represent the predominant loss channel. Furthermore, we show how broadband thermal photon fields influence the relaxation and dephasing properties of a superconducting transmon qubit. To this end, we study several second-order loss channels of the transmon qubit and find that the broadband fields introduce a larger decay rate than expected from the Purcell filter defined by the resonator. Additionally, we show that qubit dephasing at the flux-insensitive point as well as low-frequency parameter fluctuations can be enhanced by thermal fields. Finally, we study how artificial atoms react to changes in inherent properties of the light fields. We perform a detailed analysis of the photon statistics of thermal fields using their relation to the qubits coherence properties. We quantitatively recover the expected n2+n-law for the photon number variance and confirm this result by direct correlation measurements. We then show a novel technique for the in-situ conversion of the interaction parity in light-matter interaction. To this end, we couple spatially controlled microwave fields to a flux qubit with two degrees of freedom.
Microwave filtering for superconducting qubits is a key element of quantum computing technology, enabling high coherence and fast state detection. This work presents the design and implementation of novel microwave Purcell filters for superconducting quantum circuits, integrated within a multilayer printed circuit board (PCB). The off-chip design removes all filter components from the qubit substrate, reducing device complexity, improving layout footprint and allowing better scalability to large qubit counts. Each embedded filter can couple up to nine readout resonators, enabling efficient multiplexed readout. Electromagnetic simulations of the filter predict a thousand-fold improvement in qubit isolation from the readout port. The design was experimentally validated under cryogenic conditions in conjunction with a 35-qubit device, demonstrating compatibility of the PCB-based filter with high-coherence superconducting qubits. The comparison of the measured qubit median T1 of 84 μs with the expected radiative limit from electromagnetic simulations validated the presence of Purcell filtering in the system.
We analyze a single-shot readout for superconducting qubits via the controlled catch, dispersion, and release of a microwave field. A tunable coupler is used to decouple the microwave resonator from the transmission line during the dispersive qubit-resonator interaction, thus circumventing damping from the Purcell effect. We show that, if the qubit frequency tuning is sufficiently adiabatic, a fast high-fidelity qubit readout is possible, even in the strongly nonlinear dispersive regime. Interestingly, the Jaynes-Cummings nonlinearity leads to the quadrature squeezing of the resonator field below the standard quantum limit, resulting in a significant decrease of the measurement error.
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 readout. Circuit Quantum Electrodynamics (cQED) is at the heart of most advanced superconducting quantum technologies. Different types of superconducting qubits can be strongly coupled to microwave resonators thus achieving regimes and phenomenena which cannot be reached within the realm of quantum optics [1]. More recently, strong coupling between microwave resonators and a variety of other quantum systems not necessarily involving superconductors has been achieved [2], extending further the realm of cQED. In all these applications the measurement of the qubit or the hybrid device state is achieved by monitoring the resonator properties. Theoretically , two regimes have been approached using disconnected descriptions [3]: the dispersive regime, where the qubit-resonator detuning is larger than the coupling strength yet small enough to allow the exchange of virtual photons, and the adiabatic regime, where the de-tuning is sufficiently large for virtual processes to be strongly suppressed. The dispersive regime, which describes level repulsion between those of the quantum circuit and of the resonator, is typically dealt with using a Jaynes-Cummings Hamiltonian within different levels of approximation [3-10]. In contrast, the adiabatic regime accounts for the renormalization of the resonator capaci-tance/inductance by the effective capacitance of the circuit , including its "quantum capacitance" [11, 12], or its effective inductance [13, 14], which modifies the resonator frequency [15, 16]. However, there is no actual border between these two regimes which could justify a separate treatment, as illustrated by recent experiments on hybrid cQED setups [17] that reveal features of both regimes for the same device. This situation claims for a unified description of quantum circuits readout, going beyond the standard Jaynes-Cummings model, which could be applied to different types of devices over a large range of parameters. * Corresponding author : a.l.yeyati@uam.es In the present Letter we derive a general expression for the resonator frequency shift when coupled to a generic quantum circuit. This expression naturally interpolates between the adiabatic and the dispersive regimes, thus allowing to clarify their origin from the same coupling Hamiltonian. In addition our formalism is not restricted to the usual two-level approximations but any multilevel situation can be described on the same footing. We illustrate the importance of the different terms in our expression by analyzing well-known models like a short single channel superconducting weak link hosting Andreev states, the RF-SQUID and the Cooper pair box. Resonator-quantum circuit coupling.-The system we consider comprises a resonant circuit and a quantum circuit coupled through phase or charge fluctuations as depicted in Figs. 1(a), 2(a) and in the inset of Fig. 3. The resonant circuit is represented as a lumped-element LC resonator with bare resonance frequency f r = ω r /2π, with ω r = 1/ √ L r C r. Introducing the photon annihilation (creation) operators a (a †), it can be described by the Hamiltonian H r = ω r a † a. On the other hand, the quantum circuit Hamiltonian,Ĥ qc (x), depends on a dimensionless control parameter x, corresponding to an excess charge on a capacitor or a flux through a loop. We denote by |Φ i (x) the eigenstates of the uncoupled quantum circuit,Ĥ qc (x)|Φ i (x) = E i (x)|Φ i (x). Flux (charge) fluctuations in the resonator lead to x → x 0 +x r , wherex r = λ(s a + s * a †) with a coupling constant λ, depending on a coupling scheme [19], and s = 1 (−i). We assume λ 1 in accordance with experiments. The resonator-quantum circuit coupling HamiltonianĤ c is obtained by expandingĤ qc (x 0 +x r) up to second order inx rĤ c (x 0) =x rĤ qc (x 0) +x 2 r 2Ĥ qc (x 0), (1) where the prime stands for the derivative with respect to x. The Hamiltonian describing resonator, quantum