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In this short perspective article we present our personal highlights on how the Jaynes-Cummings model has become a central model to describe spin-boson couplings underpinning much of modern quantum optics. To the current authors, the key contribution is a demonstration of a measurable effect that showed the discreteness of the quantized radiation field.

A hybrid system with tunable coupling between phonons and qubits shows great potential for advancing quantum information processing. In this work, we demonstrate strong and tunable coupling between a surface acoustic wave (SAW) resonator and a transmon qubit based on galvanic-contact flip-chip technique. The coupling strength varies from $2π\times$7.0 MHz to -$2π\times$20.6 MHz, which is extracted from different vacuum Rabi oscillation frequencies. The phonon-induced ac Stark shift of the qubit at different coupling strengths is also shown. Our approach offers a good experimental platform for exploring quantum acoustics and hybrid systems.

Quantum circuits utilizing real time feedback techniques (such as active reset and mid-circuit measurement) are a powerful tool for NISQ-era quantum computing. Such techniques are crucial for implementing error correction protocols, and can reduce the resource requirements of certain quantum algorithms. Realizing these capabilities requires flexible, low-latency classical control. We have developed a custom FPGA-based processor architecture for QubiC, an open source platform for superconducting qubit control. Our architecture is distributed in nature, and consists of a bank of lightweight cores, each configured to control a small (1-3) number of signal generator channels. Each core is capable of executing parameterized control and readout pulses, as well as performing arbitrary control flow based on mid-circuit measurement results. We have also developed a modular compiler stack and domain-specific intermediate representation for programming the processor. Our representation allows users to specify circuits using both gate and pulse-level abstractions, and includes high-level control flow constructs (e.g. if-else blocks and loops). The compiler stack is designed to integrate with quantum software tools and programming languages, such as TrueQ, pyGSTi, and OpenQASM3. In this work, we will detail the design of both the processor and compiler stack, and demonstrate its capabilities with a quantum state teleportation experiment using transmon qubits at the LBNL Advanced Quantum Testbed.

Two-level systems (TLS) of unclear physical origin are a major contributor to decoherence in superconducting qubits. The interactions of individual TLS with a qubit can be detected via various spectroscopic methods, most of which have relied on the tunability of the qubit frequency. We propose a novel method that requires only a microwave drive and dispersive readout, and thus also works fixed-frequency qubits. The proposed two-tone spectroscopy involves a microwave pulse of varying frequency and length to excite TLSs of unknown frequencies, followed by a second pulse at the qubit frequency. TLS parameters can be estimated from the qubit population as a function of the first pulse frequency and length.

We consider the Jaynes-Cummings (JC) model embedded in a structured environment, where the atom inside an optical cavity will be affected by a hierarchical environment consisting of the cavity and its environment. We propose several effective strategies to control and suppress the decoherence effects to protect the quantum coherence of the JC atom. We study the non-perturbative control of the system dynamics by means of the leakage elimination operators. We also investigate a full quantum state reversal scheme by engineering the system and its coupling to the bath via the Petz recovery map. Our findings conclude that, with the Petz recovery map, the dynamics of the JC atom can be fully recovered regardless of Markov or non-Markovian noises. Finally, we show that our quantum control and recovery methods are effective at protecting different aspects of the system coherence.

We investigate a generic tripartite quantum system featuring a single qubit interacting concurrently with two quantized harmonic oscillators via nonlinear multiphoton Jaynes-Cummings (MPJC) interactions. Assuming the qubit is initially prepared in a superposition state and the two oscillators are in arbitrary Fock states, we analytically trace the temporal evolution of this tripartite pure initial state. We identify four broad cases, each further divided into two subcases, and derive exact analytical solutions for most cases. Notably, we obtain perfect transfer of excitations between the oscillators by carefully selecting system parameters. In addition, we extensively examine the manner in which the nonclassicalities of various initial oscillator Fock states, quantified by the volume of negative regions in the associated Wigner functions, evolve under the MPJC Hamiltonian, considering diverse system parameters including environmental effects. Besides producing substantial enhancements in the initial value for higher photon number states, our analysis reveals that driven solely by the initial qubit energy, with both oscillators initialized in the vacuum state, the nonlinear MPJC interaction yields a significant amount of nontrivial Wigner negativity in the oscillators. The additional nonlinearity introduced by the multiphoton process plays a pivotal role in surpassing the initial nonclassicalities of the photon number states.

The supersymmetric connection that exists between the Jaynes-Cummings (JC) and anti-Jaynes Cummings (AJC) models in quantum optics is unraveled entirely. A new method is proposed to obtain the temporal evolution of observables in the AJC model using supersymmetric techniques, providing an overview of its dynamics and extending the calculation to full photon counting statistics. The approach is general and can be applied to determine the high-order cumulants given an initial state. The analysis reveals that engineering the collapse-revival behavior and the quantum properties of the interacting field is possible by controlling the initial state of the atomic subsystem and the corresponding atomic frequency in the AJC model. The substantial potential for applications of supersymmetric techniques in the context of photonic quantum technologies is thus demonstrated.

We determine the form of the unitary transformation that diagonalizes the Jaynes-Cummings Hamiltonian. This leads to operators the action of which has a simple interpretation in terms of the dressed states, the energy eigenstates. This suggests a set of coherent states and spin coherent states based on the dressed states.

Semiconductor double quantum dot (DQD) qubits coupled via superconducting microwave resonators provide a powerful means of long-range manipulation of the qubits' spin and charge degrees of freedom. Quantum gates can be implemented by parametrically driving the qubits while their transition frequencies are detuned from the resonator frequency. Long-range two-qubit CZ gates have been proposed for the DQD spin qubit within the rotating-wave approximation (RWA). Rapid gates demand strong coupling, but RWA breaks down when coupling strengths become significant relative to system frequencies. Therefore, understanding the detrimental impact of time-dependent terms ignored by RWA is critical for high-fidelity operation. Here, we go beyond RWA to study CZ gate fidelity for both DQD spin and charge qubits. We propose a novel parametric drive on the charge qubit that produces fewer time-dependent terms and show that it outperforms its spin counterpart. We find that drive amplitude - a parameter dropped in RWA - is critical for optimizing fidelity and map out high-fidelity regimes. Our results demonstrate the necessity of going beyond RWA in understanding how long-range gates can be realized in DQD qubits, with charge qubits offering considerable advantages in high-fidelity operation.

We introduce a novel superconducting qubit architecture utilizing parallel arrays of Josephson junctions. This design offers a substantialy improved relative anharmonicity, typically within the range of $|α_r| \approx 0.1 - 0.3$, while maintaining transition matrix elements in both the charge and flux channels that are on par with those of transmon qubits. Our proposed device also features exceptional tunability and includes a parameter regime akin to an enhanced version of the fluxonium qubit. Notably, it enables an additional order of magnitude reduction in matrix elements influenced by flux noise, thus further enhancing its suitability for quantum information processing applications.

In recent years, the lack of a conclusive detection of WIMP dark matter at the 10 GeV/c$^{2}$ mass scale and above has encouraged development of low-threshold detector technology aimed at probing lighter dark matter candidates. Detectors based on Cooper-pair-breaking sensors have emerged as a promising avenue for this detection due to the low (meV-scale) energy required for breaking a Cooper pair in most superconductors. Among them, devices based on superconducting qubits are interesting candidates for sensing due to their observed sensitivity to broken Cooper pairs. We have developed an end-to-end G4CMP-based simulation framework and have used it to evaluate performance metrics of qubit-based devices operating in a gate-based "energy relaxation" readout scheme, akin to those used in recent studies of qubit sensitivity to ionizing radiation. We find that for this readout scheme, the qubit acts as a phonon sensor with an energy threshold ranging down to $\simeq$0.4 eV for near-term performance parameters.

Quantum entanglement is one of the primary features which distinguishes quantum computers from classical computers. In gate-based quantum computing, the creation of entangled states or the distribution of entanglement across a quantum processor often requires circuit depths which grow with the number of entangled qubits. However, in teleportation-based quantum computing, one can deterministically generate entangled states with a circuit depth that is constant in the number of qubits, provided that one has access to an entangled resource state, the ability to perform mid-circuit measurements, and can rapidly transmit classical information. In this work, aided by fast classical field programmable gate array-based control hardware with a feedback latency of only 150 ns, we explore the utility of teleportation-based protocols for generating non-local, multi-partite entanglement between superconducting qubits. First, we demonstrate well-known protocols for generating Greenberger-Horne-Zeilinger (GHZ) states and non-local CNOT gates in constant depth. Next, we utilize both protocols for implementing a quantum fan-out gate in constant depth among three non-local qubits (i.e., controlled-NOT-NOT). Finally, we demonstrate deterministic state teleportation and entanglement swapping between qubits on opposite sides of our quantum processor. Throughout this work, we find that the fidelity of our teleportation-based protocols is limited by measurement-induced dephasing on idling spectator qubits. Therefore, our work serves as a useful study of the current benefits and limitations of teleportation-based protocols on contemporary superconducting quantum processors.

Quantum computing is currently hindered by hardware noise. We present a freestyle superconducting pulse optimization method, incorporating two-qubit channels, which enhances flexibility, execution speed, and noise resilience. A minimal 0.22 ns pulse is shown to determine the H2 groundstate to within chemical accuracy upon real-hardware, approaching the quantum speed limit. Similarly, a pulse significantly shorter than circuit-based counterparts is found for the LiH molecule, attaining state-of-the-art accuracy. The method is general and can potentially accelerate performance across various quantum computing components and hardware.

Gate-tunable transmons (gatemons) employing semiconductor Josephson junctions have recently emerged as building blocks for hybrid quantum circuits. In this study, we present a gatemon fabricated in planar Germanium. We induce superconductivity in a two-dimensional hole gas by evaporating aluminum atop a thin spacer, which separates the superconductor from the Ge quantum well. The Josephson junction is then integrated into an Xmon circuit and capacitively coupled to a transmission line resonator. We showcase the qubit tunability in a broad frequency range with resonator and two-tone spectroscopy. Time-domain characterizations reveal energy relaxation and coherence times up to 75 ns. Our results, combined with the recent advances in the spin qubit field, pave the way towards novel hybrid and protected qubits in a group IV, CMOS-compatible material.

Superconducting qubits are a promising platform for building fault-tolerant quantum computers, with recent achievement showing the suppression of logical error with increasing code size. However, leakage into non-computational states, a common issue in practical quantum systems including superconducting circuits, introduces correlated errors that undermine QEC scalability. Here, we propose and demonstrate a leakage reduction scheme utilizing tunable couplers, a widely adopted ingredient in large-scale superconducting quantum processors. Leveraging the strong frequency tunability of the couplers and stray interaction between the couplers and readout resonators, we eliminate state leakage on the couplers, thus suppressing space-correlated errors caused by population propagation among the couplers. Assisted by the couplers, we further reduce leakage to higher qubit levels with high efficiency (98.1%) and low error rate on the computational subspace (0.58%), suppressing time-correlated errors during QEC cycles. The performance of our scheme demonstrates its potential as an indispensable building block for scalable QEC with superconducting qubits.

We present a framework that combines the adjoint-state method together with reverse-time backpropagation to solve prohibitively large open-system quantum control problems. Our approach enables the optimization of arbitrary cost functions with fully general controls applied on large open quantum systems described by a Lindblad master equation. It is scalable, computationally efficient, and has a low-memory footprint. We apply this framework to optimize two inherently dissipative operations in superconducting qubits which lag behind in terms of fidelity and duration compared to other unitary operations: the dispersive readout and all-microwave reset of a transmon qubit. Our results show that while standard pulses for dispersive readout are nearly optimal, adding a transmon drive during the protocol can yield 2x improvements in fidelity and duration. We further demonstrate a 2x improvement in reset fidelity and duration through pulse shaping, indicating significant potential for enhancement in reset protocols. Our approach can readily be applied to optimize quantum controls in a vast range of applications such as reservoir engineering, autonomous quantum error correction, and leakage-reduction units.

Superconducting transmon qubits with strong anharmonicity and insensitivity to offset charge are highly desirable for low-error implementation. In this work we propose a c-axis junction, comprising triplet superconductors, and set at a relative twist angle. Invoking spin-orbit coupling and spin polarization, which are known to occur in the material platform of choice, we examine the resulting transmon Hamiltonian. This junction allows for direct control of the single and double Cooper pair tunneling strength, and most remarkably, an anomalous magnetic flux -- i.e. a phase offset equivalent to magnetic flux, yet in zero magnetic field. Having control over these three parameters -- single and double pair tunneling and anomalous flux -- allows for optimal design of the transmon qubit. Interestingly, in this architecture, the anomalous flux is determined by the twist angle of the junction, thereby offering a novel zero-field functionality. Our key results rely on symmetry arguments, for concreteness we demonstrate the implementation of our concept using a model of moiré graphene-based c-axis junctions.

The Jaynes-Cummings model provides a simple and accurate description of the interaction between a two-level quantum emitter and a single mode of quantum radiation. Due to the multimode continuum of eigenmodes in free space and in waveguides, the Jaynes-Cummings model should not be expected to properly describe the interaction between an emitter and a traveling pulse of quantum radiation. In this article, we review a cascaded quantum system approach that accurately describes the interaction of a quantum system with an incident quantum pulse of radiation. This approach leads to different formulations of the theory, each of a similar structure as the Jaynes-Cummings model but with important modifications.

In state-of-the-art superconducting quantum processors, each qubit is controlled by at least one control line that delivers control pulses generated at room temperature to qubits operating at millikelvin temperatures. While this strategy has been successfully applied to control hundreds of qubits, it is unlikely to be scalable to control thousands of qubits, let alone millions or even billions of qubits needed in fault-tolerance quantum computing. The primary obstacle lies in the wiring challenge, wherein the number of accommodated control lines is limited by factors, such as the cooling power, physical space of the cryogenic system, the control footprint area at the qubit chip level, and so on. Here, we introduce a multiplexed control architecture for superconducting qubits with two types of shared control lines, row and column lines, providing an efficient approach for parallel controlling $N$ qubits with $O(\sqrt{N})$ control lines. With the combination of the two-type shared lines, unique pairs of control pulses are delivered to qubits at each row-column intersection, enabling parallel qubit addressing. Of particular concern here is that, unlike traditional gate schemes, both single- and two-qubit gates are implemented with pairs of control pulses. Considering the inherent parallelism and the control limitations, the integration of the architecture into quantum computing systems should be tailored as much as possible to the specific properties of the quantum circuits to be executed. As such, the architecture could be scalable for executing structured quantum circuits, such as quantum error correction circuits.

Significant progress is required in the engineering of large, interacting quantum systems in order to realize the promises of gate-model quantum computing. Designing such systems is challenging, as the dynamics of continuous variable quantum systems are generally unintuitive, and brute-force numerical solutions are difficult to impossible in more than a few dimensions. In this work, I draw analogies between modern superconducting qubits and mechanical mass-spring systems in attempt to gain a simple intuition for what makes each design special. In particular, I analyze superconducting qubits that are inherently protected from noise, and connect this protection to features of the corresponding mechanical system. The hope is that intuition gained from analyzing these systems mechanically will allow for intuitive design of useful superconducting circuits in the future.