Fast control of long-lived quantum registers often relies on an auxiliary degree of freedom, a mediator, but real mediator excitation can introduce decoherence, leakage, or loss when the mediator is not the coherence-optimized component. We introduce dispersive interaction via analytical linear inversion (DIAL), an analytical control construction for excitation-suppressed interaction engineering in mediator-coupled quantum registers. In the dispersive regime, we show that off-resonant driving of an effective two-level mediator transition yields a diagonal Hamiltonian whose Pauli-\(Z\) interaction rates depend linearly on the drive intensities through a transfer matrix determined by the register-resolved transition spectrum. This establishes a direct linear map from experimentally accessible controls to induced multi-qubit interactions, enabling control design without iterative propagation of the full driven dynamics. We turn this structure into the target-aware DIAL algorithm, which selects favorable off-resonant tones and determines their drive intensities for a prescribed target interaction. We benchmark the resulting controls across 100 register realizations for each register size \(n=2,3,4,5\), targeting the highest-order interaction \(Z_1\cdots Z_n\) with an interaction phase of magnitude \(π/4\), which generates an \(n\)-qubit GHZ state up to local equivalence. Propagation under the full driven mediator-register dynamics yields typical gate fidelities above \(0.997\), while the maximum transient mediator excitation remains near \(1\%\) on average, far below what is typically possible with resonant Rabi drives. The manuscript is accompanied by an open-source Python package implementing the target-aware DIAL algorithm and the associated numerical validation workflow.
Fast control of long-lived quantum registers often relies on an auxiliary degree of freedom, a mediator, but real mediator excitation can introduce decoherence, leakage, or loss when the mediator is not the coherence-optimized component. We introduce dispersive interaction via analytical linear inversion (DIAL), an analytical control construction for excitation-suppressed interaction engineering in mediator-coupled quantum registers. In the dispersive regime, we show that off-resonant driving of an effective two-level mediator transition yields a diagonal Hamiltonian whose Pauli-(Z) interaction rates depend linearly on the drive intensities through a transfer matrix determined by the register-resolved transition spectrum. This establishes a direct linear map from experimentally accessible controls to induced multi-qubit interactions, enabling control design without iterative propagation of the full driven dynamics. We turn this structure into the target-aware DIAL algorithm, which selects favorable off-resonant tones and determines their drive intensities for a prescribed target interaction. We benchmark the resulting controls across 100 register realizations for each register size (n=2,3,4,5), targeting the highest-order interaction (Z_1\cdots Z_n) with an interaction phase of magnitude (π/4), which generates an (n)-qubit GHZ state up to local equivalence. Propagation under the full driven mediator-register dynamics yields typical gate fidelities above (0.997), while the maximum transient mediator excitation remains near (1%) on average, far below what is typically possible with resonant Rabi drives. The manuscript is accompanied by an open-source Python package implementing the target-aware DIAL algorithm and the associated numerical validation workflow.
Accurate control of quantum degrees of freedom is promising for sensing, communication, and computing, but building a useful quantum computer faces a central isolation-and-control challenge: qubits must remain well isolated from their environment to preserve coherence, yet also be coupled strongly enough for control, readout, and reset. Existing approaches address this challenge only partially, using separate reset elements, drive schemes, and Purcell filters, often with added complexity and tradeoffs such as heating and crosstalk. Here we introduce and demonstrate a first-generation quantum dial: a device that on demand mediates the coupling of a qubit to selected auxiliary degrees of freedom. Our implementation uses a band-stop filter between a high-coherence transmon qubit and a broadband transmission line, enabling the coupling strength to be tuned by several orders of magnitude on nanosecond timescales without significant Stark shift. In the reset configuration, we reduce the qubit energy relaxation time T1 from >150 μs to about 200 ns and demonstrate reset independent of the initial state. In the control configuration, we obtain 99.99% idle fidelity and 99.9% gate fidelities for 40 ns pulses at about -110 dBm. The same device also enables thermometry of the qubit environment, reaching a noise-equivalent temperature of 0.6 mK/Hz at 60 mK and approaching the Cramér-Rao bound at higher temperatures. The quantum dial thus offers fast, on-demand switching between isolation and strong coupling, with potential to reduce noise and errors in future quantum processors.
In multi-qubit quantum control, target unitary operations are commonly specified through full-unitary target descriptions and assessed through global comparison measures. In this work, we introduce an interaction-resolved decomposition of n-qubit unitaries that provides explicit access to their many-body interaction structure through computational-basis phases collected in a diagonalizing frame. Such a frame is conveniently given by local rotations for many operationally relevant operations, including gates generated by single Pauli strings or commuting sets of Pauli strings, such as stabilizer operations, controlled-phase gates, Toffoli-type operations, and Ising interactions. We derive parity-weighted sums of these computational-basis phases that exactly and uniquely resolve k-body interaction terms supported on arbitrary qubit subsets, which we term support-selective phase invariants. These invariants provide an interaction-resolved coordinate system that organizes unitary operations according to their multipartite interaction structure, giving direct access to local, pairwise, tripartite, and general k-partite interaction content underlying entangling operations. This enables the formulation of selective quantum optimal control targets for synthesizing desired combinations of many-body interactions. We supplement this with numerical demonstrations for a representative hardware model, a realistic nitrogen-vacancy spin register, where we synthesized isolated tripartite interactions up to local equivalence within a single control pulse, guided by these invariants, for both diagonal (ZZZ) and non-diagonal (XZZ) terms.
Achieving very fast gates that undercut the natural limits set by decoherence requires going into the strong driving limit. Realizing single-qubit control predicted beyond semi-classical, time-dependent modeling has yet to be experimentally realized on superconducting and most other computing platforms. In this regime, the common model of dynamics within a three-level manifold breaks down, and instead, we see new quantum error channels growing abruptly with decreasing time. To identify these error processes we systematically calculate the effect of multi-photon transitions that occur out of the computational space. We then derive analytical formulas to suppress these effects, as well as amplitude and phase errors on the qubit space; we term these R1D for suppressing the ∣0⟩−∣2⟩ transition and R2D when also suppressing ∣1⟩−∣3⟩ leakage. We also answer long-standing questions about the optimal values of the DRAG prefactor as well as constant detuning, when accounting for time-ordering, and also show how to calibrate other prefactors for further performance improvement. Upon correcting these varied sources of error, we numerically demonstrate gate infidelities below 10−5 for a 7ns π-rotation when incorporating existing decoherence rates.
We develop a general theory for multiphoton qubit-resonator interactions enhanced by a qubit drive. The interactions generate qubit-conditional operations in the resonator when the driving is near n-photon cross resonance, i.e., when the qubit drive is n times the resonator frequency. We pay special attention to the strong driving regime, where the resulting effective interactions are conditioned on the qubit dressed states. Next, we investigate the use of a two-tone drive to engineer an effective n-photon Rabi Hamiltonian with widely tunable effective system parameters, which could enable the realization of new regimes that have so far been inaccessible. Then, we discuss applications for the specific case where n=2, which results in qubit-conditional squeezing (QCS). We show that the QCS protocol can be used to generate a superposition of orthogonally squeezed states following a properly chosen qubit measurement. We outline quantum information processing applications for these states, including encoding a qubit in a resonator via the superposition of orthogonally squeezed states. We show how the QCS operation can be used to realize a controlled-squeeze gate and its use in bosonic phase estimation. The QCS protocol can also be utilized to achieve faster unitary operator synthesis on the joint qubit-resonator Hilbert space. Finally, we propose a multiphoton circuit QED implementation based on a transmon qubit coupled to a resonator via an asymmetric SQUID. We provide realistic parameter estimates for the two-photon operation regime that can host the aforementioned two-photon protocols. We use numerical simulations to show that, even in the presence of spurious terms and decoherence, our analytical predictions are robust.
Realizing coherent quantum computation requires precise and robust manipulation of quantum systems through quantum control protocols. Most quantum control techniques rely on heuristic methods for designing the driving pulses that steer the system towards a target state. Such methods are often based on brute-force optimization and offer limited understanding of the solution landscape. In contrast, quantum algorithms offer a rich body of analytical methods with rigorous error guarantees for implementing unitary and non-unitary transformations, which suggests a promising direction for developing new approaches to quantum control. Among various such algorithms, quantum signal processing (QSP) has emerged as a powerful framework for quantum algorithm design, implementation, and optimization. However, its potential for quantum control remains largely unexplored. In this work, we establish QSP-Control, an analytical framework for quantum control of qubit-oscillator dynamics. We focus on dispersively coupled qubit-oscillator systems and employ the QSP formalism to mitigate unwanted nonlinear effects arising from cross-Kerr interactions. In addition, we develop constructions for precise manipulation of Fock states by designing Fock-state-selective operators, based on structural parallels between the Jaynes-Cummings interaction and QSP. These findings demonstrate how several practically relevant problems in quantum control can be mapped to forms amenable to QSP, offering both a systematic design framework and an interpretable perspective on quantum control.
Abstract Robust qubit-qubit interactions mediated by bosonic modes are central to many quantum technologies. Existing proposals combining fast oscillator-mediated gates with dynamical decoupling require strong pulses or fast control over the qubit-boson coupling. Here, we present a method based on dynamical decoupling techniques that leads to faster-than-dispersive entanglement gates with low-intensity pulses. Our method is general, i.e., it is applicable to any quantum platform that has qubits interacting with bosonic mediators via longitudinal coupling. Moreover, the protocol provides robustness to fluctuations in qubit frequencies and control fields, while also being resistant to common errors such as frequency shifts and heating in the mediator as well as crosstalk effects. We illustrate our method with an implementation for trapped ions coupled via magnetic field gradients. With detailed numerical simulations, we show that entanglement gates with infidelities of 10−3 or 10−4 are possible with current or near-future experimental setups, respectively.