We demonstrate a dispersive measurement pulse shaping technique that allows for arbitrarily fast quantum non-demolition, single-quadrature measurements of non-linear systems and unconditionally leaves the measurement resonator empty. For single-qubit measurements, current measurements are limited to the 99% fidelity range due to relaxation during the process. However, trying to go to shorter times to circumvent this with square or composite digital pulses leads to leftover cavity population after measurement of the same order of error. These effects can be suppressed using simple smooth pulse shapes from a similar family of pulses as DRAG shaping, used in the context of leakage removal in superconducting qubits; here, it can be derived exactly for arbitrarily many measured modes. Beyond single qubits, the measurement pulses are fully general to dispersive measurement systems. This includes multi-qubit and multi-state (leakage) measurements where the measurement can be done in a single shot and with a single homodyne phase. Another major challenge for fast measurement is depopulating Purcell filter cavities, which we show can readily be achieved using derivative shaping. Finally, we show how to apply the technique to cascaded cavity systems, e.g~for fast remote entanglement generation.
We demonstrate a dispersive measurement pulse shaping technique that allows for arbitrarily fast quantum non-demolition, single-quadrature measurements of non-linear systems and unconditionally leaves the measurement resonator empty. For single-qubit measurements, current measurements are limited to the 99% fidelity range due to relaxation during the process. However, trying to go to shorter times to circumvent this with square or composite digital pulses leads to leftover cavity population after measurement of the same order of error. These effects can be suppressed using simple smooth pulse shapes from a similar family of pulses as DRAG shaping, used in the context of leakage removal in superconducting qubits; here, it can be derived exactly for arbitrarily many measured modes. Beyond single qubits, the measurement pulses are fully general to dispersive measurement systems. This includes multi-qubit and multi-state (leakage) measurements where the measurement can be done in a single shot and with a single homodyne phase. Another major challenge for fast measurement is depopulating Purcell filter cavities, which we show can readily be achieved using derivative shaping. Finally, we show how to apply the technique to cascaded cavity systems, e.g~for fast remote entanglement generation.
Dispersive readout, the current standard for measuring superconducting qubits, relies on relatively easy to engineer, static transverse coupling between a qubit and a detuned cavity mode. However, this method requires circuit design trade-offs between qubit-cavity coupling, cavity-feedline coupling, detuning, and the resultant decoherence introduced by the cavity mode. Additionally, the criteria for performing quantum nondemolition measurements, including reduced cavity photon numbers, further limits speed and fidelity. In this work, we introduce a circuit with pulse-tunable qubit-cavity and cavity-feedline couplings so that the entire qubit-measurement process can be fully optimized. Here, the core measurement process resembles a quantum gate operation between the qubit and the cavity, with the cavity acting like an ancilla, storing the qubit-state information. To fully explore time-dependent effects of the full qubit-cavity dynamics, we go beyond the rotating-wave, Jaynes-Cummings, or dispersive approximations, to develop a pulsed-measurement protocol. In addition, we propose a realistic circuit architecture that can provide a very fast, high-fidelity, QND measurement with near-unit efficiency.
Quantum error correction protocols require rapid and repeated qubit measurements. While multiplexed readout in superconducting quantum systems improves efficiency, fast probe pulses introduce spectral broadening, leading to signal leakage into neighboring readout resonators. This crosstalk results in qubit dephasing and degraded readout fidelity. Here, we introduce a pulse-shaping technique inspired by the derivative removal by adiabatic gate protocol to suppress measurement crosstalk during fast readout. By engineering a spectral notch at neighboring resonator frequencies, the method effectively mitigates spurious signal interference. Our approach integrates seamlessly with existing readout architectures, enabling fast, low-crosstalk multiplexed measurements without additional hardware overhead—a critical advancement for scalable quantum computing.
High-fidelity control of superconducting qubits requires carefully shaped microwave pulses to avoid several different kinds of error at once. This article is a pedagogical bridging text aimed at upper-level undergraduate and early graduate students who have completed an introductory quantum mechanics course and a first course in quantum computing or quantum information, but who have not yet encountered the physical implementation of qubit gates. We integrate physical intuition for pulse design, analytical gate-level descriptions, and practical hardware considerations into a single, derivation-driven narrative, with explicit learning objectives. We begin with simple pulse envelopes and their spectral properties, showing how finite bandwidth produces leakage outside the computational subspace. This motivates the derivative removal by adiabatic gate (DRAG) technique, which we derive explicitly using the Magnus expansion, obtaining a clear, order-by-order account of which physical error channel appears at which order and why DRAG's cancellation is necessarily incomplete. We discuss the practical hardware realities of control pulse generation, focusing on arbitrary waveform generators (AWG), local oscillators (LO), and IQ mixing. Finally, we extend the discussion to two-qubit operation via the cross-resonance gate, and interpret how driving the control qubit at the target qubit's transition frequency necessarily produces several unwanted interaction terms alongside the desired one, and how successive generations of pulse-engineering strategies have been designed to suppress them.
A fundamental challenge in quantum computing is to increase the number of operations within the qubit coherence time. While this can be achieved by decreasing the gate duration, the use of shorter signals increases their bandwidth and can cause leakage into energetically separated states. A common method to suppress leakage for short pulses is the Derivative Removal by Adiabatic Gate (DRAG) method, which, however, relies on IQ modulation of radio-frequency (RF) signals, thus cannot be applied to the baseband signals, e.g., for semiconductor spin qubits. This paper proposes a novel technique, Delayed Leakage Reduction (DLR), that suppresses leakage at targeted frequencies even for baseband control by using time-delayed repetitions of the control signal to enable rapid, high-fidelity operations. We apply DLR on the adiabatic CZ gate between two spin qubits and achieve fidelities exceeding 99.9% within 9.4 ns for a resonance frequency difference of only 100 MHz. Towards the experimental realization of the proposed control method, we also assess the impact on the fidelity of the sampling rate, noise, and signal quantization of the electronic hardware generating the control pulse, thus setting the minimum hardware requirements for any experimental demonstration.
The potential of superconducting qubits as the medium for a scalable quantum computer has motivated the pursuit of improved interactions within this system. Two challenges for the field of superconducting qubits are measurement fidelity, to accurately determine the state of the qubit, and the efficient transfer of quantum states. In measurement, the current state-of-the-art method employs dispersive readout, by coupling the qubit to a cavity and reading the resulting shift in cavity frequency to infer the qubit's state; however, this is vulnerable to Purcell relaxation, as well as being modeled off a simplified two-level abstraction of the qubit. In state transfer, the existing proposal for moving quantum states is mostly untested against non-idealities that will likely be present in an experiment. In this dissertation, we examine three problems within these two areas.We first describe a new scheme for fast and high-fidelity dispersive measurement specifically designed to circumvent the Purcell Effect. To do this, the qubit-resonator interaction is turned on only when the resonator is decoupled from the environment; then, after the resonator state has shifted enough to infer the qubit state, the qubit-resonator interaction is turned off before the resonator and environment are recoupled. We also show that the effectiveness of this ``Catch-Disperse-Release'' procedure partly originates from quadrature squeezing of the resonator state induced by the Jaynes-Cummings nonlinearity.The Catch-Disperse-Release measurement scheme treats the qubit as a two-level system, which is a common simplification used in theoretical works. However, the most promising physical candidate for a superconducting qubit, the transmon, is a multi-level system. In the second work, we examine the effects of including the higher energy levels of the transmon. Specifically, we expand the eigenstate picture developed in the first work to encompass multiple qubit levels, and examine the resulting changes to the system. In particular, we analyze the population of the non-target eigenstates as a result of this expanded model, and provide an analytical form for these deviations from the simpler model in Catch-Disperse-Release (i.e., the dressed state approximation).Lastly, we assess the robustness of the existing quantum state transfer protocol, testing its performance under typical experimental deviations from the ideal case. We show that the procedure is resilient to almost all non-idealities, except frequency mismatch between the two cavities. We also demonstrate a method to compensate for one such error in frequency-matching.
While relatively easy to engineer, static transverse coupling between a qubit and a cavity mode satisfies the criteria for a quantum non-demolition (QND) measurement only if the coupling between the qubit and cavity is much less than their mutual detuning. This can put significant limits on the speed of the measurement, requiring trade-offs in the circuit design between coupling, detuning, and decoherence introduced by the cavity mode. Here, we study a circuit in which the qubit-cavity and the cavity-feedline coupling can be turned on and off, which helps to isolate the qubit. We do not rely on the rotating-wave or dispersive approximations, but solve the full transverse interaction between the qubit and the cavity mode. We show that by carefully choosing the detuning and interaction time, we can exploit a recurrence in the qubit-cavity dynamics in a way that makes it possible to perform very fast, high fidelity, QND measurements. Here, the qubit measurement is performed more like a gate operation between the qubit and the cavity, where the cavity state can be amplified, squeezed, and released in a time-sequenced fashion. In addition, we also show that the non-demolition property of the off-resonant approximation breaks down much faster than its dispersive property, suggesting that many of the dispersive measurements to date have been implemented outside the QND regime.