Session Q38: Quantum Control I

Shortcuts to adiabaticity for non-Hermitian dynamics in the vicinity of higher-order exceptional points

The complex energy spectrum of an effective non-Hermitian Hamiltonian can possess unique topology in the space of Hamiltonian parameters. Tuning these parameters allows us to realize non-trivial phenomena and invariants associated with their special degeneracies. We investigate how real-time parameter tuning can be used to observe these topology-dependent phenomena. In practice, however, adiabatic processes require long evolution times, which are not desirable for practical purposes, nor possible in many experimental setups in open quantum systems, especially those described by effective non-Hermitian Hamiltonians. Shortcuts to adiabaticity emulate the dynamics expected from slow adiabatic evolution in a fast time-dependent process. We harness a superconducting circuit platform to realize dynamical control of the system in the vicinity of its Hamiltonian exceptional points. Additional counter-diabatic controls improve the fidelity of the system's evolution.   

Coherent Non-Local Subspace Dynamics Induced by Zeno Measurements

We describe how an entangling operation related to a CPHASE gate may be implemented by drawing on unique features of quantum measurement. The dynamics of a quantum system can be frozen by sufficiently strong monitoring, i.e., by the quantum Zeno effect. We show here that it is possible to combine local unitary operations and Zeno blocking of a single transition within a larger quantum system, in such a way that an effective non-local quantum operation is performed in an unmonitored subspace. We illustrate ideal realizations of such a process in detail, and then further describe the conditions under which it may be implemented using the dispersive continuous monitoring techniques commonly used in superconducting qubit systems. The scheme is experimentally feasible, and an implementation of it will be described in the talk by E. Blumenthal et al.   

Model predictive control for robust quantum state preparation

A critical engineering challenge in quantum computing is the accurate control of quantum dynamics. To design classical control fields sufficient for high-fidelity quantum processes, model-based numerical methods for quantum optimal control are essential.  These open-loop control strategies are known to be limited by systematic modeling errors and noise. Closed-loop strategies provide critical performance enhancements by bringing experimental data to task. Model predictive control (MPC) is a model-based feedback strategy complimentary to existing model-free feedback strategies used for quantum optimal control. MPC naturally accommodates experimental constraints and is robust in the presence of systematic modeling errors and noise. We show how MPC can be used to generate practical optimal control sequences in representative examples of quantum state preparation and, by extension, quantum gate synthesis. Our examples showcase why MPC makes a welcome addition to the quantum engineer's toolbox.   

Systematically Realizing Unconventional Coherent Filters for High Precision Sensing

Linear processing of broadband traveling quantum fields are of interest in a variety of applications such as continous variable quantum information processing with Gaussian states and linear precision sensing in devices such as gravitational-wave interferometers.  The processing is carried out by linear quantum systems that are realized by open oscillator systems with a quadratic internal Hamiltonian and linear coupling to external traveling fields. They are distinguised by the linear dynamics of the amplitude and phase quadratures of the oscillators and traveling fields. The last decade has seen a systematic realization theory for this class of quantum systems being developed, extending well-established techniques for classical linear state-space systems that have been central in the development of modern control theory.

In this talk I will present recent research on the application  of linear quantum systems theory for the systematic realization of coherent filters for high precision measurements. This results in a procedure that starts from a specification of the desired transfer function or frequency-domain response for  the coherent filter and ends with the filter's quantum optical realization. This approach not only facilitates the  construction of coherent filters that defy conventional intuition, but also opens a path towards the systematic design of optimal quantum measurement devices. An application of the methodology is described for realizing an active unstable filter with anomalous dispersion, proposed for improving the quantum-limited sensitivity of gravitational-wave detectors.

Hamiltonian Engineering of Dipolar Coupled Spin Systems Using Reinforcement Learning

Hamiltonian engineering of quantum many-body systems is central to many quantum simulation and sensing protocols. Average Hamiltonian theory (AHT) has historically been the methodology used to both design pulses sequences to engineer effective Hamiltonians in solid-state spin systems, as well as to characterize their sensitivity to error.  Recently, reinforcement learning (RL) has emerged as another avenue to engineer effective Hamiltonians.  RL algorithms treat the system's dynamics as a black box with the potential to provide robustness to experimental imperfections.  However, unconstrained RL algorithms have not outperformed conventional methods to date.  There are multiple ways in which additional physical constraints can be imposed on the RL algorithm.  Here, we use theoretical insights into the quantum dynamics of the interacting spin systems to constrain the action space of the RL algorithm.  For the problem of decoupling magnetic dipolar interactions in solid-state spin systems, this approach allows us to find multiple pulse sequences that perform at a similar level to conventional sequences, and at a significantly higher level than unconstrained RL algorithms.   

Adiabatic resonance for fast and robust quantum control

Adiabatic passage is a useful technique to realize quantum control and quantum gates. It is in general robust, albeit slow. Here we propose a universal scheme to achieve fast adiabatic passage with high-fidelity based on the so-called "adiabatic resonance": By designing a cyclic evolution in the adiabatic frame, the evolution path periodically returns to the adiabatic path, leading to high operation fidelity near resonance points. We first reveal the general condition of adiabatic resonance, then derive the specific condition for a two-level system, and apply it to a double quantum dot. With such a designed detuning pulse we can realize adiabatic Landau-Zener transition rapidly. Compared to other schemes aiming at accelerating the adiabatic passage, such as transitionless quantum driving, this adiabatic resonance scheme has the advantage that it does not require any additional control Hamiltonian. Lastly, we discuss the possibility of optimization and built-in robustness against noise.   

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Precise steering of quantum systems has found many modern applications, e.g. in quantum computation. One fruitful approach has been in the area of quantum transitionless driving (QTD), or more general shortcuts to adiabaticity (STA), where one drives quantum systems to a desired state that is an instantaneous eigenstate of a given time-dependent Hamiltonian H₀(t). There is some freedom in the driving Hamiltonian H₁(t), which partly depends on whether one wants strict QTD or more general approaches to STA. Unfortunately, in all but the simplest cases, direct implementation of H₁(t) is impractical (due, e.g. to its being nonlocal), and one must resort to approximation schemes. In our work, we expand upon the ideas in STA by studying the geometrical structure behind the relationship between H₀(t) and H₁(t), and we make use of this structure to generate families of the driving term H₁(t) that can be used to eliminate undesirable properties that render implementation impractical. Having families of Hamiltonians H₁(t) available also allows the possibility of optimization for a given task, e.g., driving in the presence of noise. To illustrate our ideas, we present results on driving a particle on a ring geometry with a scattering potential and threaded by a time-dependent flux.            

Fast superconducting qubit control with sub-harmonic drives

Increasing the fidelity of single-qubit gates requires a combination of faster pulses and increased qubit coherence.   However, with traditional resonant qubit driving via a capacitively coupled port, these two objectives are mutually contradictory, as higher qubit quality factor requires a weaker coupling, necessitating longer pulses for the same applied power.  Increasing drive power, on the other hand, can heat the qubit's environment and degrade coherence. In this talk, we will introduce a new parametric scheme for performing single-qubit gates by pumping at approximately 1/3 the qubit's resonant frequency.  The large separation in qubit and drive frequencies enables us to use filtering to perform rapid gates while protecting the qubit's coherence at the same time.  In addition, the Rabi rate of this process is proportional to driving voltage cubed, allowing rapidly increased gate speed with only modest increases in applied power. We will present our recent results, especially our gate calibration and tune up methods, which currently allow pi-pulses as short as tens of nanoseconds with gate error rate as low as 0.5% limited by qubit coherence.   

Topological characterization of discontinuous control pulses

We apply a topological analysis to the dynamics of a qubit when driven by discontinuous control pulses that do not end where they start when repeated. This builds on results where multiple drives of incommensurate frequencies create synthetic dimensions which cause the driving dynamics to obtain topological properties [P. J. D. Crowley, et al. Phys. Rev. B 99 064306 (2019)]. We find that truncating a two-frequency quasiperiodic drive and repeating it preserves much of its topological nature, with important changes. The pulse discontinuities shift the quasienergy eigenstate diabatically. The consequence of this depends on the topological class. In the topologically trivial phase, when Chern number C=0, the dynamics are still localized within each control pulse but can become delocalized over multiple time steps. As the system transitions to its non-trivial topological state with C≠0 the dynamics become sensitive to small perturbations of the initial drive even after starting in an eigenstate, suggestive of chaotic dynamics. We then discuss generalizations of these findings to generic control pulses.   

Landau-Zener-Stuckelberg-Majorana transitions for interferometry and quantum control

Since the pioneering works by Landau, Zener, Stuckelberg, and Majorana (LZSM), it is known that driving a quantum two-level system results in tunneling between its states. Even though the interference between these transitions was known to be important, it is only recently that it became both accessible, controllable, and useful for engineering quantum systems [1]. An LZSM transition is a non-adiabatic transition of population between two tuned energy levels. We study many important properties of the LZSM transitions, such as constructive and destructive interference, occupation conservation transition, and single-qubit gates based on LZSM transitions.   

Fast Landau-Zener-Stückelberg-Majorana quantum logic gates

The most common realization of quantum gates and control is based on Rabi oscillations, which cause a periodic resonant excitation of the system. However, certain limitations may arise under resonant driving, including achievable gate speeds and additional complications, like counter-rotating terms.  We study a qubit control technique based on Landau-Zener-Stückelberg-Majorana (LZSM) interferometry, which allows a complementary approach to quantum control based on non-resonant driving with the alternation of adiabatic evolution and non-adiabatic transitions. Compared to the Rabi oscillations method, the main differences are a non-resonant excitation frequency and a small number of periods in the external excitation. This allows us to achieve a higher speed of qubit operations without losing fidelity. Both of these characteristics have major importance for experimental realizations of quantum computers, as these define the number of quantum operations that could be performed during the coherence time of the system. We study different aspects of LZSM excitations: qubit dynamics, relaxation, and coupling with the environment. We explore related mechanisms and dynamics for a universal set of quantum operations.   

Implementation of quantum driving for high-fidelity and energy-efficient single-qubit gates.

Single-qubit gates (SQG) are typically implemented by directly driving the qubit through an open transmission line. We study an alternative driving scheme, called quantum driving (QD), where the qubit is controlled by a quantized electromagnetic field, here a single mode of a coplanar waveguide (CPW) resonator. The estimated error is inversely proportional to the average number of photons in the resonator, which enables high-fidelity of SQG in this QD scheme. Furthermore, QD is energy efficient since the single-mode CPW resonator consumes two orders of magnitude less energy compared with an open transmission line in direct driving. Energy-efficient high-fidelity SQG with QD is a promising driving scheme for superconducting qubits to build a scalable quantum processor. We present numerical and experimental results of the single-qubit gate using the QD scheme.

Acceleration and deceleration of quantum dynamics and shortcuts to adiabaticity based on inter-trajectory travel with fast-forward scaling theory

Quantum information processing requires fast manipulations of quantum systems to overcome dissipative effects. In this talk, we show a method to accelerate quantum dynamics to obtain a desired target state in a shorter time compared to unmodified dynamics. We apply the theory to a system consisting of two linearly coupled qubits. Our method enables one to derive control parameters which realize target end states of adiabatic dynamics in shorter periods of time, thus realizing a shortcut to adiabaticity. Furthermore, we address experimental limitations to the rate of change of control parameters for quantum devices which often limit one’s ability to generate a desired target state with high fidelity. Naively scaling down the rate of change of control parameters will in general not produce the desired target state, leading to a loss of fidelity. We show that an initial state following decelerated dynamics can reach a target state while varying control parameters more slowly, enabling more experimentally feasible driving schemes.