Advances in Quantum Control - Techniques, Applications, and Challenges

As quantum computing advances, variational quantum algorithms (VQAs) are among the most promising approaches to leverage near-term quantum devices for tasks that could demonstrate quantum advantage. Two primary challenges VQAs face are the design of the ansatz and the need to solve a non-convex classical optimization problem to update the parameters of the parameterized quantum circuit. Inspired by control theory, feedback-based quantum algorithms are proposed as an alternative approach by replacing the classical optimizer with a control law that directly updates the quantum circuit’s parameters. This work will present feedback-based quantum algorithms tailored for calculating excited states and solving constrained optimization problems, highlighting their potential advantages and applications in quantum optimization.

Quantum systems are susceptible to noise and imperfections from external controls, which pose significant challenges to the practical realization of quantum technologies. These noise factors limit the precision of quantum gates, making their mitigation essential for developing reliable quantum systems. In this study, we apply Optimal Control Theory (OCT) within a thermodynamically consistent framework to investigate the creation and stabilization of quantum gates in noisy environments.

Quantum optimal control plays a crucial role in the development of quantum technologies. By optimizing the shape of a control pulse, we can prepare quantum states needed to initialize algorithms in a quantum computer and implement unitary operations on the system. However, most currently used optimization methods rely on gradient-based techniques, which are inherently non-convex and can lead to complex landscapes where they may get stuck in local minima. We propose QCPOP, a new approach that reformulates quantum optimal control as a polynomial optimization problem. This allows us to apply standard polynomial optimization methods to find global solutions more effectively.

I consider the problem of optimally driving the ground state of a many-body quantum system across a quantum phase transition in finite time. In this context, excitations caused by the breakdown of adiabaticity can be minimized by adjusting the schedule of the control parameter that drives the transition. Drawing inspiration from the Kibble-Zurek mechanism, we characterize the timescale of onset of adiabaticity for several optimal control procedures. Our analysis reveals that schedules relying on local adiabaticity, such as Roland-Cerf’s local adiabatic driving and the quantum adiabatic brachistochrone, offer limited speedup over traditional adiabatic evolution in the transverse-field Ising model. As an alternative, we introduce a framework that, by exploiting the Landau-Zener formula and taking into account the role of higher-excited states, outperforms schedules obtained via both local adiabaticity and state-of-the-art numerical optimization. REF: Grabarits, Balducci, Sanders, and del Campo, Phys. Rev. A 111, 012215 (2025)

The counterdiabatic (CD) ansatz has demonstrated significant potential for optimizing quantum circuits and offers valuable insights into the development of more efficient and robust quantum algorithms. In this talk, I will present two examples of digital quantum simulation of dynamics in fermionic lattice models utilizing the CD ansatz. The Su-Schrieffer-Heeger (SSH) chain serves as a paradigmatic model for understanding topological phases and their associated edge states, playing a crucial role in quantum materials. The nonadiabatic yet high-fidelity transfer of edge states in an SSH chain [1] is achieved by leveraging an approximate time-dependent CD interaction derived from adiabatic gauge potentials. To simplify experimental implementation and mitigate computational complexity, we identify next-nearest-neighbor hopping terms between sublattice A sites as the dominant CD driving terms and further optimize them using variational quantum circuits. Our digital quantum simulation demonstrates the ability to achieve rapid and robust state transfer, even in the presence of disorder. We also introduce an adaptive CD quantum algorithm designed to efficiently compute the ground-state energy of the one-dimensional Fermi-Hubbard (FH) model. By simulating Coulomb interaction strengths in quantum circuits, we explore the phase transition from a conducting phase to a Mott-insulating phase. Key physical properties, including double occupancy, charge correlations, and spin correlations, are analyzed to characterize this transition. Furthermore, we apply an external electric field to examine the system’s current response across different interaction strengths [2]. References [1] Sebastián V. Romero, Xi Chen, Gloria Platero, and Yue Ban, Optimizing edge-state transfer in a Su-Schrieffer-Heeger chain via hybrid analog-digital strategies, Phys. Rev. Applied 21, 034033 (2024). [2] Quantum Simulation of Phase Transition in the Fermi-Hubbard Model with Adaptive Counterdiabatic Ansatz, in preparation.

Modern-day quantum technologies – from quantum sensing to information processing and quantum simulations – require an efficient control of the quantum dynamics. Optimal control theory allows us to address this problem, optimizing the microscopic dynamics to satisfy experiment-dependent requirements, including the preparation of physically interesting quantum states and the minimization of physical observables (like, e.g., the energy or the total spin magnetization). In this framework, the optimization procedure amounts to finding the global minima of a high-dimensional cost function, assigning a figure of merit to each choice of control variables (i.e., the time-dependent parameters appearing in the Hamiltonian). In this talk, I will analyze abrupt transitions occurring in the cost function upon varying a control parameter. A prime example is the quantum speed limit (QSL), which mark the onset of controllability as the protocol duration is increased [1]. In particular, I will discuss analytical and numerical methods designed to unravel the connection between (i) structural changes in the cost function and (ii) non-analytic points in statistical order parameters that capture properties of near-to-optimal control variables [2, 3]. [1] Phys. Rev. Lett. 122 (2019) [2] arXiv:2408.11110 [3] arXiv:2411.08736

Controlling chaos is a well-established technique that leverages the exponential sensitivity of classical chaotic systems for efficient control. This concept has been generalized to single-particle quantum systems [1] and, more recently, extended to bosonic many-body quantum systems described by the Bose-Hubbard model [2]. In direct analogy to the classical paradigm, a localized quantum state can be transported along a specific trajectory to a desired target state. In the latter context, this approach reduces to time-dependent control of the chemical potentials, making it suitable for implementation in optical lattice experiments. Highlighted potential applications are rapid, customizable state preparation and stabilization of quantum many-body scars in one-, two-, and three-dimensional lattices. Recent progress includes potential applications to large time-crystal platforms and preparation protocols for entangled states, such as cat-like states. [1] S. Tomsovic, J. D. Urbina, and Klaus Richter, Controlling Quantum Chaos: Optimal Coherent Targeting, PRL 130.2 (2023): 020201. [2] L. Beringer, M. Steinhuber, J. D. Urbina, K. Richter, S. Tomsovic, Controlling many-body quantum chaos: Bose-Hubbard systems, New J. Phys (2024): 26 073002.

Continuous-time quantum walks (CTQWs) offer a quantum advantage over classical random walks, enabling speed-up in tasks relevant to quantum computation and algorithms. While most studies have focused on closed-system scenarios, continuous measurement and quantum trajectories have emerged as powerful tools for characterizing and controlling quantum systems beyond standard quantum formalism. In this work, we explore a novel approach to spatial search on a cycle graph by integrating CTQWs with continuous measurement and feedback control. Unlike conventional search protocols where the oracle is static, i.e. a projector on the target state, we implement a dynamic oracle through a feedback Hamiltonian. By continuously monitoring the quantum walker’s position and applying a unitary feedback operation based on the measurement outcomes, we dynamically adjust the couplings between nodes. The feedback is optimized numerically at each step, and we assess the protocol’s performance by simulating stochastic trajectories for graphs up to $N=15$. The search efficiency is quantified through the average fidelity between the walker’s state and the target node. Our results show that unbounded control strategies enable rapid localization of the walker, while imposing upper bounds on the control couplings reduces performance. Additionally, a digital feedback protocol is found to perform comparably to the continuous bounded one. Beyond spatial search, this framework has broader implications for quantum transport, state transfer, and quantum routing, suggesting potential applications in near-term quantum devices. Future directions include exploring chiral quantum walks and external magnetic fields to enhance control strategies within an adiabatic optimal control framework.

Spin-squeezed states are highly entangled quantum states with important metrological applications. Interest in these states has grown recently, as spin-squeezing inequalities enable the detection of quantum entanglement through collective measurements. This makes them ideal for generating and verifying metrologically useful quantum entanglement in quantum simulation platforms, such as Rydberg atom arrays. However, current methods typically rely on evolving a coherent spin state over time, hoping that a spin-squeezed state will emerge. Experimentally, this approach is challenging, as it requires numerous measurements to determine the optimal squeezing direction and estimate squeezing using the Wineland criterion. We propose employing quantum control techniques to achieve richer spin squeezing, leading to higher entanglement while also allowing precise control over the squeezing direction. Our results show that in few-body systems, the most optimal spin-squeezed states can be attained—something not achievable through simple quench dynamics. Moreover, this approach enables manipulation of both the amount and type of squeezing, facilitating the creation of non-trivial quantum-entangled states.

Quantum walks, particularly continuous-time quantum walks (CTQW), have emerged as powerful tools for modeling quantum transport, simulating complex dynamics, and developing quantum algorithms with potential speedups over classical counterparts. In this work, we present a scalable quantum circuit approach to simulate CTQW on random graph structures, specifically focusing on Erdős–Rényi random graphs. Our quantum circuit construction efficiently implements the time evolution of the graph Laplacian, using the Trotterization scheme. We investigate key dynamical properties of the CTQW including the mixing time, hitting time, and the localization behavior, providing insights into the ergodic properties of the system. Our quantum circuit implementation over random graph to probe CTQW ensures that the circuit design can work on any graph structure, laying the foundation for realizing CTQW-based quantum simulations efficiently.

Thouless pumping is a transport phenomenon in which a time-periodic Hamiltonian transfers a quantized charge per driving cycle in the quasi-adiabatic limit. In this work, we accelerate Thouless pumping using shortcuts to adiabaticity. Specifically, we apply counterdiabatic driving to the Rice-Mele model—one of the simplest realizations of Thouless pumping—to ensure the system remains in its ground state at any driving speed. We demonstrate that the pumped charge across each bond is topologically quantized by a Chern number. While counterdiabatic driving typically requires long-range hopping terms, we show that experimentally viable, nearest-neighbor counterdiabatic Hamiltonians can be constructed either by selecting specific Rice-Mele model parameters or through numerical optimization, enabling fast and practical implementations of Thouless pumping.

The characterisation of quantum networks is fundamental to understanding how energy and information propagates through complex systems, with applications in control, communication, error mitigation and energy transfer. In this work, we explore the use of external probes to infer the network topology in the context of continuous-time quantum walks, where a single excitation traverses the network with a pattern strongly influenced by its topology. The probes act as decay channels for the excitation, and can be interpreted as performing an indirect measurement on the network dynamics. By making use of a Genetic Optimisation algorithm, we demonstrate that the data collected by the probes can be used to successfully reconstruct the topology of any quantum network with high success rates, where performance is limited only by computational resources for large network sizes. Moreover, we show that increasing the number of probes significantly simplifies the reconstruction task, revealing a tradeoff between the number of probes and the required computational power.

This work aims to utilize sub-Riemannian geometry to design energetically optimal control fields for quantum gates in the presence of undesired interactions. We first study the case of a single noisy qubit. By treating the computation as a curve in the unitary group, we seek geodesics that connect the identity to a unitary operation sufficiently close to the ideal case, despite the presence of noise. Next, we analyze the case of two physical qubits under a time-constant cross-talk interaction, where we aim to implement both single- and two-qubit gates. The main challenge lies in determining the unknown initial conditions of the geodesic equation that lead to the desired unitary operators. We present a Monte Carlo approach for solving the geodesic equation and discuss its advantages and limitations.

A quantum control protocol is proposed for the creation of NOON states with $N$ ultracold bosonic atoms on two modes, corresponding to the coherent superposition $\vert N,0\rangle + \vert 0,N\rangle$. This state can be prepared by using a third mode where all bosons are initially placed and which is symmetrically coupled to the two other modes. Tuning the energy of this third mode across the energy level of the other modes allows the adiabatic creation of the NOON state. While this process normally takes too much time to be of practical usefulness, due to the smallness of the involved spectral gap, it can be drastically boosted through counterdiabatic driving which allows for efficient gap engineering. We demonstrate that this process can be implemented in terms of static parameter adaptations that are experimentally feasible with ultracold quantum gases. Gain factors in the required protocol speed are obtained that increase exponentially with the number of involved atoms and thus counterbalance the exponentially slow collective tunneling process underlying this adiabatic transition. Besides optimizing the protocol speed, our NOON state preparation scheme achieves excellent fidelities that are competitive for practical applications.

Quantum impurity problems have long relied on the simplifying assumptions of spherically symmetric, additive interaction potentials—yet real-world interactions are often inherently anisotropic and non-additive. Here, a Rydberg impurity immersed in a Bose–Einstein condensate presents an ideal, tunable, and experimentally accessible platform to explore these complexities. The Rydberg atom’s electronic wave function extends so far that its interaction range can rival—or even exceed—the condensate’s mean interparticle spacing. By selecting the principal quantum number and exciting to l>0 states, one breaks spherical symmetry and accesses degenerate m-levels whose mixing generates genuine non-additive forces. We calculate the full many-body absorption spectrum of such a Rydberg impurity in an ideal BEC, identifying signatures of attractive and repulsive polarons, bound molecular states, and a crossover to classical, mean-field behavior. We further show how two-body partial-wave scattering is shaped by Feshbach-type resonances and how anisotropic interactions leave distinct fingerprints in the spectrum.

Advances on quantum technologies depend on the coherent preparation and manipulation of quantum states in hybrid systems. We present a fast method for generating nonclassical states of a bosonic mode through light-matter interactions mechanism. Specifically, we employ quantum control technique to generate highly nonclassical entangled cat states with high fidelity. Our protocol is both efficient and achievable within the quantum speed limit.

Universal quantum computing requires a quantum system that is capable of performing every possible unitary operation, i.e. a system that is operator-controllable. However, the number of resources required for controllability in complex systems is not obvious. In qubit arrays, these resources come in the form of local controls and qubit couplings. Assessing controllability of a sizeable qubit array is therefore a difficult task to achieve in practice. Previously developed numerical controllability tests stop giving valid answers for a large number of qubits. Here we present a mathematically proven result that showcases an arbitrarily large quantum computing architecture that is ensured to be operator controllable. The key to our approach is the use of a modular structure that uses optimized smaller qubit arrays as building blocks to create the larger structure. This follows the trend in certain platforms for quantum computing like superconducting qubits, with leading companies like IBM and Google promising to use their quantum processors in a modular manner to scale up the devices. The mathematical proof presents which types of couplings between modules ensure that the resulting device is still operator controllable. This paves the way for a scalable approach towards the design of quantum computers while maintaining their universality. Our presented approach can also be used to vastly expand the number of cases that can be studied using previous controllability tests by breaking a large system into minor modules whose controllability can be determined. As an example, we have studied IBM’s eagle quantum processors (consisting of 127 qubits) to prove their controllability using modular decomposition. As previously mentioned, this result could not have been achieved by other numerical tests available. Finally, by using operator controllable modules that use a low number of resources, we can design scalable architectures that save on the quantity of controls and couplings that have to be added to a given qubit array to reproduce all possible quantum logic gates in a given circuit. While minimizing the number of controls and couplings can be detrimental for the speed at which the calculations can be processed on a device, this method opens a new path to find the sweet spot for the trade-off between connectivity and simplicity of the design.

We investigate the application of quantum annealing on the D-Wave Advantage 2 platform for both combinatorial optimization and quantum many-body physics. First, we explore room scheduling optimization for sports camps at the Australian Institute of Sport, formulating the problem as a binary integer programming task. By comparing classical, hybrid, and quantum annealing approaches, we assess embedding challenges and the feasibility of quantum solutions given current hardware limitations. We explore and propose solutions for problem-aware calibration, correcting long-range interactions detrimental to the model. Second, we investigate the experimental realization of a classical Z_2 spin liquid using a native embedding on the Advantage 2 hardware. We present progress toward studying defect transport by initializing defects and tracking their evolution, demonstrating the potential of quantum annealing for probing emergent phenomena, even in noisy environments.

In critical quantum metrology, the extreme sensitivity of a system's stationary state to minimal changes in system parameters often causes the quantum Fisher information to scale super-quadratic with the system's energy. From the Heisenberg limit, which constrains the optimal scaling of precision with resources to a quadratic dependence, it follows that the time required to reach such a stationary state must be sufficiently long. By analyzing a continuous measurement performed on the steady state of a critical system, similar conclusions can be drawn about the correlation time of the light interacting with the system. In this work, we investigate parametric Kerr resonators undergoing driven-dissipative phase transitions [1], demonstrating how fundamental constraints on measurement precision [2] determine the scaling of correlation time with the average photon number [3]. The proposed method provides a framework applicable to a wider class of problems. [1] U. Alushi, W. G´orecki, S. Felicetti, and R. Di Candia, Optimality and Noise Resilience of Critical Quantum Sensing, Phys. Rev. Lett. 133, 040801 (2024). [2] W. G´orecki, F. Albarelli, S. Felicetti, R. Di Candia, and L. Maccone, Interplay between time and energy in bosonic noisy quantum metrology, arXiv preprint 10.48550/arXiv.2409.18791 (2024). [3] W. Gorecki, S. Felicetti, R. Di Candia, and L. Maccone, In preparation.

Optomechanics with levitated particles offers a powerful platform to explore quantum physics at macroscopic scales, including ground-state cooling. A major outstanding goal is to entangle the motion of two levitated nanoparticles, creating a genuine quantum state to study decoherence mechanisms. However, weak interactions between particles have so far prevented this. We address this challenge by employing electrostatic (Coulomb) interactions between two optically trapped silica nanoparticles. We systematically study active and passive charging methods and demonstrate strong coupling with an interaction strength reaching 12\% of the mechanical frequency (g = 0.12\omega). We also achieve ground-state cooling and readout of the coupled normal modes. Since steady-state entanglement still requires significantly stronger coupling, we propose a protocol based on optimal quantum control of continuously measured systems with time-dependent interactions. This approach relaxes the coupling requirements and enables unconditional entanglement under current experimental conditions. We will discuss the stabilization of the strongly coupled system, feedback control of the normal modes, and the impact of noise near the ground state.

Continuous quantum error correction (QEC) is required in many situations in which the limit of a strong projective measurement cannot be applied. Recently, Atalaya et al. [Phys. Rev. A 103, 042406 (2021)] proposed a continuous QEC scheme for quantum information applications which involve continuously varying Hamiltonians. This scheme relies on a sufficiently strong and continuous two-qubit parity measurement to extract the error syndromes. To implement such a measurement is particularly challenging, since one has to perform a fast, nonlocal measurement while at the same time not introducing any errors to the information encoded in the qubits. We investigate to what extent this task can be accomplished using current circuit QED architecture. Recent proposals for continuous parity measurements in this field rely on the so-called dispersive regime in which the transmons are far detuned from a resonator which acts as the meter for the parity measurement. As a result, transmons and resonator are only weakly coupled and the measurement is slow. We explore how one can achieve speedups by going to the quasi-dispersive regime. Measurements based on the quasi-dispersive regime could then be utilized to enhance the resilience of Atalaya et al.'s and future QEC protocols.

The Surrogate Hamiltonian is a method used to study non-Markovian dynamics in open quantum systems [1]. Here, an infinitely large thermal bath is represented by a surrogate bath made up of a finite number of two-level systems that strongly interact with the system we are interested in. The system and the primary bath are then propagated as a closed system. As expected, this model reproduces true dynamics only for short times due to the unitary evolution of the system and the surrogate bath. 
 The Stochastic Surrogate Hamiltonian is a Markovian embedding technique that improves on this by implementing a stochastic reset of the surrogate modes to the thermal state. This allows for extended simulation times [2]. However, so far, this method has only been presented heuristically and in a thermodynamically inconsistent manner [3]. We aim to formulate this method in a more rigorous way while ensuring thermodynamic consistency on average. 
 [1] Baer et al., J. Chem. Phys. 106, 8862 (1997) 
[2] Katz et al., J. Chem. Phys. 129, 034108 (2008) 
[3] Kosloff, J. Chem. Phys. 150, 204105 (2019)

Quantum universal computation relies on scalable, noise-resilient architectures with efficient error correction and high-fidelity gates. A key challenge is enabling scalable two-qubit operations, often constrained to neighboring qubits. Several works have proposed selectively coupling any pair of qubits through a common data bus. Typically, the coupling mechanism requires that the characteristic frequencies of the qubits and the bus are of the same order. We explore an alternative approach where strongly driven qubits achieve resonance with the bus via dressing. This method facilitates flexible qubit-qubit coupling and precise control of interaction times for gate implementation. In this work, we consider two strongly driven qubits coupled to a harmonic oscillator and analyze the effects of dissipation and thermal noise on the fidelity of the two-qubit gate.

In this work we simulate the charging process and work extraction of many-body quantum batteries on noisy intermediate-scale quantum devices and devise the variational quantum ergotropy (VQErgo) algorithm, which finds the optimal unitary operation that maximizes work extraction from the battery. We test VQErgo by calculating the ergotropy of a many-body quantum battery undergoing transverse field Ising dynamics following a sudden quench. We investigate the battery for different system sizes and charging times and analyze the minimum number of ansatz circuit repetitions needed for the variational optimization using both ideal and noisy simulators. We also discuss how the growth of long-range correlations can hamper the accuracy of VQErgo in larger systems, requiring increased repetitions of the ansatz circuit to reduce error. Finally, we optimize part of the VQErgo algorithm and calculate the ergotropy on one of IBM's quantum devices.

We have developed techniques for optimal control of open systems with Hilbert space basis sizes of up to $2^16$. This can be done on a CPU server with around 100 cores and 500 GiB memory without any special accelerators. The chosen approach is to avoid storage of operators and superoperators as sparse matrices, and instead calculate the matrix elements immediately when action on a state vector or density matrix is performed. While it is not obvious that recalculation of matrix elements should be faster than loading them from memory, we have found it to be the case for two different classes of Hamiltonians: a spin (two-level system) ensemble Hamiltonian, and circuit-QED Hamiltonian that describes a transmon coupled to a resonator. We believe that there are several related effects that conspire to make the matrix-free approach faster than a sparse-matrix-based approach. For example, the operators and superoperators can be time-dependent (especially in optimal control), and there is no overhead associated with this in the matrix-free approach, as the matrix elements are anyway recalculated every time. Another effect is that sparse matrices compete for CPU cache space with the states, and avoiding this entirely with the matrix-free approach keeps the states and (parts of) density matrices permanently in cache.

Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for probing the structure and dynamics of biological macromolecules such as proteins, RNA, and DNA in their native, physiologically relevant environments. A major challenge in these studies is the limited sensitivity due to the small energy difference between spin states. Since this energy difference is proportional to the external magnetic field (B$_{0}$), increasing B$_{0}$ enhances sensitivity approximately as B$_{0}^{3/2}$. This principle underlies the recent commercial availability of a 28.2 T superconducting magnet from Bruker. However, achieving precise unitary control over all the spins in biological samples is hampered by the power constraints of cryogenically cooled NMR probes at such high magnetic fields. In our work, we address this challenge by designing low-power optimal control radio frequency pulses that require up to 20 times less power. These pulses are tailored for large volume cryoprobes operating at 28.2 T magnets. Specifically, we developed universal rotation pulses and a new class of multiband pulses each capable of arbitrary nutation in its respective band to support the pulse sequences commonly used in biomolecular NMR. An additional benefit of our optimized pulses is their ability to compensate for inhomogeneities, thus resulting in up to a 26% improvement in signal-to-noise ratio and a 40% reduction in experimental time. The optimal control pulse sequence we developed has already enabled Bruker to build a cryoprobe that we have successfully tested at our facility. In addition, our optimal control pulses are now being adopted at other institutions with 28.2 T magnets to achieve superior performance in biomolecular NMR measurements. Publication: Joseph D., Griesinger C., Optimal control pulses for the 1.2-GHz (28.2-T) NMR spectrometers. Sci. Adv.9,eadj1133(2023)

S. G. Kosionis1, S. Biswas2, C. Fouseki3, D. Stefanatos1, E. Paspalakis1 1Materials Science Department, School of Natural Sciences, University of Patras, Patras 26504, Greece 2Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi 67100, Greece 3Physics Department, School of Natural Sciences, University of Patras, Patras 26504, Greece Semiconductor quantum dots are considered one of the most promising candidates for quantum information technologies. Controlled population transfer from the ground state to the exciton state with efficiency, despite decoherence and dissipation, is essential for fully harnessing the potential of such solid-state systems in quantum information processing. A theoretical approach supported by experimental evidence suggests that the main dephasing process in a quantum dot system is the coupling to acoustic phonons, which results in non-Markovian dynamics [1, 2]. In order to successfully induce the desired population transfer, one of the most efficient coherent control methods that have been applied is the rapid adiabatic passage [1, 2], which robustly drives the system from the ground to the exciton state smoothly along the adiabatic path. To speed up slow adiabatic dynamics while preserving robustness, various techniques, collectively referred to as shortcuts to adiabaticity [3], have been proposed which provide faster pathways to predetermined final states. Here, the transitionless quantum driving shortcut technique [3] designed to suppress non-adiabatic transitions in rapid quantum dynamics is employed to generate pulses, that enable efficient ground-to-exciton population transfer in a GaAs/InGaAs quantum dot experiencing acoustic phonon-induced dephasing. By subjecting the quantum dot system to the shortcut pulses—modulating the time-dependent Rabi frequency and detuning—and employing the time-evolving matrix product operator (TEMPO) technique [4], we demonstrate that, for temperatures below 20 K and pulse durations shorter than 10 ps, the transfer efficiency is quite high. We further analyze these results based on a set of Bloch-like equations derived from a generalized Lindblad equation, which effectively capture the behavior of the quantum dot system under these low-temperature conditions. However, at higher temperatures, transfer efficiency declines, except for subpicosecond-duration pulses, where the shortcut Rabi frequency compresses into a delta-like pulse, enabling rapid population transfer. References [1] S. Lüker, K. Gawarecki, D. E. Reiter, A. Grodecka-Grad, V. M. Axt, P. Machnikowski, and T. Kuhn, Phys. Rev. B 85, 121302 (2012). [2] T. Kaldewey et al., Phys. Rev. B 95, 241306(R) (2017). [3] D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, Rev. Mod. Phys. 91, 045001 (2019). [4] G. E. Fux et al., Phys. Rev. Lett. 126, 200401 (2021); J. Chem. Phys. 161, 124108 (2024).

Anyons are quasiparticles with unusual exchange statistics; that is, exchanging two of them results in a phase different from 0 or $\pi$. In the case of non-Abelian anyons, this can even lead to a change in the state. Due to their nonlocal nature rooted in topological order, anyons are highly robust, making them a promising basis for intrinsically fault-tolerant topological quantum computing. In that framework, quantum gates might be implemented via the braiding of anyons, i.e., their exchange in real space. While this process is well understood from a mathematical perspective, such analyses typically assume ideal systems and adiabatic evolution. Recent advances in quantum simulation platforms have renewed interest in realizing and manipulating non-Abelian anyons. We study practical aspects and quantum control protocols for creating non-Abelian anyons and braiding them at finite speeds, where non-adiabatic transitions become relevant. In particular, we study the Kitaev model of spin liquids on a honeycomb lattice, which is exactly solvable and can, nevertheless, be realized in both analog and digital quantum simulators. Despite the exact solvability of the model, the dynamics during non-adiabatic braiding and excitation protocols—particularly those involving non-Abelian anyons—remain underexplored. On the one hand, we investigate mechanisms for exciting anyons by initializing the system in the more easily prepared Toric code phase and ramping through a phase transition by tuning the system couplings. On the other hand, we analyze and compare practical braiding protocols, focusing on the observability of the resulting braiding effects. Our findings aim to inform the design of future experimental protocols for near-term quantum simulators.

To overcome the challenges posed by finite coherence time, an important task in quantum technology involves devising rapid and precise driving schemes. Rather than relying solely on numerical optimization, analytical control based on the knowledge of the Hamiltonian and error dynamics is especially beneficial for scalable hardware. In this presentation, I will introduce a method of analytical control with multi-derivative pulse shaping, based on the widely used Derivative Removal via Adiabatic Gate (DRAG) technique for superconducting qubits architecture. This approach provides efficient but concise parameterized pulse Ansatz that can simultaneously suppress multiple control errors, including nonperturbative and multi-photon dynamics. Our analysis demonstrates the versatility of this method across various applications, including single- and two-qubit gates, crosstalk suppression, and improving qudit operations. I will also discuss its relation to the counter-diabatic driving technique and its potential applications in the quantum simulation of many-body dynamics.

Shortcuts to adiabaticity (STA) is a versatile and powerful toolbox for achieving rapid quantum state transitions without the constraints of slow adiabatic evolution. In this paper, we introduce STA techniques in the quantum super impulse regime by integrating semi-classical methods of super impulse with the inverse engineering approach of STA. This combined technique enables simple and efficient control of various systems through the inverse engineered potentials, allowing for operations such as fast transport, coherent splitting, expansion, and rotation of wave packets. These capabilities collectively enhance the applicability of STA, broadening its potential use in diverse quantum systems.

Ensemble control of two-level quantum systems has been extensively studied in recent years. However, there remains a lack of systematic methods for control design with rigorous theoretical guarantees. In this work, we address this gap by focusing on a one-parameter family of driftless two-level quantum systems. We propose an explicit control design strategy based on Fourier transform and provide a rigorous mathematical proof of approximate controllability. Moreover, our construction yields an upper bound on the optimal ensemble control cost. The effectiveness of the proposed method is demonstrated through numerical simulations in different scenarios.

In the current NISQ era as well as in error corrected qubits, achieving quantum advantage requires the design of highly precise quantum gates, thus needing detailed knowledge and simulation of the specific qubit platform. Here, we show advancements that are being done towards the simulation of parametrically activated two-qubit gates in a multi-qubit transmon platform. This is done specifically for a system of fixed-frequency transmons connected by tunable couplers, and by including model details as well as the effects of flux noise.

The deterministic preparation of the excited state in a quantum emitter is essential for photonic quantum technologies \cite{obrien2009photonic, wang2020integrated}, which depend on high-purity single-photon sources for applications in quantum communication and computing \cite{pan2012multiphoton, wang2019boson}. Conventional approaches to achieving population inversion—and thereby preparing such states—typically rely on resonant excitation \cite{PhysRevLett.87.133603, PhysRevLett.87.246401}, where a laser pulse is tuned to the emitter’s transition energy to generate a single excitation. A major limitation of this technique is that excitation and detection occur at the same frequency, requiring sophisticated filtering to isolate the emitted photons. As an alternative, the Swing-UP of Quantum Emitter Population (SUPER) scheme \cite{PRXQuantum.2.040354} employs two red-detuned laser pulses to coherently drive population inversion, effectively addressing the filtering challenge. Despite its potential, the experimental implementation of SUPER is challenging due to the high energy demands of the excitation pulses and the complexity of optimizing control fields with numerous variable parameters. In this work, we employ Bayesian optimization (BO) \cite{Močkus1989} with an infinite-width Bayesian Neural Network (iBNN) surrogate model to refine the control protocols of the SUPER scheme \cite{li2024studybayesianneuralnetwork}. Our results demonstrate that population inversion close to unity can be achieved while significantly reducing energy of the pulses, improving the scheme's practical feasibility. Additionally, we explore the incorporation of chirped pulses using Adiabatic Rapid Passage (ARP) \cite{PhysRevB.95.241306, PhysRevLett.106.166801, PhysRevLett.106.067401}, a well-established technique for robust state preparation. By integrating ARP within the SUPER framework, we can further enhance the excitation efficiency while maintaining operation at lower pulse energies.

Quantum Fisher Information (QFI) related quantities provide fundamental bounds on the precision of a quantum sensor. Notably, the beyond standard quantum limit scaling of the QFI is desirable to achieve Heisenberg-limited sensing. In this work, we discuss the hierarchy of QFI quantities possible when considering a Markovian continuously monitored quantum optical sensor.

Open loop optimization of a quantum system involves computing gradients of propagators with respect to control parameters. One of the most commonly used optimal control methods is GRAPE, which assumes a piece-wise constant (PWC) pulse ansatz. While GRAPE allows for an easy evaluation of the gradients, it is harder to implement in experiments due to deviation from the ideal pulse shape. These pulses are also susceptible to be problem specific and hard to interpret. Analytic controls on the other hand have fewer parameters, making it easier to implement, and provide interpretable results. In this work, we construct a general framework for computing analytical gradients of quantum dynamics for both open and closed system, for any general pulse shape. These are derived from the analytic solution to gradients, and can be evaluated in parallel using only a few state propagation. Additionally, by evaluating operator growth, we present cases where the computation of the gradients can be done by propagating only a single state, making it useful for systems with large Hilbert space. Finally, we show that these can be extended also to open quantum systems.

Many important optimization tasks can be mapped to the search of ground states of effective Hamiltonians, allowing for the solution of computationally hard problems in physics, finance, logistics and other fields. In quantum annealing, an initial easy-to-prepare Hamiltonian, cooled down to its ground state, gets gradually changed towards a more complex one, whose ground state represents the solution to a specific optimization problem. Despite its evident success, quantum annealing faces the challenge of diabatic transitions that tend to excite the systems towards energetically higher states, ruining the performance of adiabatic protocols. In this work we propose a new mechanism to cool down diabatic transitions in many-body chains by coupling one of their ends to an auxiliary qubit that is frequently being reset to its ground state. In contrast to previously existing protocols that rely on knowledge of the time-dependent spectrum, our protocol relies on stochastic choices of the auxiliary qubit's energy at each reset. Using our protocol, we demonstrate the ability to effectively cool static spins chains down to their ground states, independent of their initial state or size. Our results are also generalized to time-dependent Hamiltonians, showing the efficiency of our protocol in improving the performance of several quantum annealing tasks.

Quantifying the thermodynamic work done on or by a quantum mechanical system is subtle, since one must account for the destructive stochastic measurements of the energetic state at the start and end of the process. This popular framework, known as the two-point measurement scheme provides a probability distribution of work outcomes. We investigate this work done in the setting of transport in a spin chain. In particular, we consider how this differs in the case of perfect or imperfect state transfer of a qubit through the chain. We further quantify the thermodynamics of the process using the ergotropy of the transported state.

Recently, Villanueva and Kappen (2024) proposed a new method for quantum state preparation of open quantum circuits using the path integral control formalism. The method, called quantum diffusion control (QDC), relies on the fact that one can simulate the Lindblad equation using a quantum diffusion process. The state preparation problem then becomes a stochastic optimal control (SOC) problem that, under certain assumptions, is of the path integral form. As a result, the optimal control can be estimated by sampling, instead of solving the notoriously hard HJB or PMP equations. Notably, the PI method does not require the computation of gradients and can be optimized using the quantum hardware directly, instead of in simulation. In this work, we summarize the work in Villanueva and Kappen (2024). Additionally, we apply QDC to compute the ground state of commonly used quantum chemistry benchmark problems and compare its performance with the Variational Quantum Eigensolver (VQE) algorithm, optimized using the SPSA optimizer, one of the most efficient and widely used optimizers for quantum variational algorithms. We show that by annealing from dissipative dynamics to non-dissipative unitary dynamics, we are able to find better solutions with QDC. Our benchmark on the H4 molecule (where the atoms are aligned along the x-axis with equal interatomic distances between neighboring atoms) demonstrates that QDC is at least one order of magnitude more accurate than VQE optimized with SPSA over a range of distances, achieving an error below chemical accuracy — while VQE remains above the chemical accuracy threshold. **Reference:** Villanueva, A., & Kappen, H. (2024). Stochastic optimal control of open quantum systems. arXiv preprint arXiv:2410.18635.

We present a unified optimization framework for a coherent controlled measurement-based thermal machines whose working medium is a coupled quantum system. We derive a feedback Hamiltonian transformed by local unitary rotations and establish self-consistent protocol of the optimal feedback angles that maximizes the work extraction and performance of the machine, owing to the Ising-like interaction mechanism. We further introduce two novel strategies – an iterative update scheme and grid-based search – for optimizing the complex energy landscape imposed by the system coupling. Our approach provides insight on the effects of interplay between local control and global interaction on the performance of quantum information thermodynamic machine. Finally, we present numerical and quantum circuit realization of our model on a superconducting quantum hardware. Collaborators: Chinonso Onah, RWTH Aachen University, Aachen, Germany Obinna P. Uzoh, Simon Fraser University, Burnaby, Canada Obinna Abah Newcastle University, Newcastle Upon Tyne, United Kingdom

Introduction: In quantum inertial sensors laser pulses are used to put atoms into a superposition of momentum states, creating the splitted arms of an interferometer. At these pulses, the laser phase is imprinted on the atomic wave packets. A combination of these laser phases forms the interferometrer phase, which can be measured with great sensitivity. Ultimately, this phase is used to deduce quantities such as the acceleration or rotation experienced by the sensor during the interferometric sequence [1]. Current Limitation: The efficiency of these laser pulses, that determines the contrast of the interferometer, are limited mainly by the temperature of the atoms and by the fluctuations in the lasers intensity. Indeed, the spread in velocity along the laser propagation direction leads to inhomogeneous Doppler broadening. Similarly, fluctuations in the laser intensity and in the positions of the atoms within the laser beam induce variations in atom-light coupling and hence different efficiencies. Our aim is to use optimal control to find temporal modulations of the phase, and possibly of the intensity of the laser beams, to limit the loss of efficiency associated with these effects. Current work: We have implemented the GRAPE algorithm [2] and the BFGS quasi-Newton optimization method [3] to optimize the fidelity of the pulses by modulating the phase. In a first use case, we apply our algorithm to optimize the selectivity of a preparation Raman pulse performed upstream of the interferometer sequence. For a standard square $\pi$ pulse, of Rabi frequency $\Omega_\text{eff}$, the longitudinal velocity distribution is a cardinal sine to the square of typical width $\sigma_v = \frac{\lambda}{4\pi\Omega_\text{eff}}$, which exhibits lobes for velocities greater than $\sigma_v$. Instead, we wish to maximize the transfer between the two coupled states within a velocity interval $I_v = \left[ v_\text{min}, v_\text{max}\right]$ and minimize this probability outside, in order to select only atoms within this velocity range. Future work: The phase profiles we have obtained are to be tested experimentally. Beyond this Raman selection, which does not require taking into account the phase imprinted onto the wave packet during the pulse, we wish to develop our algorithms in order to tailor phase and amplitude profiles to optimize the Raman and multi-photon Bragg pulses used in our instruments. Bibliography: [1] Remi Geiger, Arnaud Landragin, Sébastien Merlet, and Franck Pereira Dos Santos. High-accuracy inertial measurements with cold-atom sensors. AVS Quantum Science, 2(2):024702, 06 2020. (https://doi.org/10.1116/5.0009093) [2] Navin Khaneja, Timo Reiss, Cindie Kehlet, Thomas Schulte-Herbrüggen, and Steffen J. Glaser. Optimal control of coupled spin dynamics: design of nmr pulse sequences by gradient ascent algorithms. Journal of Magnetic Resonance, 172(2):296–305, 2005. (https://doi.org/10.1016/j.jmr.2004.11.004) [3] Jorge Nocedal and Steffen J. Wright. Numerical Optimization.

We study the nonequilibrium work distributions of randomly sampled density matrices, which generally represent mixed quantum states. By sampling according to a unitarily invariant measure such as the Hilbert-Schmidt or Bures-Hall random matrix ensembles, we derive an analogue of the Crooks fluctuation theorem for ensembles of states driven out of equilibrium via a time-reversal invariant Hamiltonian protocol. A Crooks relation holds for (i) microcanonically distributed mixed states with fixed energy expectation values $\Tr H_0 \rho = E$, and (ii) canonically distributed mixed states with a continuous Gibbsian measure. The work cumulants for the two-level Rabi model are computed, and we compare and contrast the predictions when sampling from different choices of random state ensembles. As a second example we study a quench process applied to a pair of non-interacting spins, where an interaction between them is suddenly switched on, and investigate signatures of criticality in the work fluctuations. Formulae are then presented for the mean and variance of the microcanonical work distribution for a $d$-level system in which the initial and final Hamiltonians commute.

Long-range interactions, where two-body potentials decay as a power law, $V(r) \propto r^{-\alpha}$, with $r$ being the inter-particle distance, are a common feature of several experimental platforms relevant to quantum technologies. These include Rydberg atom arrays, dipolar quantum gases, polar molecules, quantum gases coupled to optical cavities, and trapped-ion systems [1]. While their impact on classical statistical mechanics has been widely studied, revealing profound effects on dynamics and universal critical behavior [2], the role of long-range interactions in quantum control remains largely unexplored. In this contribution, I will present some recent results exploring how such systems respond to an external driving, demonstrating their robustness against dynamic excitations and enhanced adiabaticity with respect their nearest-neighbor counterpart, features which are typically of great relevance for quantum control applications. Focusing on the universal behavior of quantum work and defect statistics when the system is driven out of equilibrium across a quantum critical point, we analyze its response under different driving protocols [3]. Our findings highlight the distinctive resilience of long-range systems to finite-time drivings, which substantially suppresses defect generation in non-adiabatic processes. To establish a unified understanding of these effects, we employ the effective dimension approach, which maps the universal behavior of a long-range system in $d$ spatial dimensions to that of a local system in an effective fractal dimension $d_{\mathrm{eff}}$ [4]. This framework allows us to draw general conclusions, applicable across a wide range of experimentally relevant platforms. References: [1] N. Defenu, T. Donner, T. Macrì, G. Pagano, S. Ruffo, and A. Trombettoni, Long-range interacting quantum systems, Rev. Mod. Phys. 95, 035002 (2023). [2] A Campa, Thierry Dauxois, D Fanelli, and S Ruffo, Physics of long-range interacting systems. Oxford Univ. Press, (2014). [3] A. Solfanelli, N. Defenu, Universal work statistics in long-range interacting quantum systems, Phys. Rev. Lett. 134, 030402 (2025). [4] A. Solfanelli, N. Defenu, Universality in long-range interacting systems: the effective dimension approach, Phys. Rev. E 110, 044121 (2024).

We demonstrate that spinor Bose-Einstein condensates (BEC) can be operated as an analog simulator of the triatomic vibron model. This model is widely used in theoretical studies of molecular vibrations and the characterization of molecular configurations, particularly the transition between linear and bent geometries. Spinor BECs can be engineered to simulate states that correspond to linear or bent triatomic molecules, with the BEC’s Wigner function encoding information about the molecular configuration. We show how quantum simulations of the bending dynamics of linear molecules can be realized, and how the straightening of a bent molecule leads to a dynamical instability. In the dynamics triggered by the corresponding instability, significant amount of entanglement is generated, and we characterise the dynamics with squeezing parameter and quantum Fisher information (QFI). The scaling of the non-Gaussian sensitivity, described by the difference between squeezing and QFI, grows remarkably once the spinor system crosses the boundary from the linear phase to the bent phase. This enables us to detect the dynamical phase transition.

The advancement of digital neutral-atom quantum computers relies on the availability of fast and robust protocols for high-fidelity operations. In this work, we present and optimize a novel protocol for global entangling gates using four atomic levels per atom: a ground state qubit and two Rydberg states. The qubit is coupled to a Rydberg state by a laser field, while a microwave field coupling the two Rydberg states enables a resonant dipole-dipole interaction between different atoms. With respect to conventional protocols, the microwave field allows for additional control on the interaction, enabling controlled-Z gates that are faster and less sensitive to Rydberg decay. Moreover, we stabilize our protocol against fluctuations in interatomic distance, and further analyze its performance in realistic setups with rubidium or cesium atoms. Our results open up new avenues to the use of dipolar interactions for robust universal quantum computation with neutral atoms.

Kick drives form a natural set of functions in the setting of quantum control and simulation for studying rich, complex phenomena such as chaos and thermalization. However, when trying to place these drives within the extended Floquet space construction, the shortcomings of the Fourier basis become manifest, and convergence is understandably poor. We explore an alternative periodic basis of square wave functions, called the Walsh basis, which performs better under truncation for strong kick drives. We re-formulate the extended Floquet Hilbert space construction in this basis addressing issues due to non-analyticity of the basis functions. We find that in the high-frequency regime with strong kicking, the Walsh basis can outperform the Fourier in accurately describing the evolution of a periodically driven system. We explain these results within the framework of a single-particle localization problem, where the localization occurs in the reciprocal space of driving modes. This work guides the way for future investigations involving the Walsh basis for studying digital drives in experimentally relevant platforms.

Quantum state preparation is crucial for quantum technologies, yet its fidelity is often compromised by experimental imperfections. In this work, we employ optimal control to uncover an adiabatic echo protocol that significantly enhances robustness against decoherence induced by these imperfections. We validate our approach by demonstrating improved Greenberger–Horne–Zeilinger (GHZ) state preparation in Rydberg atom arrays under disorder in atom position, and we present a toy model to clarify the underlying mechanism analytically. Moreover, we show our method can address similar challenges in the dynamical preparation of quantum spin liquid states and is applicable to non-Rydberg systems, such as GHZ state preparation in the ferromagnetic Ising model. These findings highlight the versatility of our protocol, offering a pathway toward robust quantum state preparation across diverse platforms.

We propose a quantum optimal control framework based on the Pontryagin Maximum Principle to design energy- and time-efficient pulses for open quantum systems. By formulating the Langevin equation of a dissipative LC circuit as a linear control problem, we derive optimized pulses with exponential scaling in energy cost, outperforming conventional shortcut-to-adiabaticity methods such as counter-diabatic driving. When applied to a resonator dispersively coupled to a qubit, these optimized pulses achieve an excellent signal-to-noise ratio comparable to longitudinal coupling schemes across varying critical photon numbers. Our results provide a significant step toward efficient control in dissipative open systems and improved qubit readout in circuit quantum electrodynamics.