Control Of Quantum Systems Research Articles

Quantum Fluctuation Theorem for Arbitrary Measurement and Feedback Schemes.

Fluctuation theorems and the second law of thermodynamics are powerful relations constraining the behavior of out-of-equilibrium systems. While there exist generalizations of these relations to feedback controlled quantum systems, their applicability is limited, in particular when considering strong and continuous measurements. In this Letter, we overcome this shortcoming by deriving a novel fluctuation theorem, and the associated second law of information thermodynamics, which remain applicable in arbitrary feedback control scenarios. In our second law, the entropy production is bounded by the coarse-grained entropy production that is inferrable from the measurement outcomes, an experimentally accessible quantity that does not diverge even under strong continuous measurements. We illustrate our results by a qubit undergoing discrete and continuous measurement, where our approach provides a useful bound on the entropy production for all measurement strengths.

A COMPARATIVE STUDY OF A CLASS OF LINEAR AND NONLINEAR PANTOGRAPH DIFFERENTIAL EQUATIONS VIA DIFFERENT ORTHOGONAL POLYNOMIAL WAVELETS

We propose a wavelet approach on different orthogonal polynomials for solving linear and nonlinear pantograph equations with stretch kind. The pantograph differential equation is a unique proportional delay functional differential equation class. It has been used to deal with numerous physics, mathematics, and engineering applications, such as quantum mechanics, control systems, electrodynamics, and number theory. This scheme is based on constructing the operational matrix for integration via different wavelets with their collocation nodes. This study aims to examine the numerical dynamics of the pantograph equation under stretch kind through different orthogonal polynomial wavelets. Illustrative examples are presented to highlight the flexibility of this scheme, and comparisons are made between the mentioned scheme and other existing schemes using tables and graphs. These numerical results correctly predict the applicability and effectiveness of the mentioned scheme.

Universal scalable characterization and correction of pulse distortions in controlled quantum systems

Universal scalable characterization and correction of pulse distortions in controlled quantum systems

From certainty to chance: probabilistic insights into quantum control

This study introduces an innovative control methodology designed specifically for quantum physical systems. It bridges a critical gap by accounting for the full spectrum of uncertainties and noise that could affect the time evolution of these systems. In contrast to conventional methods, our pioneering approach utilizes probability density functions (pdfs) to characterize quantum dynamics, providing a more detailed and accurate description of their temporal behavior. We propose a strategy that seeks to minimize the discrepancy between the actual pdf, which encapsulates the combined dynamics of the quantum system and an external electric field, and a desired pdf that aligns with the system’s intended outcomes. This strategy marks a significant shift from traditional quantum control techniques. Initially, we present a solution for controlling quantum systems defined by general pdfs. This solution is then demonstrated on quantum systems described by Gaussian pdfs, with an in-depth account of the resulting optimized controller’s structure. The study culminates with practical demonstrations, showcasing the approach’s efficacy and practicality, thus endorsing its potential as a formidable instrument in quantum control.Graphical abstract

High fidelity control of a many-body Tonks-Girardeau gas with an effective mean-field approach

Shortcuts to adiabaticity (STA) are powerful tools that can be used to control quantum systems with high fidelity. They work particularly well for single particle and noninteracting systems which can be described exactly and which possess invariant or self-similar dynamics. However, finding an exact STA for strongly correlated many-body systems can be difficult, as their complex dynamics may not be easily described, especially for larger systems that do not possess self-similar solutions. Here, we design STAs for one-dimensional bosonic gas in the Tonks-Girardeau limit by using a mean-field approach that succinctly captures the strong interaction effects through a quintic nonlinear term in the Schrödinger equation. We show that for the case of the harmonic oscillator with a time-dependent trap frequency the mean-field approach works exactly and recovers the well-known STA from literature. To highlight the robustness of our approach we also show that it works effectively for anharmonic potentials, achieving higher fidelities than other typical control techniques. Published by the American Physical Society 2024

Ultrafast Excitation Exchange in a Maxwell Fish-Eye Lens.

The strong coupling of quantum emitters to a cavity mode has been of paramount importance in the development of quantum optics. Recently, also the strong coupling to more than a single mode of an electromagnetic resonator has drawn considerable interest. We investigate how this multimode strong coupling regime can be harnessed to coherently control quantum systems. Specifically, we demonstrate that a Maxwell fish-eye lens can be used to implement a pulsed excitation exchange between two distant quantum emitters. This periodic exchange is mediated by single-photon pulses and can be extended to a photon-exchange between two atomic ensembles, for which the coupling strength is enhanced collectively.

Bound on the distance between controlled quantum state and target state under decoherence

To implement quantum information technologies, carefully designed control for preparing a desired state plays a key role. However, in realistic situation, the actual performance of those methodologies is severely limited by decoherence. Therefore, it is important to evaluate how close we can steer the controlled state to a desired target state under decoherence. In this paper, we provide an upper bound of the distance between the two controlled quantum systems in the presence and absence of decoherence. The bound quantifies the degree of achievement of the control for a given target state under decoherence, and can be straightforwardly calculated without solving any equation. Moreover, the upper bound is applied to derive a theoretical limit of the probability for obtaining the target state under decoherence.

Topological phase in one-dimensional momentum space lattice of ultracold atoms without chiral symmetry

Symmetry plays a crucial role in understanding topological phases in materials. In one-dimensional systems, such as the Su-Schrieffer-Heeger (SSH) model, chiral symmetry is thought to ensure the quantization of the Zak phase and the nontrivial topological phase. However, our work demonstrates that the one-dimensional lattice system with broken chiral symmetry can still possess quantized Zak phase and nontrivial topological phase. Specifically, we use a Bose-Einstein condensate of <sup>87</sup>Rb atoms in a momentum space lattice of ultracold atoms to effectively simulate a one-dimensional Zigzag model of 26 sites, which intrinsically breaks the chiral symmetry by additional next-nearest-neighbor coupling. To ensure the existence of the nontrivial topological phase, where the Zak phase can be measured from the time-averaged displacement during the system’s evolution, we need to preserve the inversion symmetry by modulating laser power so that all next-nearest-neighbor coupling strengths are equal. Furthermore, by changing the ratio of nearest-neighbor coupling strengths, we observe a topological phase transition from a nontrivial topological phase to a trivial topological phase at the point where the ratio equals 1. Our work demonstrates that the ultracold atom system provides a controllable platform for studying the symmetrical phase and topological phase, with the potential to explore nonlinear topological phenomena by increasing the interactions among atoms. In addition, our system can be used to investigate other interesting topological phenomena with more complex models, such as critical phenomena at the phase transitions and flat band structures in the extended SSH model with long-range coupling. By controlling the coupling strengths, we can also explore the influence of different symmetries on the topological properties of extended SSH models in the future. Moreover, our platform makes it possible to studythe models with more energy bands, such as the Aharonov-Bohm caging model with a three-level structure, which shows peculiar flat-band properties. This work provides opportunities for various studies in the fields of symmetry, topology, and the interaction of controllable quantum systems.

Measurement-Based Deterministic Imaginary Time Evolution.

We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by a Suzuki-Trotter decomposition, an evolution approximating imaginary time evolution can be realized. The randomness due to measurement is corrected using conditional unitary operations, making the evolution deterministic. Both the measurements required for the algorithm and the conditional unitary operations can be constructed efficiently. We show that the algorithm converges only below a specified energy threshold and the complexity is estimated for some specific problem instances.

Control limit for the quantum state preparation under stochastic control errors

We investigate the effect of stochastic control errors on the Hamiltonian that controls a closed quantum system. Quantum information technologies require careful control for preparing a desired state used as an information resource. However, because the stochastic control errors inevitably appear in realistic situations, it is difficult to completely implement the control Hamiltonian. Under this error, the actual performance of quantum control is far away from the ideal one, and thus it is of great importance to evaluate the effect of the control errors. In this paper, we derive a lower bound of the fidelity between two closed quantum systems obeying the dynamics with and without errors. This bound reveals a reachable and unreachable set of the controlled quantum system under stochastic noises. Also, it is easily computable without considering the stochastic process and needing the full dynamics of the states. We demonstrate the actual performance of this bound via a simple control example. Furthermore, based on this result, we quantitatively evaluate the probability of obtaining the target state in the presence of control errors.

An Integrated Reconfigurable Spin Control System on 180 nm CMOS for Diamond NV Centers

Solid-state electron spins are key building blocks for emerging applications in quantum information science, including quantum computers, quantum communication links, and quantum sensors. These solid-state spins are mainly controlled using complex microwave pulse sequences, which are typically generated using benchtop electrical instruments. Integration of the required electronics will enable realization of a scalable low-power and compact optically addressable quantum system. Here, we report an integrated reconfigurable quantum control system, which is used to find electron-spin resonance (ESR) frequency and perform Rabi, Ramsey, and Hahn-echo measurements for a nitrogen-vacancy (NV) center spin qubit in diamond. The chip can be programmed to synthesize an RF signal tunable from 1.6 to 2.6 GHz, which is modulated with a sequence of up to 4098 reconfigurable pulses with a pulse width and pulse-to-pulse delay adjustable from 10 ns to 42 ms and 18 ns to 42 ms, respectively, at a resolution of 2.5 ns. The 180-nm CMOS chip is fabricated within a footprint of 3.02 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{2}$</tex-math> </inline-formula> and has a power consumption of 80 mW.

Equivalent quantum systems

We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects the Hamiltonian operators associated with each quantum system. This bridge allows us to connect different quantum systems, in such a way that studying one of them allows to understand the other through a gauge transformation. Furthermore, we included the case where the Hamiltonian operator can be time-dependent. An application for this construction will be achieved in the theory of control quantum systems.

Compensating for Nonlinear Distortions in Controlled Quantum Systems

Predictive design and optimization methods for controlled quantum systems depend on the accuracy of the system model. Any distortion of the input fields in an experimental platform alters the model accuracy and eventually disturbs the predicted dynamics. These distortions can be nonlinear with a strong frequency dependence so that the field interacting with the microscopic quantum system has limited resemblance to the input signal. We present an effective method for estimating these distortions, which is suitable for nonlinear transfer functions of arbitrary lengths and magnitudes provided the available training data has enough spectral components. Using a quadratic estimation, we have successfully tested our approach for a numerical example of a single Rydberg atom system. The transfer function estimated from the presented method is incorporated into an open-loop control optimization algorithm allowing for high-fidelity operations in quantum experiments.

Realization of a fractional quantum Hall state with ultracold atoms.

Strongly interacting topological matter1 exhibits fundamentally new phenomena with potential applications in quantum information technology2,3. Emblematic instances are fractional quantum Hall (FQH) states4, in which the interplay of amagnetic field and strong interactions gives rise to fractionally charged quasi-particles, long-ranged entanglement and anyonic exchange statistics. Progress in engineering synthetic magnetic fields5-21 has raised the hope to create these exotic states in controlled quantum systems. However, except for a recent Laughlin state of light22, preparing FQH states in engineered systems remains elusive. Here we realize a FQH state with ultracold atoms in an optical lattice. The state is a lattice version of a bosonic ν = 1/2 Laughlin state4,23 with two particles on 16 sites. This minimal system already captures many hallmark features of Laughlin-type FQH states24-28: we observe a suppression of two-body interactions, we find a distinctive vortex structure in the density correlations and we measure a fractional Hall conductivity of σH/σ0 = 0.6(2) by means of the bulk response to a magnetic perturbation. Furthermore, by tuning the magnetic field, we map out the transition point between the normal and the FQH regime through a spectroscopic investigation of the many-body gap. Our work provides a starting point for exploring highly entangled topological matter with ultracold atoms29-33.

Some Controllable and Uncontrollable Degenerate Four-Level Quantum Systems

Some Controllable and Uncontrollable Degenerate Four-Level Quantum Systems

Some Controllable and Uncontrollable Degenerate Four-Level Quantum Systems

Анализируется управляемость трех квантовых систем, принадлежащих некоторому классу четырехуровневых квантовых систем с дважды вырожденным высшим возбужденным энергетическим уровнем и с одним запрещенным переходом между остальными двумя невырожденными уровнями. Для этого проведены численные вычисления, построены динамические алгебры Ли, порожденные всеми коммутаторами свободного гамильтониана и гамильтониана взаимодействия, и показано, что две из рассматриваемых квантовых систем являются неприводимыми и управляемыми, а одна - приводимой и, следовательно, неуправляемой. Приводимость и неуправляемость доказываются построением сохраняющегося эрмитова оператора (физической наблюдаемой). Управляемость подтверждается построением динамической алгебры Ли и доказательством того, что она имеет максимальный ранг. Проведенный анализ показывает, что в зависимости от значений некоторых конкретных матричных элементов гамильтониана взаимодействия квантовые системы из рассмотренного класса являются либо неуправляемыми, либо управляемыми.

Observation of critical phase transition in a generalized Aubry-André-Harper model with superconducting circuits

Quantum simulation enables study of many-body systems in non-equilibrium by mapping to a controllable quantum system, providing a powerful tool for computational intractable problems. Here, using a programmable quantum processor with a chain of 10 superconducting qubits interacted through tunable couplers, we simulate the one-dimensional generalized Aubry-André-Harper model for three different phases, i.e., extended, localized and critical phases. The properties of phase transitions and many-body dynamics are studied in the presence of quasi-periodic modulations for both off-diagonal hopping coefficients and on-site potentials of the model controlled respectively by adjusting strength of couplings and qubit frequencies. We observe the spin transport for initial single- and multi-excitation states in different phases, and characterize phase transitions by experimentally measuring dynamics of participation entropies. Our experimental results demonstrate that the recently developed tunable coupling architecture of superconducting processor extends greatly the simulation realms for a wide variety of Hamiltonians, and can be used to study various quantum and topological phenomena.

On-demand assembly of optically levitated nanoparticle arrays in vacuum

Realizing a large-scale fully controllable quantum system is a challenging task in current physical research and has broad applications. In this work, we create a reconfigurable optically levitated nanoparticle array in vacuum. Our optically levitated nanoparticle array allows full control of individual nanoparticles to form an arbitrary pattern and detect their motion. As a concrete example, we choose two nanoparticles without rotation signals from an array to synthesize a nanodumbbell in situ by merging them into one trap. The nanodumbbell synthesized in situ can rotate beyond 1 GHz. Our work provides a platform for studying macroscopic many-body physics and quantum sensing.

Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources

Our aim is twofold: First, we rigorously analyse the generators of quantum-dynamical semigroups of thermodynamic processes. We characterise a wide class of gksl-generators for quantum maps within thermal operations and argue that every infinitesimal generator of (a one-parameter semigroup of) Markovian thermal operations belongs to this class. We completely classify and visualise them and their non-Markovian counterparts for the case of a single qubit. Second, we use this description in the framework of bilinear control systems to characterise reachable sets of coherently controllable quantum systems with switchable coupling to a thermal bath. The core problem reduces to studying a hybrid control system (“toy model”) on the standard simplex allowing for two types of evolution: (i) instantaneous permutations and (ii) a one-parameter semigroup of [Formula: see text]-stochastic maps. We generalise upper bounds of the reachable set of this toy model invoking new results on thermomajorisation. Using tools of control theory we fully characterise these reachable sets as well as the set of stabilisable states as exemplified by exact results in qutrit systems.

Optimal quantum control via genetic algorithms for quantum state engineering in driven-resonator mediated networks

We employ a machine learning-enabled approach to quantum state engineering based on evolutionary algorithms. In particular, we focus on superconducting platforms and consider a network of qubits—encoded in the states of artificial atoms with no direct coupling—interacting via a common single-mode driven microwave resonator. The qubit-resonator couplings are assumed to be in the resonant regime and tunable in time. A genetic algorithm is used in order to find the functional time-dependence of the couplings that optimise the fidelity between the evolved state and a variety of targets, including three-qubit GHZ and Dicke states and four-qubit graph states. We observe high quantum fidelities (above 0.96 in the worst case setting of a system of effective dimension 96), fast preparation times, and resilience to noise, despite the algorithm being trained in the ideal noise-free setting. These results show that the genetic algorithms represent an effective approach to control quantum systems of large dimensions.