Schulte-Herbrüggen group
Technical University of Munich, Munich, Germany
- Tracked papers
- 24 (2005–2025)
Topics
The most frequent field-map topics among the PI' tracked papers.
Recent papers
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On the convergence of the variational quantum eigensolver and quantum optimal control
Abstract
When do variational quantum algorithms converge to a globally optimal solution? Despite extensive work, this question remains largely open. We develop a convergence theory for the variational quantum eigensolver (VQE), using quantum control landscape terminology to prove a sufficient criterion guaranteeing convergence to a Hamiltonian's ground state for almost all initial parameters. Specifically, we show that if (i) the parameterized unitary transformation allows movement in all tangent-space directions in a bounded manner (local surjectivity), and (ii) the gradient descent terminates, then VQE converges almost surely to a ground state. Under similar assumptions, we also guarantee almost-sure convergence to a global optimum on a smaller, closed unitary Lie subgroup, with representation theory providing a criterion for when this optimum is a ground state. We construct examples satisfying condition (i) and analyze two common circuit ansatz families, then discuss regularization techniques that ensure gradient descent terminates and connect to the halting problem.
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Bringing Quantum Systems under Control: A Tutorial Invitation to Quantum Computing and Its Relation to Bilinear Control Systems
Abstract
Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can be developed with capabilities that are unprecedented by classical computers. However, the experimental realization of quantum devices is an active field of research with enormous open challenges, including robustness against noise and scalability. While systems and control theory plays a crucial role in tackling these challenges, the principles of quantum physics lead to a (perceived) high entry barrier for entering the field of quantum computing. This tutorial paper aims at lowering the barrier by introducing basic concepts required to understand and solve research problems in quantum systems. First, we introduce fundamentals of quantum algorithms, ranging from basic ingredients such as qubits and quantum logic gates to prominent examples and more advanced concepts, e.g., variational quantum algorithms. Next, we formalize some engineering questions for building quantum devices in the real world, which requires the careful manipulation of microscopic quantities obeying quantum effects. To this end for N-level systems, we introduce basic concepts of (bilinear) quantum systems and control theory including controllability, observability, and optimal control in a unified frame. Finally, we address the problem of noise in real-world quantum systems via robust quantum control, which relies on a set-membership uncertainty description frequently employed in control.
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Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
Abstract
Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The last few years have seen a rapid evolution and expansion of the field. We review here recent progress in our understanding of the controllability of open quantum systems and in the development and application of quantum control techniques to quantum technologies. We also address key challenges and sketch a roadmap for future developments.
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Reachability in Infinite Dimensional Unital Open Quantum Systems with Switchable GKS-Lindblad Generators
Abstract
In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinite dimensional open quantum dynamical systems following a unital Kossakowski-Lindblad master equation extended by controls. More precisely, their time evolution shall be governed by an inevitable potentially unbounded Hamiltonian drift term $H_0$, finitely many bounded control Hamiltonians $H_j$ allowing for (at least) piecewise constant control amplitudes $u_j(t)\in{\mathbb R}$ plus a bang-bang (i.e. on-off) switchable noise term $\mathbfΓ_V$ in Kossakowski-Lindblad form. Generalizing standard majorization results from finite to infinite dimensions, we show that such bilinear quantum control systems allow to approximately reach any target state majorized by the initial one, as up to now only has been known in finite dimensional analogues.---The proof of the result is currently limited to the control Hamiltonians $ H_j$ being bounded and noise terms $\mathbfΓ_V$ with compact normal $V$.
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Optimal Control of Hybrid Optomechanical Systems for Generating Non-Classical States of Mechanical Motion
Abstract
Cavity optomechanical systems are one of the leading experimental platforms for controlling mechanical motion in the quantum regime. We exemplify that the control over cavity optomechanical systems greatly increases by coupling the cavity also to a two-level system, thereby creating a hybrid optomechanical system. If the two-level system can be driven largely independently of the cavity, we show that the non-linearity thus introduced enables us to steer the extended system to non-classical target states of the mechanical oscillator with Wigner functions exhibiting significant negative regions. We illustrate how to use optimal control techniques beyond the linear regime to drive the hybrid system from the near ground state into a Fock target state of the mechanical oscillator. We base our numerical optimization on realistic experimental parameters for exemplifying how optimal control enables the preparation of decidedly non-classical target states, where naive control schemes fail. Our results thus pave the way for applying the toolbox of optimal control in hybrid optomechanical systems for generating non-classical mechanical states.
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Arbitrary n-Qubit State Transfer Implemented by Coherent Control and Simplest Switchable Local Noise
Abstract
We study reachable sets of open n-qubit quantum systems, whose coherent parts are under full unitary control, by adding as a further degree of incoherent control switchable Markovian noise on a single qubit. In particular, adding bang-bang control of amplitude damping noise (non-unital) allows the dynamic system to act transitively on the entire set of density operators. Thus one can transform any initial quantum state into any desired target state. Adding switchable bit-flip noise (unital) instead suffices to get all states majorised by the initial state. Our open-loop optimal control package DYNAMO is extended by incoherent control to exploit these unprecedented reachable sets in experiments. We propose implementation by a GMon, a superconducting device with fast tunable coupling to an open transmission line, and illustrate how open-loop control with noise switching achieves all state transfers without measurement-based closed-loop feedback and resettable ancilla.
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Training Schrödinger's cat: quantum optimal control
Abstract
It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a system from a given initial state into a desired target state with minimized expenditure of energy and resources -- as famously applied in the Apollo programme. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. --- Here state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium uniting expertise in optimal control theory and applications to spectroscopy, imaging, quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap to future developments.
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Controlling Several Atoms in a Cavity
Abstract
We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of infinite-dimensional system algebras. Hence we address problems arising with infinite-dimensional Lie algebras and those of unbounded operators. For the models considered, these problems can be solved by splitting the set of control Hamiltonians into two subsets: The first obeys an abelian symmetry and can be treated in terms of infinite-dimensional Lie algebras and strongly closed subgroups of the unitary group of the system Hilbert space. The second breaks this symmetry, and its discussion introduces new arguments. Yet, full controllability can be achieved in a strong sense: e.g., in a time dependent Jaynes-Cummings model we show that, by tuning coupling constants appropriately, every unitary of the coupled system (atoms and cavity) can be approximated with arbitrarily small error.
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Quantum error correction in a solid-state hybrid spin register
Abstract
Hybrid quantum systems seek to combine the strength of its constituents to master the fundamental conflicting requirements of quantum technology: fast and accurate systems control together with perfect shielding from the environment, including the measurements apparatus, to achieve long quantum coherence. Excellent examples for hybrid quantum systems are heterogeneous spin systems where electron spins are used for readout and control while nuclear spins are used as long-lived quantum bits. Here we show that joint initialization, projective readout and fast local and non-local gate operations are no longer conflicting requirements in those systems, even under ambient conditions. We demonstrate high-fidelity initialization of a whole spin register (99 %) and single-shot readout of multiple individual nuclear spins by using the ancillary electron spin of a nitrogen-vacancy defect in diamond. Implementation of a novel non-local gate generic to our hybrid electron-nuclear quantum register allows to prepare entangled states of three nuclear spins, with fidelities exceeding 85 %. An important tool for scalable quantum computation is quantum error correction. Combining, for the first time, optimal-control based error avoidance with error correction, we realize a three-qubit phase-flip error correction algorithm. Utilizing optimal control, all of the above algorithms achieve fidelities approaching fault tolerant quantum operation, thus paving the way to large scale integrations. Our techniques can be used to improve scaling of quantum networks relying on diamond spins, phosphorous in silicon or other spin systems like quantum dots, silicon carbide or rare earth ions in solids.
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High fidelity spin entanglement using optimal control
Abstract
Precise control of quantum systems is of fundamental importance for quantum device engineering, such as is needed in the fields of quantum information processing, high-resolution spectroscopy and quantum metrology. When scaling up the quantum registers in such devices, several challenges arise: individual addressing of qubits in a dense spectrum while suppressing crosstalk, creation of entanglement between distant nodes, and decoupling from unwanted interactions. The experimental implementation of optimal control is a prerequisite to meeting these challenges. Using engineered microwave pulses, we experimentally demonstrate optimal control of a prototype solid state spin qubit system comprising thirty six energy levels. The spin qubits are associated with proximal nitrogen-vacancy (NV) centers in diamond. We demonstrate precise single-electron spin qubit operations with an unprecedented fidelity F \approx 0.99 in combination with high-efficiency storage of electron spin states in a nuclear spin quantum memory. Matching single-electron spin operations with spin-echo techniques, we further realize high-quality entangled states (F > 0.82) between two electron spins on demand. After exploiting optimal control, the fidelity is mostly limited by the coherence time and imperfect initialization. Errors from crosstalk in a crowded spectrum of 8 lines as well as detrimental effects from active dipolar couplings have been simultaneously eliminated to unprecedented extent. Finally, by entanglement swapping to nuclear spins, nuclear spin entanglement over a length scale of 25 nm is demonstrated. This experiment underlines the importance of optimal control for scalable room temperature spin-based quantum information devices.