arXiv subjects

Matthias M. Müller

Publications and source records attributed to Matthias M. Müller.

At least 19 recordsLinked to original sources

arXiv2026

Control Protocols for Entangling Gates for Group-IV Color-Centers in Diamond

Accurately controlling entangling gates remains a major challenge for quantum technology applications with solid-state spin qubits. Here, we study a group-IV color-center with a strongly-coupled nuclear spin and approach the problem from a quantum control perspective. We show that there are three different types of entangling gates where the entanglement is mediated by the parallel hyperfine-coupling component, the orthogonal one or both. We derive the respective quantum speed limits (QSL) and show by means of dynamical decoupling, resonant driving of single- and double-quantum transitions, quantum optimal control and algebraic gate decomposition how these gates can be realized. We finally discuss the experimental applicability.

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arXiv2026

Optimal Two-Qubit Gates for Group-IV Color-Centers in Diamond

Color centers associated with group-IV dopants in diamond with long-lived nuclear spins have emerged as major candidates for distributed quantum computing nodes and quantum repeaters. Several proof-of-principle experiments have already been demonstrated. A key operation for long-distance entanglement-distribution protocols are fast and robust gates between the electron spin and a nuclear spin. Here, we investigate numerically for an existing experimental platform of a Germanium-vacancy (GeV) center with a strongly-coupled ${}^{13}$C spin, how such gates can be implemented via quantum optimal control. In the presence of realistic noise we investigate different parameter regimes and gate operations and obtain robust two-qubit gates with fidelities exceeding $99.9 \%$. The framework provides a scalable strategy for group-IV quantum nodes and can be adapted to related architectures.

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arXiv2026

Gate Optimization via Efficient Two-Qubit Benchmarking for NV Centers in Diamond

High-fidelity gate implementation requires sophisticated control pulses that steer the quantum system to undergo the desired transformation. Quantum Optimal Control allows to derive these control pulses in an open-loop fashion based on numerical simulations. However, their precision can be limited by incomplete knowledge of the system. Closed-loop optimization overcomes this limitation by incorporating feedback from measurements, provided a suitable and efficient measure of the gate performance can be defined. In this article, we present an efficient method to evaluate the performance of a two-qubit gate by preparation and measurement of only two quantum states, enabling experimental closed-loop optimization with a metric previously believed to be limited to open-loop control. We tailor the approach to nitrogen-vacancy centers in diamond and, through numerical simulations, demonstrate how the method can optimize a two-qubit gate while reducing the number of required measurements by two orders of magnitude compared to standard process tomography under realistic experimental settings.

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arXiv2025

High-Fidelity Single-Shot Readout and Selective Nuclear Spin Control for a Spin-1/2 Quantum Register in Diamond

Quantum networks offer a way to overcome the size and complexity limitations of single quantum devices by linking multiple nodes into a scalable architecture. Group-IV color centers in diamond, paired with long-lived nuclear spins, have emerged as promising building blocks demonstrating proof-of-concept experiments such as blind quantum computing and quantum-enhanced sensing. However, realizing a large-scale electro-nuclear register remains a major challenge. Here we establish the germanium-vacancy (GeV) center as a viable platform for such network nodes. Using correlation spectroscopy, we identify single nuclear spins within a convoluted spin environment, overcoming limitations imposed by the color center's spin-$1/2$ nature and thereby enabling indirect control of these nuclear spins. We further demonstrate high-fidelity single-shot readout of both the GeV center ($95.8\,\%$) and a neighboring ${}^{13}\text{C}$ nuclear spin ($93.7\,\%$), a key tool for feed-forward error correction. These critical advances position the GeV center as a compelling candidate for next-generation quantum network nodes.

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arXiv2025

High-Fidelity Electron Spin Gates for Scaling Diamond Quantum Register

Diamond is a promising platform for quantum information processing as it can host highly coherent qubits that could allow for the construction of large quantum registers. A prerequisite for such devices is a coherent interaction between nitrogen vacancy (NV) electron spins. Entanglement between dipolar-coupled NV spin pairs has been demonstrated, but with a limited entanglement fidelity and its error sources have not been characterized. Here, we design and implement a robust, easy to implement entangling gate between NV spins in diamond and quantify the influence of multiple error sources on the gate performance. Experimentally, we demonstrate a record gate fidelity of $F=(96.0 \pm 2.5)$ % under ambient conditions. Our identification of the dominant errors paves the way towards NV-NV gates beyond the error correction threshold.

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arXiv2025

Circuit Design for a Star-shaped Spin-Qubit Processor via Algebraic Decomposition and Optimal Control

As quantum processing units grow in size and precision we enter the stage where quantum algorithms can be tested on actual quantum devices. To implement a given quantum circuit on a given quantum device, one has to express the circuit in terms of the gates that can be efficiently realized on the device. We propose an algorithm based on algebraic circuit decomposition for tailored application of optimal-control gates for quantum computing platforms with star-shaped topologies. We then show numerically how the resulting circuits can be implemented on a quantum processing unit consisting of a nitrogen-vacancy center in diamond and surrounding nuclear spins.

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arXiv2025

Analytical solutions for optimal photon absorption into inhomogeneous spin memories

We investigate for optimal photon absorption a quantum electrodynamical model of an inhomogeneously-broadened spin ensemble coupled to a single-mode cavity. Solutions to this problem under experimental assumptions are developed in the Schrödinger picture without using perturbation theory concerning the cavity-spin interactions. Furthermore, we exploit the possibility of modulating the frequency and coupling rate of the resonator. We consider a one-photon input pulse and show some optimal scenarios, where exact formulas and numerical results are obtained for the absorption probabilities and the optimal pulse shapes. In particular, if the external loss dominates the internal loss of the cavity, we find the optimal cooperativity for different parameters and identify cases where absorption with a success probability larger than $99\%$ is achieved.

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arXiv2025

Coherent Control of a Long-Lived Nuclear Memory Spin in a Germanium-Vacancy Multi-Qubit Node

The ability to process and store information on surrounding nuclear spins is a major requirement for group-IV color center-based repeater nodes. We demonstrate coherent control of a ${}^{13}$C nuclear spin strongly coupled to a negatively charged germanium-vacancy center in diamond with coherence times beyond 2.5s at mK temperatures, which is the longest reported for group-IV defects. Detailed analysis allows us to model the system's dynamics, extract the coupling parameters, and characterize noise. We estimate an achievable memory time of 18.1s with heating limitations considered, paving the way to successful applications as a quantum repeater node.

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arXiv2024

Gate-set evaluation metrics for closed-loop optimal control on nitrogen-vacancy center ensembles in diamond

A recurring challenge in quantum science and technology is the precise control of their underlying dynamics that lead to the desired quantum operations, often described by a set of quantum gates. These gates can be subject to application-specific errors, leading to a dependence of their controls on the chosen circuit, the quality measure and the gate-set itself. A natural solution would be to apply quantum optimal control in an application-oriented fashion. In turn, this requires the definition of a meaningful measure of the contextual gate-set performance. Therefore, we explore and compare the applicability of quantum process tomography, linear inversion gate-set tomography, randomized linear gate-set tomography, and randomized benchmarking as measures for closed-loop quantum optimal control experiments, using a macroscopic ensemble of nitrogen-vacancy centers in diamond as a test-bed. Our work demonstrates the relative trade-offs between those measures and how to significantly enhance the gate-set performance, leading to an improvement across all investigated methods.

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arXiv2024

Large spin shuttling oscillations enabling high-fidelity single qubit gates

Semiconductor quantum dots have shown impressive breakthroughs in the last years, with single and two qubit gate fidelities matching other leading platforms and scalability still remaining a relative strength. However, due to qubit wiring considerations, mobile electron architectures have been proposed to facilitate upward scaling. In this work, we examine and demonstrate the possibility of significantly outperforming static EDSR-type single-qubit pulsing by taking advantage of the larger spatial mobility to achieve larger Rabi frequencies and reduce the effect of charge noise. Our theoretical results indicate that fidelities are ultimately bottlenecked by spin-valley physics, which can be suppressed through the use of quantum optimal control, and we demonstrate that, across different potential regimes and competing physical models, shuttling based single-qubit gates retain significant advantage over existing alternatives.

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arXiv2024

Exponentiation of Parametric Hamiltonians via Unitary interpolation

The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit compilation, or Monte-Carlo sampling. We introduce two ideas for the time-efficient approximation of matrix exponentials of linear multi-parametric Hamiltonians. We modify the Suzuki-Trotter product formula from an approximation to an interpolation schemes to improve both accuracy and computational time. This allows us to achieve high fidelities within a single interpolation step, which can be computed directly from cached matrices. We furthermore define the interpolation on a grid of system parameters, and show that the infidelity of the interpolation converges with $4^\mathrm{th}$ order in the number of interpolation bins.

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arXiv2023

Analyzing the collective emission of a Rydberg-blockaded single-photon source based on an ensemble of thermal atoms

An ensemble of Rubidum atoms can be excited with lasers such that it evolves into an entangled state with just one collective excitation within the Rydberg blockade radius. The decay of this state leads to the emission of a single, antibunched photon. For a hot vapor of Rubidium atoms in a micro cell we numerically study the feasibility of such a single-photon source under different experimental conditions like the atomic density distribution and the choice of electronic states addressed by the lasers. For the excitation process with three rectangular lasers pulses, we simulate the coherent dynamics of the system in a truncated Hilbert space. We investigate the radiative behavior of the moving Rubidum atoms and optimize the laser pulse sequence accordingly. We find that the collective decay of the single-excitation leads to a fast and directed photon emission and further, that a pulse sequence similar to a spin echo increases the directionality of the photon. Finally, we analyze the residual double-excitations and find that they do not exhibit these collective decay properties and play only a minor deleterious role.

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arXiv2023

Information Theoretical Limits for Quantum Optimal Control Solutions: Error Scaling of Noisy Channels

Accurate manipulations of an open quantum system require a deep knowledge of its controllability properties and the information content of the implemented control fields. By using tools of information and quantum optimal control theory, we provide analytical bounds (information-time bounds) to characterize our capability to control the system when subject to arbitrary sources of noise. Moreover, since the presence of an external noise field induces open quantum system dynamics, we also show that the results provided by the information-time bounds are in very good agreement with the Kofman-Kurizki universal formula describing decoherence processes. Finally, we numerically test the scaling of the control accuracy as a function of the noise parameters, by means of the dressed chopped random basis (dCRAB) algorithm for quantum optimal control.

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arXiv2022

QuOCS: The Quantum Optimal Control Suite

Quantum optimal control includes the family of pulse-shaping algorithms that aim to unlock the full potential of a variety of quantum technologies. Our Quantum Optimal Control Suite (QuOCS) unites experimental focus and model-based approaches in a unified framework. The easy usage and installation of QuOCS and the availability of various combinable optimization strategies is designed to improve the performance of many quantum technology platforms, such as color defects in diamond, superconducting qubits, atom- or ion-based quantum computers. It can also be applied to the study of more general phenomena in physics. In this paper, we describe the software and the main toolbox of gradient-free and gradient-based algorithms. We then show how the user can connect it to their experiment. In addition, we provide illustrative examples where our optimization suite solves typical quantum optimal control problems, in both open- and closed-loop settings. Integration into existing experimental control software is already provided for the experiment control software Qudi [J. M. Binder et al., SoftwareX, 6, 85-90, (2017)], and further extensions are investigated and highly encouraged. QuOCS is available from GitHub, under Apache License 2.0, and can be found on the PyPI repository.

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arXiv2022

Robust Magnetometry with Single NV Centers via Two-step Optimization

Shallow Nitrogen-Vacancy (NV) centers are promising candidates for high-precision sensing applications; these defects, when positioned a few nanometers below the surface, provide an atomic-scale resolution along with substantial sensitivity. However, the dangling bonds and impurities on the diamond surface result in a complex environment which reduces the sensitivity and is unique to each shallow NV center. To avoid the environment's detrimental effect, we apply feedback-based quantum optimal control. We first show how a direct search can improve the initialization/readout process. In a second step, we optimize microwave pulses for pulsed Optically Detected Magnetic Resonance (ODMR) and Ramsey measurements. Throughout the sensitivity optimizations, we focus on robustness against errors in the control field amplitude. This feature not only protects the protocols' sensitivity from drifts but also enlarges the sensing volume. The resulting ODMR measurements produce sensitivities below 1$μ$T\,Hz$^{-\frac{1}{2}}$ for an 83\% decrease in control power, increasing the robustness by approximately one third. The optimized Ramsey measurements produce sensitivities below 100\,nT\,Hz$^{-\frac{1}{2}}$ giving a two-fold sensitivity improvement. Being on par with typical sensitivities obtained via single NV magnetometry, the complementing robustness of the presented optimization strategy may provide an advantage for other NV-based applications.

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arXiv2022

Macroscopic Hyperpolarization Enhanced with Quantum Optimal Control

Hyperpolarization of nuclear spins enhances nuclear magnetic resonance signals, which play a key role for imaging and spectroscopy in the natural and life sciences. This signal amplification unlocks previously inaccessible techniques, such as metabolic imaging of cancer cells. In this work, electron spins from the photoexcited triplet state of pentacene-doped naphthalene crystals are used to polarize surrounding protons. As existing strategies are rendered less effective by experimental constraints, they are replaced with optimal control pulses designed with RedCRAB. In contrast to previous optimal control approaches, which consider an average single nucleus, this closed-loop optimization is macroscopic. A 28% improvement in signal and 15% faster polarization rate is observed. Additionally, a strategy called Autonomously-optimized Repeated Linear Sweep (ARISE) is introduced to efficiently tailor existing hyperpolarization sequences in the presence of experimental uncertainty to enhance their performance. ARISE is expected to be broadly applicable in many experimental settings.

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arXiv2021

One decade of quantum optimal control in the chopped random basis

The Chopped RAndom Basis (CRAB) ansatz for quantum optimal control has been proven to be a versatile tool to enable quantum technology applications, quantum computing, quantum simulation, quantum sensing, and quantum communication. Its capability to encompass experimental constraints -- while maintaining an access to the usually trap-free control landscape -- and to switch from open-loop to closed-loop optimization (including with remote access -- or RedCRAB) is contributing to the development of quantum technology on many different physical platforms. In this review article we present the development, the theoretical basis and the toolbox for this optimization algorithm, as well as an overview of the broad range of different theoretical and experimental applications that exploit this powerful technique.

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arXiv2020

Information flow and error scaling for fully-quantum control

The optimally designed control of quantum systems is playing an increasingly important role to engineer novel and more efficient quantum technologies. Here, in the scenario represented by controlling an arbitrary quantum system via the interaction with an another optimally initialized auxiliary quantum system, we show that the quantum channel capacity sets the scaling behaviour of the optimal control error. Specifically, we prove that the minimum control error is ensured by maximizing the quantum capacity of the channel mapping the initial control state into the target state of the controlled system, i.e., optimizing the quantum information flow from the controller to the system to be controlled. Analytical results, supported by numerical evidences, are provided when the systems and the controller are either qubits or single Bosonic modes and can be applied to a very large class of platforms for controllable quantum devices.

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