arXiv subjects

Sabine Wölk

Publications and source records attributed to Sabine Wölk.

At least 19 recordsLinked to original sources

arXiv2026

Sparse quantum state preparation with improved Toffoli cost

The preparation of quantum states is one of the most fundamental tasks in quantum computing, and a key primitive in many quantum algorithms. Of particular interest to areas such as quantum simulation and linear-system solvers are sparse quantum states, which contain only a small number $s$ of non-zero computational basis states compared to a generic state. In this work, we present an approach that prepares $s$-sparse states on $n$ qubits, reducing the number of Toffoli gates required compared to prior art. We work in the established framework of first preparing a dense state on a $\lceil{\log(s)}\rceil$-qubit sub-register, and then mapping this state to the target state via an isometry, with the latter step dominating the cost of the full algorithm. The speed-up is achieved by designing an efficient algorithm for finding and implementing the isometry. The worst-case Toffoli cost of our isometry circuit, which may be viewed as a batched version of an approach by Malvetti et al., is essentially $2s$ for sufficiently large values of $n$, yielding roughly a $\log(s)/2$ improvement factor over the state-of-the-art. In numerical benchmarks on randomly chosen states, the cost is closer to $s$. With the improved isometry circuit, we examine the dense-state preparation step and present ways to optimize the joint cost of both steps, particularly in the case of target states with purely real coefficients, by outsourcing some sub-tasks from the dense-state preparation to the isometry.

quant-ph↗

arXiv2026

Faster matrix product state preparation by exploiting symmetry-induced block-sparsity

Matrix product states (MPS) serve as a key tool for studying quantum systems from chemistry and condensed-matter physics, making their preparation on quantum computers an important task in interfacing classical and quantum simulation. Many systems of interest have $U(1)$-symmetries induced by particle number and spin projection conservation, allowing to restrict the MPS tensors to be of block-sparse form, a property widely used in the implementation of classical algorithms such as the density matrix renormalization group. We reduce the cost of fault-tolerantly preparing block-sparse MPS within the standard ancilla-assisted linear-depth approach by implementing row and column permutations that transform the block-sparse matrices into block-diagonal form. These block-diagonal unitaries are then implemented via unitary synthesis, with the cost being determined by the size of the largest block. In this context, we modify the unitary synthesis approach of Berry et al. in order to reduce the Toffoli cost for real-valued unitaries by a factor of $\sqrt{2}$. In numerical benchmarks, we achieve Toffoli cost improvement factors of $10 - 30$ compared to the state-of-the-art for MPS of various molecular systems.

quant-ph↗

arXiv2025

Quantum reinforcement learning in dynamic environments

Combining quantum computing techniques in the form of amplitude amplification with classical reinforcement learning has led to the so-called "hybrid agent for quantum-accessible reinforcement learning", which achieves a quadratic speedup in sample complexity for certain learning problems. So far, this hybrid agent has only been applied to stationary learning problems, that is, learning problems without any time dependency within components of the Markov decision process. In this work, we investigate the applicability of the hybrid agent to dynamic RL environments. To this end, we enhance the hybrid agent by introducing a dissipation mechanism and, with the resulting learning agent, perform an empirical comparison with a classical RL agent in an RL environment with a time-dependent reward function. Our findings suggest that the modified hybrid agent can adapt its behavior to changes in the environment quickly, leading to a higher average success probability compared to its classical counterpart.

quant-ph↗

arXiv2024

A hybrid learning agent for episodic learning tasks with unknown target distance

The "hybrid agent for quantum-accessible reinforcement learning", as defined in (Hamann and Wölk, 2022), provides a proven quasi-quadratic speedup and is experimentally tested. However, the standard version can only be applied to episodic learning tasks with fixed episode length. In many real-world applications, the information about the necessary number of steps within an episode to reach a defined target is not available in advance and especially before reaching the target for the first time. Furthermore, in such scenarios, classical agents have the advantage of observing at which step they reach the target. Whether the hybrid agent can provide an advantage in such learning scenarios was unknown so far. In this work, we introduce a hybrid agent with a stochastic episode length selection strategy to alleviate the need for knowledge about the necessary episode length. Through simulations, we test the adapted hybrid agent's performance versus classical counterparts. We find that the hybrid agent learns faster than corresponding classical learning agents in certain scenarios with unknown target distance and without fixed episode length.

quant-ph↗

arXiv2021

Performance analysis of a hybrid agent for quantum-accessible reinforcement learning

In the last decade quantum machine learning has provided fascinating and fundamental improvements to supervised, unsupervised and reinforcement learning. In reinforcement learning, a so-called agent is challenged to solve a task given by some environment. The agent learns to solve the task by exploring the environment and exploiting the rewards it gets from the environment. For some classical task environments, such as deterministic strictly epochal environments, an analogue quantum environment can be constructed which allows to find rewards quadratically faster by applying quantum algorithms. In this paper, we analytically analyze the behavior of a hybrid agent which combines this quadratic speedup in exploration with the policy update of a classical agent. This leads to a faster learning of the hybrid agent compared to the classical agent. We demonstrate that if the classical agent needs on average $\langle J \rangle$ rewards and $\langle T \rangle_c$ epochs to learn how to solve the task, the hybrid agent will take $\langle T \rangle_q \leq α\sqrt{\langle T \rangle_c \langle J \rangle}$ epochs on average. Here, $α$ denotes a constant which is independent of the problem size. Additionally, we prove that if the environment allows for maximally $α_o k_\text{max}$ sequential coherent interactions, e.g. due to noise effects, an improvement given by $\langle T \rangle_q \approx α_o\langle T \rangle_c/4 k_\text{max}$ is still possible.

quant-ph↗

arXiv2021

Experimental quantum speed-up in reinforcement learning agents

Increasing demand for algorithms that can learn quickly and efficiently has led to a surge of development within the field of artificial intelligence (AI). An important paradigm within AI is reinforcement learning (RL), where agents interact with environments by exchanging signals via a communication channel. Agents can learn by updating their behaviour based on obtained feedback. The crucial question for practical applications is how fast agents can learn to respond correctly. An essential figure of merit is therefore the learning time. While various works have made use of quantum mechanics to speed up the agent's decision-making process, a reduction in learning time has not been demonstrated yet. Here we present a RL experiment where the learning of an agent is boosted by utilizing a quantum communication channel with the environment. We further show that the combination with classical communication enables the evaluation of such an improvement, and additionally allows for optimal control of the learning progress. This novel scenario is therefore demonstrated by considering hybrid agents, that alternate between rounds of quantum and classical communication. We implement this learning protocol on a compact and fully tunable integrated nanophotonic processor. The device interfaces with telecom-wavelength photons and features a fast active feedback mechanism, allowing us to demonstrate the agent's systematic quantum advantage in a setup that could be readily integrated within future large-scale quantum communication networks.

quant-ph↗

arXiv2019

Optimal distributed sensing in noisy environments

We consider distributed sensing of non-local quantities. We introduce quantum enhanced protocols to directly measure any (scalar) field with a specific spatial dependence by placing sensors at appropriate positions and preparing a spatially distributed entangled quantum state. Our scheme has optimal Heisenberg scaling and is completely unaffected by noise on other processes with different spatial dependence than the signal. We consider both Fisher and Bayesian scenarios, and design states and settings to achieve optimal scaling. We explicitly demonstrate how to measure coefficients of spatial Taylor and Fourier series, and show that our approach can offer an exponential advantage as compared to strategies that do not make use of entanglement between different sites.

quant-ph↗

arXiv2019

Distinguishing between statistical and systematic errors in quantum process tomography

It is generally assumed that every process in quantum physics can be described mathematically by a completely positive map. However, experimentally reconstructed processes are not necessarily completely positive due to statistical or systematic errors. In this paper, we introduce a test for discriminating statistical from systematic errors which is necessary to interpret experimentally reconstructed, non-completely positive maps.Wedemonstrate the significance of the test using several examples given by experiments and simulations. In particular, we demonstrate experimentally how an initial correlation between the system to be measured and its environment leads to an experimentally reconstructed map with negative eigenvalues. These experiments are carried out using atomic 171Yb+ ions confined in a linear Paul trap, addressed and coherently manipulated by radio frequency radiation.

quant-ph↗

arXiv2018

Speeding-up the decision making of a learning agent using an ion trap quantum processor

We report a proof-of-principle experimental demonstration of the quantum speed-up for learning agents utilizing a small-scale quantum information processor based on radiofrequency-driven trapped ions. The decision-making process of a quantum learning agent within the projective simulation paradigm for machine learning is implemented in a system of two qubits. The latter are realized using hyperfine states of two frequency-addressed atomic ions exposed to a static magnetic field gradient. We show that the deliberation time of this quantum learning agent is quadratically improved with respect to comparable classical learning agents. The performance of this quantum-enhanced learning agent highlights the potential of scalable quantum processors taking advantage of machine learning.

quant-ph↗

arXiv2018

Maximal Coherence and the Resource Theory of Purity

The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. We establish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this maximum identify a universal family of maximally coherent mixed states. These states are optimal resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing.

quant-ph↗

arXiv2017

Estimation of gradients in quantum metrology

We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of $N$ particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Usually gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the off-set field determining the level-splitting of the particles and results in collective dephasing. In this work we use the framework of quantum metrology to assess the maximal accuracy for gradient estimation. For arbitrary positioning of particles, we identify optimal entangled and separable states allowing the estimation of gradients with the maximal accuracy, quantified by the quantum Fisher information. We also analyze the performance of states from the decoherence-free subspace (DFS), which are insensitive to the fluctuations of the magnetic offset field. We find that these states allow to measure a gradient directly, without the necessity of estimating the magnetic offset field. Moreover, we show that DFS states attain a precision for gradient estimation comparable to the optimal entangled states. Finally, for the above classes of states we find simple and feasible measurements saturating the quantum Cramér-Rao bound.

quant-ph↗

arXiv2017

Radio-frequency sideband cooling and sympathetic cooling of trapped ions in a static magnetic field gradient

We report a detailed investigation on near-ground state cooling of one and two trapped atomic ions. We introduce a simple sideband cooling method for confined atoms and ions, using RF radiation applied to bare ionic states in a static magnetic field gradient, and demonstrate its application to ions confined at secular trap frequencies, $ω_z \approx 2π\times 117 $kHz. For a single \ybplus ion, the sideband cooling cycle reduces the average phonon number, $\left\langle\,n\,\right\rangle$ from the Doppler limit to $\left\langle\,n\,\right\rangle =$ 0.30(12). This is in agreement with the theoretically estimated lowest achievable phonon number in this experiment. We extend this method of RF sideband cooling to a system of two \ybplus ions, resulting in a phonon number of $\left\langle\,n\,\right\rangle =$ 1.1(7) in the center-of-mass mode. Furthermore, we demonstrate the first realisation of sympathetic RF sideband cooling of an ion crystal consisting of two individually addressable identical isotopes of the same species.

physics.atom-ph↗

arXiv2016

Optimized parameter estimation in the presence of collective phase noise

We investigate phase and frequency estimation with different measurement strategies under the effect of collective phase noise. First, we consider the standard linear estimation scheme and present an experimentally realisable optimization of the initial probe states by collective rotations. We identify the optimal rotation angle for different measurement times. Second, we show that sub-shot noise sensitivity - up to the Heisenberg limit - can be reached in presence of collective phase noise by using differential interferometry, where one part of the system is used to monitor the noise. For this, not only GHZ states but also symmetric Dicke states are suitable. We investigate the optimal splitting for a general symmetric Dicke state at both inputs and discuss possible experimental realisations of differential interferometry.

quant-ph↗

arXiv2016

Characterizing the width of entanglement

We introduce the concept of entanglement width as measure of the spatial distribution of entanglement in multiparticle systems. We develop criteria to detect the width of entanglement using global observables such as energy and magnetic susceptibility. Therefore, the introduced entanglement criteria can be applied to systems where addressing of single particles is not possible. We apply the criteria to different examples such as the J1-J2- Heisenberg model and point out the difference between entanglement depth and entanglement width.

quant-ph↗

arXiv2016

Generalized Effective Operator Formalism for Decaying Systems

Systems of neutral kaons can be used to observe entanglement and the violation of Bell inequalities. The decay of these particles poses some problems, however, and recently an effective formalism for treating such systems has been derived. We generalize this formalism and make it applicable to other quantum systems that can be made to behave in a similar manner. As examples, we discuss two possible implementations of the generalized formalism using trapped ions such as $^{171}$Yb or $^{172}$Yb, which may be used to simulate kaonic behavior in a quantum optical system.

quant-ph↗

arXiv2016

Quantum dynamics of trapped ions in a dynamic field gradient using dressed states

Novel ion traps that provide either a static or a dynamic magnetic gradient field allow for the use of radio frequency (rf) radiation for coupling internal and motional states of ions, which is essential for conditional quantum logic. We show that the coupling mechanism in the presence of a dynamic gradient is the same, in a dressed state basis, as in the case of a static gradient. Then, it is shown how demanding experimental requirements arising when using a dynamic gradient could be overcome. Thus, using dressed states in a dynamic gradient field could decisively reduce experimental complexity on the route towards a scalable device for quantum information science based on rf-driven trapped ions.

quant-ph↗

arXiv2014

State selective detection of hyperfine qubits

In order to faithfully detect the state of an individual two-state quantum system (qubit) realized using, for example, a trapped ion or atom, state selective scattering of resonance fluorescence is well established. The simplest way to read out this measurement and assign a state is the threshold method. The detection error can be decreased by using more advanced detection methods like the time-resolved method or the $π$-pulse detection method. These methods were introduced to qubits with a single possible state change during the measurement process. However, there exist many qubits like the hyperfine qubit of $^{171}Yb^+$ where several state change are possible. To decrease the detection error for such qubits, we develope generalizations of the time-resolved method and the $π$-pulse detection method for such qubits. We show the advantages of these generalized detection methods in numerical simulations and experiments using the hyperfine qubit of $^{171}Yb^+$. The generalized detection methods developed here can be implemented in an efficient way such that experimental real time state discrimination with improved fidelity is possible.

quant-ph↗

arXiv2014

A unified approach to entanglement criteria using the Cauchy-Schwarz and Hölder inequalities

We present unified approach to different recent entanglement criteria. Although they were developed in different ways, we show that they are all applications of a more general principle given by the Cauchy-Schwarz inequality. We explain this general principle and show how to derive with it not only already known but also new entanglement criteria. We systematically investigate its potential and limits to detect bipartite and multipartite entanglement.

quant-ph↗