arXiv subjects

Korbinian Kottmann

Publications and source records attributed to Korbinian Kottmann.

13 recordsLinked to original sources

arXiv2026

Parameter-optimal unitary synthesis with flag decompositions

We introduce the flag decomposition as a central tool for unitary synthesis. It lets us carve out a diagonal unitary with $2^n$ degrees of freedom in such a way that the remaining flag circuit is parametrized by the optimal number of $4^n-2^n$ rotations. This enables us to produce parameter-optimal quantum circuits for generic unitaries and matrix product state preparation. Our approach improves upon the state of the art, both when compiling down to the {Clifford + Rot} gate set with what we call selective de-multiplexing, and when using phase gradient resource states together with quantum arithmetic to implement multiplexed rotations. All of our synthesis methods are efficiently implementable in terms of recursive Cartan decompositions realized by standard linear algebra routines, making them applicable to all practically relevant system sizes.

quant-ph↗

arXiv2025

Unitary synthesis with optimal brick wall circuits

We present quantum circuits with a brick wall structure using the optimal number of parameters and two-qubit gates to parametrize $SU(2^n)$, and provide evidence that these circuits are universal for $n\leq 5$. For this, we successfully compile random matrices to the presented circuits and show that their Jacobian has full rank almost everywhere in the domain. Our method provides a new state of the art for synthesizing typical unitary matrices from $SU(2^n)$ for $n=3, 4, 5$, and we extend it to the subgroups $SO(2^n)$ and $Sp^\ast(2^n)$. We complement this numerical method by a partial proof, which hinges on an open conjecture that relates universality of an ansatz to it having full Jacobian rank almost everywhere.

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arXiv2024

Multicritical dissipative phase transitions in the anisotropic open quantum Rabi model

We investigate the nonequilibrium steady state of the anisotropic open quantum Rabi model, which exhibits first-order and second-order dissipative phase transitions upon varying the degree of anisotropy between the coupling strengths of rotating and counterrotating terms. Using both semiclassical and quantum approaches, we find a rich phase diagram resulting from the interplay between the anisotropy and the dissipation. First, there exists a bistable phase where both the normal and superradiant phases are stable. Second, there are multicritical points where the phase boundaries for the first- and second-order phase transitions meet. We show that a new set of critical exponents governs the scaling of the multicritical points. Finally, we discuss the feasibility of observing the multicritical transitions and bistability using a pair of trapped ions where the anisotropy can be tuned by controlling the intensity of the Raman transitions. Our study enlarges the scope of critical phenomena that may occur in finite-component quantum systems, which could be useful for applications in critical quantum sensing.

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arXiv2023

Reducing Entanglement With Physically-Inspired Fermion-To-Qubit Mappings

In ab-initio electronic structure simulations, fermion-to-qubit mappings represent the initial encoding step of the fermionic problem into qubits. This work introduces a physically-inspired method for constructing mappings that significantly simplify entanglement requirements when simulating states of interest. The presence of electronic excitations drives the construction of our mappings, reducing correlations for target states in the qubit space. To benchmark our method, we simulate ground states of small molecules and observe an enhanced performance when compared to classical and quantum variational approaches from prior research employing conventional mappings. In particular, on the quantum side, our mappings require a reduced number of entangling layers to achieve accuracy for $LiH$, $H_2$, $(H_2)_2$, the $H_4$ stretching and benzene's {\pi} system using the RY hardware efficient ansatz. In addition, our mappings also provide an enhanced ground state simulation performance in the density matrix renormalization group algorithm for the $N_2$ molecule.

quant-ph↗

arXiv2023

Evaluating analytic gradients of pulse programs on quantum computers

Parametrized pulse programs running on quantum hardware can be differentiated via the stochastic parameter-shift (SPS) rule. We overcome the intrinsically approximate nature of SPS by introducing a new analytic method for computing gradients of pulse programs, that we coin ODEgen. In this new method, we find effective generators of pulse gates using a differentiable ordinary differential equation (ODE) solver. These effective generators inform parameter-shift rules that can be evaluated on quantum hardware. We showcase simulated VQE examples with realistic superconducting transmon systems, for which we obtain lower energies with fewer quantum resources using ODEgen over SPS. We further demonstrate a pulse VQE run with gradients computed via ODEgen entirely on quantum hardware.

quant-ph↗

arXiv2022

Investigating Quantum Many-Body Systems with Tensor Networks, Machine Learning and Quantum Computers

We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical simulations are done with state-of-the-art tensor network methods in one and two spatial dimensions. For one dimensional systems, we utilize matrix product states (MPS) that have many practical advantages and can be optimized using the efficient density matrix renormalization group (DMRG) algorithm. The data for two dimensional systems is obtained from entangled projected pair states (PEPS) optimized via imaginary time evolution. Data in form of observables, entanglement spectra, or parts of the state vectors from these simulations, is then fed into a deep learning (DL) pipeline where we perform anomaly detection to map out the phase diagram. We extend this notion to quantum computers and introduce quantum variational anomaly detection. Here, we first simulate the ground state and then process it in a quantum machine learning (QML) manner. Both simulation and QML routines are performed on the same device, which we demonstrate both in classical simulation and on a physical quantum computer hosted by IBM.

quant-ph↗

arXiv2022

PennyLane: Automatic differentiation of hybrid quantum-classical computations

PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for hardware providers including the Xanadu Cloud, Amazon Braket, and IBM Quantum, allowing PennyLane optimizations to be run on publicly accessible quantum devices. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.

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arXiv2022

Variational Quantum Anomaly Detection: Unsupervised mapping of phase diagrams on a physical quantum computer

One of the most promising applications of quantum computing is simulating quantum many-body systems. However, there is still a need for methods to efficiently investigate these systems in a native way, capturing their full complexity. Here, we propose variational quantum anomaly detection, an unsupervised quantum machine learning algorithm to analyze quantum data from quantum simulation. The algorithm is used to extract the phase diagram of a system with no prior physical knowledge and can be performed end-to-end on the same quantum device that the system is simulated on. We showcase its capabilities by mapping out the phase diagram of the one-dimensional extended Bose Hubbard model with dimerized hoppings, which exhibits a symmetry protected topological phase. Further, we show that it can be used with readily accessible devices nowadays and perform the algorithm on a real quantum computer.

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arXiv2021

Supersolid-Superfluid phase separation in the extended Bose-Hubbard model

Recent studies have suggested a new phase in the extended Bose-Hubbard model in one dimension at integer filling [1,2]. In this work, we show that this new phase is phase-separated into a supersolid and superfluid part, generated by mechanical instability. Numerical simulations are performed by means of the density matrix renormalization group algorithm in terms of matrix product states. In the phase-separated phase and the adjacent homogeneous superfluid and supersolid phases, we find peculiar spatial patterns in the entanglement spectrum and string-order correlation functions and show that they survive in the thermodynamic limit. In particular, we demonstrate that the elementary excitations of the homogeneous superfluid with enhanced periodic modulations are phonons, find the central charge to be $c=1$, and show that the velocity of sound, extracted from the intrinsic level splitting for finite systems, matches with the propagation velocity of local excitations in dynamical simulations. This suggests that the low-energy spectrum of the phase under investigation is effectively captured by a spinless Luttinger liquid, for which we find consistent results between the Luttinger parameter obtained from the linear dependence of the structure factor and the algebraic decay of the one-body density matrix.

cond-mat.quant-gas↗

arXiv2021

Detecting ergodic bubbles at the crossover to many-body localization using neural networks

The transition between ergodic and many-body localized phases is expected to occur via an avalanche mechanism, in which \emph{ergodic bubbles} that arise due to local fluctuations in system properties thermalize their surroundings leading to delocalization of the system, unless the disorder is sufficiently strong to stop this process. We propose an algorithm based on neural networks that allows to detect the ergodic bubbles using experimentally measurable two-site correlation functions. Investigating time evolution of the system, we observe a logarithmic in time growth of the ergodic bubbles in the MBL regime. The distribution of the size of ergodic bubbles converges during time evolution to an exponentially decaying distribution in the MBL regime, and a power-law distribution with a thermal peak in the critical regime, supporting thus the scenario of delocalization through the avalanche mechanism. Our algorithm permits to pin-point quantitative differences in time evolution of systems with random and quasiperiodic potentials, as well as to identify rare (Griffiths) events. Our results open new pathways in studies of the mechanisms of thermalization of disordered many-body systems and beyond.

cond-mat.dis-nn↗

arXiv2021

Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection

We demonstrate how to map out the phase diagram of a two dimensional quantum many body system with no prior physical knowledge by applying deep \textit{anomaly detection} to ground states from infinite projected entangled pair state simulations. As a benchmark, the phase diagram of the 2D frustrated bilayer Heisenberg model is analyzed, which exhibits a second-order and two first-order quantum phase transitions. We show that in order to get a good qualitative picture of the transition lines, it suffices to use data from the cost-efficient simple update optimization. Results are further improved by post-selecting ground-states based on their energy at the cost of contracting the tensor network once. Moreover, we show that the mantra of ``more training data leads to better results'' is not true for the learning task at hand and that, in principle, one training example suffices for this learning task. This puts the necessity of neural network optimizations for these learning tasks in question and we show that, at least for the model and data at hand, a simple geometric analysis suffices.

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arXiv2021

Unsupervised phase discovery with deep anomaly detection

We demonstrate how to explore phase diagrams with automated and unsupervised machine learning to find regions of interest for possible new phases. In contrast to supervised learning, where data is classified using predetermined labels, we here perform anomaly detection, where the task is to differentiate a normal data set, composed of one or several classes, from anomalous data. Asa paradigmatic example, we explore the phase diagram of the extended Bose Hubbard model in one dimension at exact integer filling and employ deep neural networks to determine the entire phase diagram in a completely unsupervised and automated fashion. As input data for learning, we first use the entanglement spectra and central tensors derived from tensor-networks algorithms for ground-state computation and later we extend our method and use experimentally accessible data such as low-order correlation functions as inputs. Our method allows us to reveal a phase-separated region between supersolid and superfluid parts with unexpected properties, which appears in the system in addition to the standard superfluid, Mott insulator, Haldane-insulating, and density wave phases.

quant-ph↗

arXiv2021

Unsupervised machine learning of topological phase transitions from experimental data

Identifying phase transitions is one of the key challenges in quantum many-body physics. Recently, machine learning methods have been shown to be an alternative way of localising phase boundaries also from noisy and imperfect data and without the knowledge of the order parameter. Here we apply different unsupervised machine learning techniques including anomaly detection and influence functions to experimental data from ultracold atoms. In this way we obtain the topological phase diagram of the Haldane model in a completely unbiased fashion. We show that the methods can successfully be applied to experimental data at finite temperature and to data of Floquet systems, when postprocessing the data to a single micromotion phase. Our work provides a benchmark for unsupervised detection of new exotic phases in complex many-body systems.

cond-mat.quant-gas↗