arXiv subjects

Petr Zapletal

Publications and source records attributed to Petr Zapletal.

10 recordsLinked to original sources

arXiv2026

Hybrid quantum-classical neural network for sample-efficient recognition of topological phases

With increasing maturity of quantum computers, standard methods for characterizing global properties of their output quantum states via direct measurements and classical post-processing are becoming increasingly impractical due to large measurement costs. Although quantum neural networks could directly process quantum states to identify underlying characteristics with reduced measurement efforts, they often require deep quantum circuits that cannot be implemented on existing devices. To overcome these challenges, we introduce a hybrid quantum-classical neural network that consists of a shallow parameterized quantum circuit, measurements, and a classical neural network. The parameterized quantum circuit performs a nonlocal transformation of the measurement basis, which is jointly trained with the classical neural network to maximize the statistical distance between data obtained by measuring different quantum states. Using supervised learning, we demonstrate that the hybrid neural network distinguishes the topological phase of the surface code from a symmetry-enriched topological phase and random product states. Moreover, this hybrid neural network reduces both inference and training sample complexities of recognizing the topological phase by approximately one order of magnitude compared to a classical neural network trained on randomized Pauli measurements. As this hybrid neural network features a shallow quantum circuit that can be readily implemented on existing quantum computers, it enables the efficient characterization of complex quantum states.

quant-ph↗

arXiv2026

Hybrid Quantum-Classical Neural Networks for Recognizing Quantum Phases

Identifying quantum phases of matter is key to understanding strongly correlated materials, but remains a challenging task for both conventional computers and current quantum processors. Here, we introduce and implement a hybrid quantum-classical neural network for quantum phase recognition by combining a hardware-efficient parameterized quantum circuit and a feedforward neural network. We jointly train both components with superconducting quantum hardware in the optimization loop, to experimentally demonstrate a classifier for the quantum phases of surface code lattices with up to 4x4 sites in a magnetic field. To learn nonlocal features of the topological phase, we train the hybrid neural network to distinguish topological ground states of the surface code from a featureless ensemble of product states. This allows the trained classifier to distinguish topological ground states from randomly chosen product states, even when subjected to any single-qubit Pauli error. The classifier reaches accuracies above 85% in single-shot measurements, and above 99% when averaging over ten measurements. We expect hybrid neural networks such as the one presented here to be a promising approach for characterizing quantum states in scenarios where classical methods exhibit an unfavorable scaling of sample complexity.

quant-ph↗

arXiv2024

Quantum Convolutional Neural Network for Phase Recognition in Two Dimensions

Quantum convolutional neural networks (QCNNs) are quantum circuits for characterizing complex quantum states. They have been proposed for recognizing quantum phases of matter at low sampling cost and have been designed for condensed matter systems in one dimension. Here we construct a QCNN that can perform phase recognition in two dimensions and correctly identify the phase transition from a Toric Code phase with $\mathbb{Z}_2$-topological order to the paramagnetic phase. The network also exhibits a noise threshold up to which the topological order is recognized. Furthermore, it captures correlations between all stabilizer elements of the Toric Code, which cannot be accessed by direct measurements. This increases the threshold for errors leading to such correlations and allows for correctly identifying the topological phase in the presence of strong correlated errors. Our work generalizes phase recognition with QCNNs to higher spatial dimensions and intrinsic topological order, where exploration and characterization via classical numerics become challenging.

quant-ph↗

arXiv2023

Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases

The analysis of noisy quantum states prepared on current quantum computers is getting beyond the capabilities of classical computing. Quantum neural networks based on parametrized quantum circuits, measurements and feed-forward can process large amounts of quantum data to reduce measurement and computational costs of detecting non-local quantum correlations. The tolerance of errors due to decoherence and gate infidelities is a key requirement for the application of quantum neural networks on near-term quantum computers. Here we construct quantum convolutional neural networks (QCNNs) that can, in the presence of incoherent errors, recognize different symmetry-protected topological phases of generalized cluster-Ising Hamiltonians from one another as well as from topologically trivial phases. Using matrix product state simulations, we show that the QCNN output is robust against symmetry-breaking errors below a threshold error probability and against all symmetry-preserving errors provided the error channel is invertible. This is in contrast to string order parameters and the output of previously designed QCNNs, which vanish in the presence of any symmetry-breaking errors. To facilitate the implementation of the QCNNs on near-term quantum computers, the QCNN circuits can be shortened from logarithmic to constant depth in system size by performing a large part of the computation in classical post-processing. These constant-depth QCNNs reduce sample complexity exponentially with system size in comparison to the direct sampling using local Pauli measurements.

quant-ph↗

arXiv2021

Realizing Quantum Convolutional Neural Networks on a Superconducting Quantum Processor to Recognize Quantum Phases

Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations become computationally expensive when increasing the system size. Quantum neural networks tailored to recognize specific features of quantum states by combining unitary operations, measurements and feedforward promise to require fewer measurements and to tolerate errors. Here, we realize a quantum convolutional neural network (QCNN) on a 7-qubit superconducting quantum processor to identify symmetry-protected topological (SPT) phases of a spin model characterized by a non-zero string order parameter. We benchmark the performance of the QCNN based on approximate ground states of a family of cluster-Ising Hamiltonians which we prepare using a hardware-efficient, low-depth state preparation circuit. We find that, despite being composed of finite-fidelity gates itself, the QCNN recognizes the topological phase with higher fidelity than direct measurements of the string order parameter for the prepared states.

quant-ph↗

arXiv2021

Stabilization of multi-mode Schrodinger cat states via normal-mode dissipation engineering

Non-Gaussian quantum states have been deterministically prepared and autonomously stabilized in single- and two-mode circuit quantum electrodynamics architectures via engineered dissipation. However, it is currently unknown how to scale up this technique to multi-mode non-Gaussian systems. Here, we upgrade dissipation engineering to collective (normal) modes of nonlinear resonator arrays and show how to stabilize multi-mode Schrodinger cat states. These states are multi-photon and multi-mode quantum superpositions of coherent states in a single normal mode delocalized over an arbitrary number of cavities. We consider tailored dissipative coupling between resonators that are parametrically driven and feature an on-site nonlinearity, which is either a Kerr-type nonlinearity or an engineered two-photon loss. For both types of nonlinearity, we find the same exact closed-form solutions for the two-dimensional steady-state manifold spanned by superpositions of multi-mode Schrodinger cat states. We further show that, in the Zeno limit of strong dissipative coupling, the even parity multi-mode cat state can be deterministically prepared from the vacuum. Remarkably, engineered two-photon loss gives rise to a fast relaxation towards the steady state, protecting the state preparation against decoherence due to intrinsic single-photon losses and imperfections in tailored dissipative coupling, which sets in at longer times. The relaxation time is independent of system size making the state preparation scalable. Multi-mode cat states are naturally endowed with a noise bias that increases exponentially with system size and can thus be exploited for enhanced robust encoding of quantum information.

quant-ph↗

arXiv2020

Long-lived elementary excitations and light coherence in topological lasers

Combining topologically-protected chiral light transport and laser amplification gives rise to topological lasers, whose operation is immune to fabrication imperfections and defects, uncovering the role of topology in a novel nonlinear non-Hermitian regime. We study a topological laser based on the photonic Haldane model with selective pumping of chiral edge modes described by saturable gain. We investigate elementary excitations around the mean-field steady state and their consequences for the coherence properties. In particular, we show that the hybridization of chiral edge modes gives rise to long-lived elementary excitations, leading to large phase fluctuations in the emitted light field and a decrease of light coherence. In contrast to topologically trivial lasers, the lifetime of elementary excitations is robust against disorder in topological lasers. However, the lifetime strongly depends on the edge-mode dispersion around the lasing frequency. As a result, the lifetime can be reduced by orders of magnitude for lasing of different edge modes, leading to a suppression of phase fluctuations and larger coherence of the emitted light. On the other hand, amplitude fluctuations and the second-order autocorrelation function are moderately increased at the same time.

cond-mat.mes-hall↗

arXiv2019

Dynamical Generation of Synthetic Electric Fields for Photons in the Quantum Regime

Optomechanics offers a natural way to implement synthetic dynamical gauge fields, leading to synthetic electric fields for phonons and, as a consequence, to unidirectional light transport. Here we investigate the quantum dynamics of synthetic gauge fields in the minimal setup of two optical modes coupled by phonon-assisted tunneling where the phonon mode is undergoing self-oscillations. We use the quantum van-der-Pol oscillator as the simplest dynamical model for a mechanical self-oscillator that allows us to perform quantum master equation simulations. We identify a single parameter, which controls the strength of quantum fluctuations, enabling us to investigate the classical-to-quantum crossover. We show that the generation of synthetic electric fields is robust against noise and that it leads to unidirectional transport of photons also in the quantum regime, albeit with a reduced isolation ratio. Our study opens the path for studying dynamical gauge fields in the quantum regime based on optomechanical arrays.

cond-mat.mes-hall↗

arXiv2018

Dynamically Generated Synthetic Electric Fields for Photons

Static synthetic magnetic fields give rise to phenomena including the Lorentz force and the quantum Hall effect even for neutral particles, and they have by now been implemented in a variety of physical systems. Moving towards fully dynamical synthetic gauge fields allows, in addition, for backaction of the particles' motion onto the field. If this results in a time-dependent vector potential, conventional electromagnetism predicts the generation of an electric field. Here, we show how synthetic electric fields for photons arise self-consistently due to the nonlinear dynamics in a driven system. Our analysis is based on optomechanical arrays, where dynamical gauge fields arise naturally from phonon-assisted photon tunneling. We study open, one-dimensional arrays, where synthetic magnetic fields are absent. However, we show that synthetic electric fields can be generated dynamically, which, importantly, suppress photon transport in the array. The generation of these fields depends on the direction of photon propagation, leading to a novel mechanism for a photon diode, inducing nonlinear nonreciprocal transport via dynamical synthetic gauge fields.

cond-mat.mes-hall↗

arXiv2017

Direct observation of phase sensitive Hong-Ou-Mandel interference

Quality of individual photons and their ability to interfere is traditionally tested by measuring the Hong-Ou-Mandel photon bunching effect. However, this phase insensitive measurement only tests the particle aspect of the quantum interference. Motivated by these limitations, we formulate a witness capable of recognizing both the quality and the coherence of two photons from a single set of measurements. We exploit the conditional nonclassical squeezing which is sensitive to both the quality of the single photons and their indistinguishability and we show that it can be used to irectly reveal both the particle and the wave aspects of the quantum interference. Finally, we experimentally test the witness by applying it to a pair of independent single photons generated on demand.

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