arXiv subjects

Zoltán Kolarovszki

Publications and source records attributed to Zoltán Kolarovszki.

10 recordsLinked to original sources

arXiv2026

General framework for anticoncentration and linear cross-entropy benchmarking in photonic quantum advantage experiments

Photonic architectures are one of the leading platforms for demonstrating quantum computational advantage, with Boson Sampling and Gaussian Boson Sampling as the primary schemes. Yet, we lack for these photonic primitives a systematic theoretical understanding of linear cross-entropy benchmarking (LXEB), which is a central tool for testing quantum advantage proposals. In this work, we develop a representation-theoretic framework for the classical computation of average LXEB scores and second moments of output probability distributions, covering a range of quantum advantage experiments based on scattering $n$-photon states through $m$-mode Haar-random interferometers. Our methods apply in any regime, including the saturated regime, where the (expected) number of photons is comparable to the number of optical modes. The same second-moment techniques also allow us to prove anticoncentration for traditional Fock-state Boson Sampling in the saturated regime. Interestingly, for Gaussian Boson Sampling second moments are not sufficient to establish a meaningful anticoncentration statement. The technical core of our approach rests on decomposing two copies of the $n$-particle bosonic space $\mathrm{Sym}^n(\mathbb{C}^m)$ into irreducible representations of $\mathrm{U}(m)$. This reduces two-copy Haar averages to computing purities of initial states after partial traces over particles, highlighting the role that particle entanglement plays for LXEB and anticoncentration.

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arXiv2026

Universality of Classically Trainable, Quantum-Deployed Boson-Sampling Generative Models

Recent work on the instantaneous quantum polynomial-time (IQP) quantum-circuit Born machine (QCBM) highlights a promising paradigm for generative modeling: train classically, deploy quantumly. In this setting, the training objective can be evaluated efficiently on a classical computer, while sampling from the resulting model may still be classically intractable. Furthermore, in the IQP-QCBM framework, extending the model family with ancillary qubits has been proven to yield universality. This paper asks whether similar results hold for linear-optical generative models. To this end, we introduce the Boson Sampling Born Machine (BSBM). Our analysis retraces analogous steps as were found for IQP-QCBMs with twists. Using recent results that enable classical approximation of broad classes of expectation values in linear optics, we show that BSBMs can be trained classically for wide families of loss functions. Next, we argue that "basic" BSBMs are not universal generative models, and that universality can be achieved by expanding the model while preserving efficient classical training and sampling hardness. In our approach, we introduce and analyze the role of constant-function postprocessing, generalizing the construction for IQP-QCBMs, which under suitable conditions can lead to universality while preserving the hardness of classically simulating the models. We showcase a family of BSBMs, characterized by a single hyperparameter, that allows for a monotonic increase in expressivity toward universality while retaining the capacity to represent ostensibly hard distributions. Furthermore, we discuss the possible modalities for the efficient classical training, in the sense of efficient estimation of gradients of the loss function.

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arXiv2026

Generative modeling with Gaussian Boson Sampling: classically trainable Bosonic Born Machines

Quantum generative modeling has emerged as a promising application of quantum computers, aiming to model complex probability distributions beyond the reach of classical methods. In practice, however, training such models often requires costly gradient estimation performed directly on the quantum hardware. Crucially, for certain structured quantum circuits, expectation values of local observables can be efficiently evaluated on a classical computer, enabling classical training without calls to the quantum hardware in the optimization loop. In these models, sampling from the resulting circuits can still be classically hard, so inference must be performed on a quantum device, yielding a potential computational advantage. In this work, we introduce a photonic quantum generative model built on parametrized Gaussian Boson Sampling circuits. The training is based on the efficient classical evaluation of expectation values enabled by the Gaussian structure of the state, allowing scalable optimization of the model parameters through the maximum mean discrepancy loss function. We demonstrate the effectiveness of the approach through numerical experiments on photonic systems with up to 805 modes and over a million trainable parameters, highlighting its scalability and suitability for near-term photonic quantum devices.

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arXiv2026

Generalized group designs: constructing novel unitary 2-, 3- and 4-designs

Unitary designs are essential tools in several quantum information protocols. Similarly to other design concepts, unitary designs are mainly used to facilitate averaging over a relevant space, in this case, the unitary group $\mathrm{U}(d)$. While it is known that exact unitary $t$-designs exist for any degree $t$ and dimension $d$, the most appealing type of designs, group designs (in which the elements of the design form a group), can provide at most $3$-designs. Moreover, even group $2$-designs can exist only in limited dimensions. In this paper, we present novel construction methods for creating exact generalized group designs based on the representation theory of the unitary group and its finite subgroups that overcome the $4$-design-barrier of unitary group designs. Furthermore, a construction is presented for creating generalized group $2$-designs in arbitrary dimensions.

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arXiv2025

Fermionic Born Machines: Classical training of quantum generative models based on Fermion Sampling

Quantum generative learning is a promising application of quantum computers, but faces several trainability challenges, including the difficulty in experimental gradient estimations. For certain structured quantum generative models, however, expectation values of local observables can be efficiently computed on a classical computer, enabling fully classical training without quantum gradient evaluations. Although training is classically efficient, sampling from these circuits is still believed to be classically hard, so inference must be carried out on a quantum device, potentially yielding a computational advantage. In this work, we introduce Fermionic Born Machines as an example of such classically trainable quantum generative models. The model employs parameterized magic states and fermionic linear optical (FLO) transformations with learnable parameters. The training exploits a decomposition of the magic states into Gaussian operators, which permits efficient estimation of expectation values. Furthermore, the specific structure of the ansatz induces a loss landscape that exhibits favorable characteristics for optimization. The FLO circuits can be implemented, via fermion-to-qubit mappings, on qubit architectures to sample from the learned distribution during inference. Numerical experiments on systems up to 160 qubits demonstrate the effectiveness of our model and training framework.

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arXiv2025

Piquasso: A Photonic Quantum Computer Simulation Software Platform

We introduce the Piquasso quantum programming framework, a full-stack open-source software platform for the simulation and programming of photonic quantum computers. Piquasso can be programmed via a high-level Python programming interface enabling users to perform efficient quantum computing with discrete and continuous variables. Via optional high-performance C++ backends, Piquasso provides state-of-the-art performance in the simulation of photonic quantum computers. The Piquasso framework is supported by an intuitive web-based graphical user interface where the users can design quantum circuits, run computations, and visualize the results.

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arXiv2024

On the learning abilities of photonic continuous-variable Born machines

This paper investigates photonic continuous-variable Born machines (CVBMs), which utilize photonic quantum states as resources for continuous probability distributions. Implementing exact gradient descent in the CVBM training process is often infeasible, bringing forward the need to approximate the gradients using an estimator obtained from a smaller number of samples, obtaining a quantum stochastic gradient descent (SGD) method. In this work, the ability to train CVBMs is analyzed using stochastic gradients obtained using relatively few samples from the probability distribution corresponding to homodyne measurement. The main obstacle to this analysis is that classically simulating CVBMs and obtaining samples is a demanding task, while a large number of iterations are needed to achieve convergence. The present research is enabled by a novel strategy to simulate homodyne detections of generic multimode photonic states using a classical computer. With this approach, a more comprehensive study of CVBMs is made possible, and the training of multimode CVBMs is demonstrated with parametric quantum circuits considerably larger than in previous articles. More specifically, we use the proposed algorithm to demonstrate learning of multimode quantum distributions using CVBMs. Moreover, successful CVBM trainings were demonstrated with the use of stochastic gradients.

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arXiv2024

Suppressing photon detection errors in nondeterministic state preparation

Photonic quantum computing has recently emerged as a promising candidate for fault-tolerant quantum computing by photonic qubits. These protocols make use of nondeterministic gates, enabling universal quantum computation. However, the suggested solutions heavily use particle number resolving detectors (PNRDs), which are experimentally hard to realize and are usually biased in practice. We investigate the possibility of suppressing such errors caused by such photodetector imperfections by adjusting the optimal beamsplitter and phaseshifter angles in the interferometer corresponding to nondeterministic gates. Moreover, we devise an optimization method for determining the adjusted angles, which may achieve higher output state fidelities while controlling the success probabilities of the nondeterministic gates.

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arXiv2023

High performance Boson Sampling simulation via data-flow engines

In this work, we generalize the Balasubramanian-Bax-Franklin-Glynn (BB/FG) permanent formula to account for row multiplicities during the permanent evaluation and reduce the complexity of permanent evaluation in scenarios where such multiplicities occur. This is achieved by incorporating n-ary Gray code ordering of the addends during the evaluation. We implemented the designed algorithm on FPGA-based data-flow engines and utilized the developed accessory to speed up boson sampling simulations up to $40$ photons, by drawing samples from a $60$ mode interferometer at an averaged rate of $\sim80$ seconds per sample utilizing $4$ FPGA chips. We also show that the performance of our BS simulator is in line with the theoretical estimation of Clifford \& Clifford \cite{clifford2020faster} providing a way to define a single parameter to characterize the performance of the BS simulator in a portable way. The developed design can be used to simulate both ideal and lossy boson sampling experiments.

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arXiv2022

Polynomial speedup in Torontonian calculation by a scalable recursive algorithm

Evaluating the Torontonian function is a central computational challenge in the simulation of Gaussian Boson Sampling (GBS) with threshold detection. In this work, we propose a recursive algorithm providing a polynomial speedup in the exact calculation of the Torontonian compared to state-of-the-art algorithms. According to our numerical analysis the complexity of the algorithm is proportional to $N^{1.0691}2^{N/2}$ with $N$ being the size of the problem. We also show that the recursive algorithm can be scaled up to HPC use cases making feasible the simulation of threshold GBS up to $35-40$ photon clicks without the needs of large-scale computational capacities.

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