arXiv subjects

Marco Ballarin

Publications and source records attributed to Marco Ballarin.

11 recordsLinked to original sources

arXiv2026

Generative IQP Circuit Learning with Physics-Informed Latent Initialization

Quantum generative learning based on instantaneous quantum polynomial-time (IQP) circuits can benefit from efficient classical training strategies. A recent latent adaptation framework for IQP-based generative modeling transfers shared circuit parameters across instances of the same task with different hyperparameters while adapting only a low-dimensional latent variable for each new instance. However, existing approaches initialize this latent variable randomly, which can limit optimization efficiency and performance. In this work, we introduce a physics-informed latent initialization scheme for IQP generative learning to improve upon existing random initialization schemes. Motivated by the platonic representation hypothesis, we use latent representations extracted from a classical physics-informed neural network (PINN) surrogate to initialize the latent variables of the quantum model for the solution of the Burgers' equation. The initialized IQP model is then adapted on a higher-resolution solution domain. We find that this structured initialization consistently outperforms random latent initialization, yielding improved adaptation behavior and stronger generative accuracy across multiple viscosity settings. These results show that classical surrogate representations can provide useful inductive bias for quantum generative models and offer a practical route to improved initialization in IQP-based learning.

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arXiv2026

Exact log-depth preparation of highly entangled matrix product states

Preparing matrix product states (MPS) on a quantum device is a key subroutine in many quantum algorithms. The most competitive methods, based on the renormalisation group, prepare translationally invariant MPS of size $L$ and bond dimension $\chi$, up to an error $\varepsilon$, in circuit depth $\tilde O(\chi^{4}\log(L/\varepsilon))$ or $\tilde O(\chi^{6}\log\log(L/\varepsilon))$. We improve multiple aspects of these methods. First, using block-encoded correction maps, whose post-selection succeeds with constant probability, we render the preparation exact without sacrificing the scaling in $L$. Second, through a generalisation of oblivious amplitude amplification to isometries, we reduce the bond-dimension dependence, improving the depth to $\tilde O(\chi^{2}\log L + \chi^{4})$ or $\tilde O(\chi^{2}\log\log L + \chi^{4})$, and even to $\tilde O(\chi^{3}\log L)$ for incoherent preparations. Finally, we extend the framework to non-translationally invariant MPS and prove logarithmic-depth exact preparation for independent and identically distributed random tensor sequences. Confirmed by numerical studies, these results constitute, to the best of our knowledge, the most efficient exact MPS preparation protocols in the relevant parameter regimes.

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arXiv2026

Scalable, self-verifying variational quantum eigensolver using adiabatic warm starts

We study an adiabatic variant of the variational quantum eigensolver (VQE) in which VQE is performed iteratively for a sequence of Hamiltonians along an adiabatic path. We derive the conditions under which gradient-based optimization successfully prepares the adiabatic ground states. These conditions show that the barren plateau problem and local optima can be avoided. Additionally, we propose using energy-standard-deviation measurements at runtime to certify eigenstate accuracy and verify convergence to the global optimum.

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arXiv2025

Efficient quantum state preparation of multivariate functions using tensor networks

For the preparation of high-dimensional functions on quantum computers, we introduce tensor network algorithms that are efficient with regard to dimensionality, optimize circuits composed of hardware-native gates and take gate errors into account during the optimization. To avoid the notorious barren plateau problem of vanishing gradients in the circuit optimization, we smoothly transform the circuit from an easy-to-prepare initial function into the desired target function. We show that paradigmatic multivariate functions can be accurately prepared such as, by numerical simulations, a 17-dimensional Gaussian encoded in the state of 102 qubits and, through experiments, a 9-dimensional Gaussian realized using 54 qubits on Quantinuum's H2 quantum processor.

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arXiv2025

Quantum algorithms for equational reasoning

As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent expressions with increasing problem size. We introduce quantum normal form reduction, a quantum computational framework designed to address this challenge. We construct an efficiently implementable quantum Hamiltonian whose ground state encodes all equivalent expressions in a quantum superposition. By preparing and manipulating these states, we tackle fundamental problems in equational reasoning, including verifying and counting equivalent expressions and identifying structural properties of equivalence classes. We demonstrate a quantum-inspired version of the algorithm, using tensor networks to solve instances involving up to 10^28 equivalent expressions, far beyond the reach of classical graph exploration. This framework opens the path for quantum symbolic computation in areas from circuit design to data compression, computational group theory, linguistics, and macromolecular modeling, unlocking previously inaccessible problems.

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arXiv2024

Benchmarking Quantum Red TEA on CPUs, GPUs, and TPUs

We benchmark simulations of many-body quantum systems on heterogeneous hardware platforms using CPUs, GPUs, and TPUs. We compare different linear algebra backends, e.g., NumPy versus the PyTorch, JAX, or TensorFlow libraries, as well as a mixed-precision-inspired approach and optimizations for the target hardware. Quantum Red TEA out of the Quantum TEA library specifically addresses handling tensors with different libraries or hardware, where the tensors are the building blocks of tensor network algorithms. The benchmark problem is a variational search of a ground state in an interacting model. This is a ubiquitous problem in quantum many-body physics, which we solve using tensor network methods. This approximate state-of-the-art method compresses quantum correlations which is key to overcoming the exponential growth of the Hilbert space as a function of the number of particles. We present a way to obtain speedups of a factor of 34 when tuning parameters on the CPU, and an additional factor of 2.76 on top of the best CPU setup when migrating to GPUs.

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arXiv2024

Quantum circuit compilation with quantum computers

Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers, paving the way for a quantum advantage in compilation. We demonstrate the effectiveness of this approach via Quantum and Simulated Annealing-based compilation: we successfully compile a Trotterized Hamiltonian simulation with up to 64 qubits and 64 time-steps and a Quantum Fourier Transform with up to 40 qubits and 771 time steps. We show that, for a translationally invariant circuit, the compilation results in a fidelity gain that grows extensively in the size of the input circuit, outperforming any local or quasi-local compilation approach.

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arXiv2024

Hybrid Tree Tensor Networks for quantum simulation

Hybrid Tensor Networks (hTN) offer a promising solution for encoding variational quantum states beyond the capabilities of efficient classical methods or noisy quantum computers alone. However, their practical usefulness and many operational aspects of hTN-based algorithms, like the optimization of hTNs, the generalization of standard contraction rules to an hybrid setting, and the design of application-oriented architectures have not been thoroughly investigated yet. In this work, we introduce a novel algorithm to perform ground state optimizations with hybrid Tree Tensor Networks (hTTNs), discussing its advantages and roadblocks, and identifying a set of promising applications. We benchmark our approach on two paradigmatic models, namely the Ising model at the critical point and the Toric code Hamiltonian. In both cases, we successfully demonstrate that hTTNs can improve upon classical equivalents with equal bond dimension in the classical part.

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arXiv2024

Optimal sampling of tensor networks targeting wave function's fast decaying tails

We introduce an optimal strategy to sample quantum outcomes of local measurement strings for isometric tensor network states. Our method generates samples based on an exact cumulative bounding function, without prior knowledge, in the minimal amount of tensor network contractions. The algorithm avoids sample repetition and, thus, is efficient at sampling distribution with exponentially decaying tails. We illustrate the computational advantage provided by our optimal sampling method through various numerical examples, involving condensed matter, optimization problems, and quantum circuit scenarios. Theory predicts up to an exponential speedup reducing the scaling for sampling the space up to an accumulated unknown probability $\epsilon$ from $\mathcal{O}(\epsilon^{-1})$ to $\mathcal{O}(\log(\epsilon^{-1}))$ for a decaying probability distribution. We confirm this in practice with over one order of magnitude speedup or multiple orders improvement in the error depending on the application. Our sampling strategy extends beyond local observables, e.g., to quantum magic.

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arXiv2023

Digital quantum simulation of lattice fermion theories with local encoding

We numerically analyze the feasibility of a platform-neutral, general strategy to perform quantum simulations of fermionic lattice field theories under open boundary conditions. The digital quantum simulator requires solely one- and two-qubit gates and is scalable since integrating each Hamiltonian term requires a finite (non-scaling) cost. The exact local fermion encoding we adopt relies on auxiliary $\mathbb{Z}_2$ lattice gauge fields by adding a pure gauge Hamiltonian term akin to the Toric Code. By numerically emulating the quantum simulator real-time dynamics, we observe a timescale separation for spin- and charge-excitations in a spin-$\frac{1}{2}$ Hubbard ladder in the $t-J$ model limit.

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arXiv2022

Entanglement entropy production in Quantum Neural Networks

Quantum Neural Networks (QNN) are considered a candidate for achieving quantum advantage in the Noisy Intermediate Scale Quantum computer (NISQ) era. Several QNN architectures have been proposed and successfully tested on benchmark datasets for machine learning. However, quantitative studies of the QNN-generated entanglement have been investigated only for up to few qubits. Tensor network methods allow to emulate quantum circuits with a large number of qubits in a wide variety of scenarios. Here, we employ matrix product states to characterize recently studied QNN architectures with random parameters up to fifty qubits showing that their entanglement, measured in terms of entanglement entropy between qubits, tends to that of Haar distributed random states as the depth of the QNN is increased. We certify the randomness of the quantum states also by measuring the expressibility of the circuits, as well as using tools from random matrix theory. We show a universal behavior for the rate at which entanglement is created in any given QNN architecture, and consequently introduce a new measure to characterize the entanglement production in QNNs: the entangling speed. Our results characterise the entanglement properties of quantum neural networks, and provides new evidence of the rate at which these approximate random unitaries.

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