arXiv subjects

Andrea Rocchetto

Publications and source records attributed to Andrea Rocchetto.

12 recordsLinked to original sources

arXiv2025

A low-loss, 24-mode laser-written universal photonic processor in a glass-based platform

We report the fabrication of the first 24-mode universal photonic processor (UPP) realized through femtosecond laser writing (FLW), marking the most complex UPP demonstrated to date. Optimized for quantum dot emission at 925 nm, the device exhibits total insertion losses averaging only 4.35 dB, enabling its direct application in advanced multi-photon quantum experiments. Leveraging the versatility of FLW, we introduce suspended waveguides and precisely engineered 2D and 3D microstructures, significantly enhancing thermal isolation and minimizing power dissipation. As a result, our processor operates efficiently at less than 10 W, requiring only a simple thermo-electric cooler for stable thermal management. The device exhibits exceptional performance after calibration, implementing Haar-random unitary transformations with an amplitude fidelity of 99.7 %. This work establishes FLW-based integrated photonics as a scalable and robust platform for advancing quantum computing, communication, and sensing technologies.

quant-ph↗

arXiv2022

Understanding holographic error correction via unique algebras and atomic examples

We introduce a fully constructive characterisation of holographic quantum error-correcting codes. That is, given a code and an erasure error we give a recipe to explicitly compute the terms in the RT formula. Using this formalism, we employ quantum circuits to construct a number of examples of holographic codes. Our codes have nontrivial holographic properties and are simpler than existing approaches built on tensor networks. Finally, leveraging a connection between correctable and private systems we prove the uniqueness of the algebra satisfying complementary recovery. The material is presented with the goal of accessibility to researchers in quantum information with no prior background in holography.

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arXiv2020

Statistical Limits of Supervised Quantum Learning

Within the framework of statistical learning theory it is possible to bound the minimum number of samples required by a learner to reach a target accuracy. We show that if the bound on the accuracy is taken into account, quantum machine learning algorithms for supervised learning---for which statistical guarantees are available---cannot achieve polylogarithmic runtimes in the input dimension. We conclude that, when no further assumptions on the problem are made, quantum machine learning algorithms for supervised learning can have at most polynomial speedups over efficient classical algorithms, even in cases where quantum access to the data is naturally available.

quant-ph↗

arXiv2020

Decomposition of Pauli groups via weak central products

For any $m \ge 1$ and odd prime power $\mathtt{q}=\mathtt{p}^m$, for $\mathtt{q}=2$, and for any $n \ge 1$, we show a result of decomposition for Pauli groups $\mathcal{P}_{n,\mathtt{q}}$ in terms of weak central products. This can be used to describe the underlying structure of Pauli groups on $n$ qudits of dimension $\mathtt{q}$ and enables us to identify abelian subgroups of $\mathcal{P}_{n,\mathtt{q}}$. As a consequence of our main results, we show a similar factorisation for the so--called `lifted' Pauli groups, recently introduced by Gottesman and Kuperberg in the context of error-correcting codes in quantum information theory.

math.GR↗

arXiv2020

Approximating Hamiltonian dynamics with the Nyström method

Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation technique whose runtime scales polynomially in the number of qubits and the Frobenius norm of the Hamiltonian. As an immediate application, we show that sample based quantum simulation, a type of evolution where the Hamiltonian is a density matrix, can be efficiently classically simulated under specific structural conditions. Our main technical contribution is a randomized algorithm for approximating Hermitian matrix exponentials. The proof leverages a low-rank, symmetric approximation via the Nyström method. Our results suggest that under strong sampling assumptions there exist classical poly-logarithmic time simulations of quantum computations.

quant-ph↗

arXiv2019

Learning DNFs under product distributions via μ-biased quantum Fourier sampling

We show that DNF formulae can be quantum PAC-learned in polynomial time under product distributions using a quantum example oracle. The best classical algorithm (without access to membership queries) runs in superpolynomial time. Our result extends the work by Bshouty and Jackson (1998) that proved that DNF formulae are efficiently learnable under the uniform distribution using a quantum example oracle. Our proof is based on a new quantum algorithm that efficiently samples the coefficients of a μ-biased Fourier transform.

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arXiv2019

Modelling Non-Markovian Quantum Processes with Recurrent Neural Networks

Quantum systems interacting with an unknown environment are notoriously difficult to model, especially in presence of non-Markovian and non-perturbative effects. Here we introduce a neural network based approach, which has the mathematical simplicity of the Gorini-Kossakowski-Sudarshan-Lindblad master equation, but is able to model non-Markovian effects in different regimes. This is achieved by using recurrent neural networks for defining Lindblad operators that can keep track of memory effects. Building upon this framework, we also introduce a neural network architecture that is able to reproduce the entire quantum evolution, given an initial state. As an application we study how to train these models for quantum process tomography, showing that recurrent neural networks are accurate over different times and regimes.

quant-ph↗

arXiv2018

Learning hard quantum distributions with variational autoencoders

Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical algorithms. Recently, machine learning techniques, in the form of restricted Boltzmann machines, have been proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. Here, we introduce a new representation of states based on variational autoencoders. Variational autoencoders are a type of generative model in the form of a neural network. We probe the power of this representation by encoding probability distributions associated with states from different classes. Our simulations show that deep networks give a better representation for states that are hard to sample from, while providing no benefit for random states. This suggests that the probability distributions associated to hard quantum states might have a compositional structure that can be exploited by layered neural networks. Specifically, we consider the learnability of a class of quantum states introduced by Fefferman and Umans. Such states are provably hard to sample for classical computers, but not for quantum ones, under plausible computational complexity assumptions. The good level of compression achieved for hard states suggests these methods can be suitable for characterising states of the size expected in first generation quantum hardware.

quant-ph↗

arXiv2018

Stabiliser states are efficiently PAC-learnable

The exponential scaling of the wave function is a fundamental property of quantum systems with far reaching implications in our ability to process quantum information. A problem where these are particularly relevant is quantum state tomography. State tomography, whose objective is to obtain a full description of a quantum system, can be analysed in the framework of computational learning theory. In this model, quantum states have been shown to be Probably Approximately Correct (PAC)-learnable with sample complexity linear in the number of qubits. However, it is conjectured that in general quantum states require an exponential amount of computation to be learned. Here, using results from the literature on the efficient classical simulation of quantum systems, we show that stabiliser states are efficiently PAC-learnable. Our results solve an open problem formulated by Aaronson [Proc. R. Soc. A, 2088, (2007)] and propose learning theory as a tool for exploring the power of quantum computation.

quant-ph↗

arXiv2018

Quantum machine learning: a classical perspective

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets are motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed-up classical machine learning algorithms. Here we review the literature in quantum machine learning and discuss perspectives for a mixed readership of classical machine learning and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in machine learning are identified as promising directions for the field. Practical questions, like how to upload classical data into quantum form, will also be addressed.

quant-ph↗

arXiv2017

Experimental learning of quantum states

The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling clearly limits our ability to do tomography to systems with no more than a few qubits and has been used to argue against the universal validity of quantum mechanics itself. However, from a computational learning theory perspective, it can be shown that, in a probabilistic setting, quantum states can be approximately learned using only a linear number of measurements. Here we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be "probably approximately learned" with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales.

quant-ph↗

arXiv2016

Stabilisers as a design tool for new forms of Lechner-Hauke-Zoller Annealer

In a recent paper Lechner, Hauke and Zoller (LHZ) described a means to translate a Hamiltonian of $N$ spin-$\frac{1}{2}$ particles with 'all-to-all' interactions into a larger physical lattice with only on-site energies and local parity constraints. LHZ used this mapping to propose a novel form of quantum annealing. Here we provide a stabiliser-based formulation within which we can describe both this prior approach and a wide variety of variants. Examples include a triangular array supporting all-to-all connectivity, and moreover arrangements requiring only $2N$ or $N\log N$ spins but providing interesting bespoke connectivities. Further examples show that arbitrarily high order logical terms can be efficiently realised, even in a strictly 2D layout. Our stabilisers can correspond to either even-parity constraints, as in the LHZ proposal, or as odd-parity constraints. Considering the latter option applied to the original LHZ layout, we note it may simplify the physical realisation since the required ancillas are only spin-$\frac{1}{2}$ systems (i.e. qubits, rather than qutrits) and moreover the interactions are very simple. We make a preliminary assessment of the impact of this design choices by simulating small (few-qubit) systems; we find some indications that the new variant may maintain a larger minimum energy gap during the annealing process.

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