Phaseonium-Driven Dynamics of Cascaded Systems

Federico Amato
Università degli Studi di Palermo

Authors: F.Amato, C. Pellitteri, G. M. Palma, S. Lorenzo, and R. Lo Franco. The search for strategies to harness the temperature of quantum systems is one of the main goals of quantum thermodynamics. Here we study the dynamics of a system made of a pair of quantum harmonic oscillators, represented by single-mode cavity fields, interacting with a thermally excited beam of phaseonium atoms, which act as ancillas. The two cavities are arranged in a cascade configuration, so that the second cavity interacts with phaseonium atoms only after their interaction with the first one. We provide exact closed dynamics of the first cavity for arbitrarily long interaction times. We highlight the role played by phaseonium, a gas of three-level atoms characterized by internal coherences between levels.Adjusting the parameters of the phaseonium atoms, we can determine the final thermodynamic state reached by the cavities. In this way, the cavities can be heated up as well as cooled down. Also, we show how the second cavity follows a non-Markovian evolution due to interactions with the “used” ancillary atoms that enable information exchange with the first cavity. These results provide useful insights into the use of different types of ancillas for thermodynamic cycles in cavity QED scenarios.

Nonlinear optical protocol for high dimensional Bell states measurement

Luca Bianchi
Università degli Studi di Firenze

Quantum communication promises to enhance the transfer of information between two distant parties leveraging on quantum phenomena such as superposition and entanglement. To this end, a common approach is to encode the information in the states of photonic platforms, which are the best candidates for the realisation of a quantum network [1]. Nevertheless, when one restricts to linear optical quantum communication, one of the main challenges is given by the impossibility to perform a complete Bell state measurement (BSM). Indeed, for two level systems, i.e., qubits, the success probability of perfect discrimination among Bell states is limited to 50% [3], while for qudits it was shown that is impossible to distinguish two arbitrary Bell states without using ancillary photons [4]. One way to circumvent this limitation is to resort to nonlinear optics, where, nevertheless, it is still not clear which is the optimal design to implement high-dimensional BMs. In our work, we propose a novel scheme for deterministic unambiguous high-dimensional BSM, where nonlinear effects are introduced through the use of polarizing media [5]. In particular, by using nonlinear optical effects we perform an unambiguous Bell state discrimination. The success of our protocol is related to the efficiency of a sequence of sum frequency generation processes followed by the measurement of the upconverted photonic degree of freedom that encodes the information. The different outcomes of this measurement are uniquely related to given Bell states, making the protocol deterministic, in contrast to linear optical setups that always rely on the probability of detecting the click patterns associated to unambiguous Bell states. Furthermore, our generalized protocol is versatile, since it is given in an encoding-free manner; this means that we can study its realization through different schemes based on different degrees of freedom of light, such as path or frequency. Our proposed BSM can be implemented experimentally, thus posing the first step towards the realization of a robust and efficient quantum network. [1] Wehner, S., Elkouss, D. & Hanson, R. Quantum internet: A vision for the road ahead. Science 362, eaam9288 (2018). [2] Cozzolino, D., Lio, B. D., Bacco, D. & Oxenlowe, L. K. High-Dimensional Quantum Communication: Benefits, Progress, and Future Challenges. Advanced Quantum Technologies 2, 1900038 (2019). [3] On Bell measurements for teleportation, N. Lütkenhaus, J. Calsamiglia, K-A. Suominen, Phys.Rev. A59 (1999) 3295. [4] Calsamiglia, J. Generalized measurements by linear elements. Physical Review A 65 (2002). [5] Yoon-Ho Kim, Sergei P. Kulik, and Yanhua Shih, Quantum Teleportation of a Polarization State with a Complete Bell State Measurement, Phys. Rev. Lett. 86, 1370 (2001)

**Bose-Fermi mixtures with pairing interactions in two dimensions**

Pietro Bovini
University of Bologna

Ultracold dilute Bose-Fermi mixtures are systems that offer a large degree of tunability and are highly controllable, allowing for the investigation of substantially different conditions and quantum effects in matter. In such a mixture with a pairing interaction, one can study the competition between the formation of fermionic composite molecules and the tendency of bosons towards condensation. One possible application is a recent proposal to obtain a quantum simulator for p-wave superfluidity ([1]). I will present the study of a 2D ultracold Bose-Fermi mixture at zero temperature. We describe the system applying to two dimensions an (imaginary time) T-matrix many-body approach in the ladder approximation. This has been previously used successfully for 3D systems ([2], [3]). Using both analytical and numerical techniques to solve the resulting integrals, we obtain quantities like the chemical potentials and the momentum distributions for both species, and the bosonic condensate fraction. We also study the minimum value of boson-boson repulsion necessary for the mixture to be stable against phase separation or mechanical collapse. To this end, we extend the Bogoliubov approximation to Popov theory, in order to better consider boson-boson interaction. Finally, we focus on single-particle spectral properties, which could be relevant for future experiments performing radio-frequency spectroscopy (like for 3D systems in [4]) on 2D Bose-Fermi mixtures. To calculate these dynamic quantities, we need to reformulate our theory for real time and frequencies (as done in 3D in [5]). Our results for the fermionic spectral weight function, from weak to strong boson-fermion attraction, show the presence of unexpected single-particle excitations at low-momenta, and a new branch at positive frequencies for sufficiently strong couplings. ***References:*** [1]: B. Bazak and D. S. Petrov. Phys. Rev. Lett.,121:263001, Dec 2018. [2]: A. Guidini, G. Bertaina, D. E. Galli, and P. Pieri. Phys. Rev. A, 91:023603, Feb 2015. [3]: M. Duda, X.-Y. Chen, A. Schindewolf, R. Bause, J. von Milczewski, R. Schmidt, I. Bloch, and X.-Y. Luo. Nature Physics, Feb 2023. [4]: I. Fritsche, C. Baroni, E. Dobler, E. Kirilov, B. Huang, R. Grimm, G. M. Bruun, and P. Massignan. Phys. Rev. A, 103:053314, May 2021. [5]: E. Fratini and P. Pieri. Phys. Rev. A, 88:013627, Jul 2013.

Parameter Reduction in Quantum Approximate Optimisation Algorithm for Combinatorial Applications

Evan Camilleri
University of Malta

The Quantum Approximate Optimisation Algorithm (QAOA) is a hybrid variational quantum algorithm designed to produce approximate solutions for combinatorial problems that are difficult to solve using classical algorithms. Herrman et al. introduce multi-angle QAOA (ma-QAOA), where each rotational gate is given a separate classical parameter, thus reducing the quantum circuit depth. Shi et al. show that if an automorphism exists in the graph of the problem, then the number of classical parameters in ma-QAOA can be reduced further. In this study, we find that one can further reduce the number of classical parameters.

Quantum correlated twin beams in cascaded optical parametric oscillator

Salvatore Castrignano
CNR-INO

TBD

Global quantum thermometry based on the optimal biased bound

Shoukang Chang
Xi’an Jiaotong University, China / University of Milan, Italy

Thermometry is a fundamental parameter estimation issue that is crucial in the advancement of natural sciences. One way to solve this issue is the widely used local thermometry theory, which makes use of classical and quantum Cramér-Rao bounds as the benchmarks of thermometry precision. However, such a thermometry theory can only be used for decreasing temperature fluctuations around a known temperature value, hardly tackling the precision thermometry problem over a wide temperature range. For this reason, we derive two basic bounds on thermometry precision based on the global framework, i.e., classical and quantum optimal biased bounds. By implementing the energy measurement on the thermal equilibrium system, the quantum optimal biased bound can be saturated. Further, we show their thermometry performance by taking two specific applications, including a noninteracting spin-1/2 gas and a thermalized quantum harmonic oscillator. Our results indicate that compared with the local thermometry, the global thermometry can provide superior temperature estimation performance. More interestingly, the global error bound can approach its local approximation under asymptotic cases.

Improving BBM92 protocols with high-dimensional encoding

Giovanni Chesi
Università degli Studi di Pavia

High-dimensional encodings can boost the performance of a quantum-key-distribution protocol both in terms of key rates and of tolerance to errors. In this talk, a BBM92-like protocol is presented, where the dimension of the systems can be larger than two and more than two mutually unbiased bases (MUBs) can be employed. Indeed, it is known that, for a system whose dimension d is a prime or the power of a prime, d + 1 MUBs can be found. An analytic expression for the asymptotic key rate with d + 1 MUBs and the effects of using different numbers of MUBs are shown. Then, the non-asymptotic case is considered, where we opimize the finite key rate against collective and coherent attacks for generic dimension of the systems and all possible numbers of MUBs.

Multimode-cavity picture of non-Markovian waveguide QED

Dario Cilluffo
Universität Ulm

We introduce a picture to describe and intrepret waveguide-QED problems in the non-Markovian regime of long photonic retardation times resulting in delayed coherent feedback. The framework is based on an intuitive spatial decomposition of the waveguide into blocks. Among these, the block directly coupled to the atoms embodies an effective lossy multimode cavity leaking into the rest of the waveguide, in turn embodying an effective white-noise bath. The dynamics can be approximated by retaining only a finite number of cavity modes that yet eventually grows with the time delay. This description captures the atomic as well as the field's dynamics, even with many excitations, in both emission and scattering processes. As an application, we show that the recently identified non-Markovian steady states can be understood by retaining very few or even only one cavity modes.

Approximate inverse measurement channel for shallow shadows

Riccardo Cioli
University of Bologna

Classical shadows are a powerful tool to probe many-body quantum systems, consisting in a combination of local randomised measurements and classical post-processing. In a recently-introduced version of the protocol, the randomization step is performed via unitary circuits of variable depth t, defining the so-called shallow shadows. For sufficiently large t, this approach allows one to get around the use of global unitaries to probe global properties such as the fidelity with respect to a target state or the purity. Still, shallow shadows involve the inversion of a many-body map, the measurement channel, which requires non-trivial computations in the post-processing step, thus limiting its applicability when the number of qubits N is large. In this work, we put forward a simple approximate post-processing scheme where the infinite-depth inverse channel is applied to the finite-depth classical shadows, and study its performance for fidelity and purity estimation. The scheme allows for different circuit connectivity, as we illustrate for geometrically local circuits in one and two spatial dimensions, and for geometrically non-local circuits made of two-qubit gates. For the fidelity, we find that the resulting estimator coincides with a known linear cross entropy, achieving an arbitrary small approximation error δ at depth t = O(log(N/δ)) (independent of the circuit connectivity). For the purity, we show that the estimator becomes accurate at a depth O(N ) and O(log N ) for 1D local and non-local circuits, respectively. At those depths, we show that the estimator variance for both the fidelity and purity coincides with that obtained via global random unitaries. We establish these bounds by analytic arguments and extensive numerical computations in several cases of interest. Our work extends the applicability of shallow shadows to large system sizes and general circuit connectivity, and is expected to be practically useful for current experiments in quantum platforms.

Quantum Extreme Learning Machine for classification tasks

Annalisa De Lorenzis
IFAE & UAB & QILIMANJARO, Barcelona

Interest in quantum machine learning is increasingly growing due to the possibility of developing more efficient solutions to problems that are difficult to tackle with classical methods. In this context the research work presented here focuses on the use of quantum machine learning techniques for image classification tasks. We exploit a quantum extreme learning machine by taking advantage of its rich feature map provided by the quantum reservoir substrate. In particular, we present different methods currently used through the whole quantum machine learning pipeline, from the dataset preparation to the final classification task. Among them we explore the impact of Principal Component Analysis and Auto-Encoders for feature engineering, different feature mappings and several Hamiltonians for the time evolution of the quantum reservoir.

Quantum thermometry through a moving probe in a relativistic scenario

Samira Ebrahimi AslMamaghani
University of Palermo

We study the interaction of a two-level moving atom at constant velocity, which acts as a quantum probe (sensor), with a thermal massless scalar field. This interaction allows us to extract the temperature of the field's initial state. We consider two coupling situations between the probe and the field: time derivative (TD) and Unruh-DeWitt (UDW) coupling. These couplings are studied under various temperature ranges, such as low temperature and normal temperature compared to the reference room temperature. By computing Quantum Fisher Information (QFI), we find that the control of the probe velocity plays a key role in achieving optimal accuracy. Additionally, the impacts of the Lamb shift, the sensor's initial state, and environmental control parameters on thermometer sensitivity are thoroughly examined to improve quantum estimation. A practical technique for implementing such quantum thermometry is also proposed. Finally, we demonstrate the advantage of joint parameter estimation over individual estimation when using a high-velocity thermal sensor.

Authors: Samira Ebrahimi Asl Mamaghani, Hossein Rangani Jahromi, Rosario Lo Franco

Entanglement dynamics in photonic quantum memristors

Alberto Ferrara
Unipa (Università degli studi di Palermo)

Memristive systems exhibit dynamics that depend on their past states. This is evidenced by the characteristic hysteresis loops observed in their input-output relationships. Since their first formulations [1] and subsequently their first experimental implementation [2], they manifested great potential as memory units and for their functional resemblance to real synapses [3]. These advantages make them ideal devices in neuromorphic computing for artificial intelligence applications and, more generally, in the simulation of synapses. Moreover, they can be used as building blocks for neural networks for a variety of tasks. Recently, quantum memristor models that retain quantum coherence while still manifesting non-linearities in their dynamics have been proposed and experimentally proven [4]. In this work, we explore and characterize various quantum properties that emerge from a specific model of photonic quantum memristor. We find that a network made of multiple memristors can retain memory on the entanglement of correlated photons traveling through the network at past times. Furthermore, we exploit this memristor-based system to propose a procedure which generates periodic entanglement between photons. We build and run a circuit-model of the memristor on a real quantum computer (IBM-Q), showing that: (i) this system can effectively be used for quantum computing under specific conditions, and that (ii) the results from a genuine real quantum system are in line with our predictions. We compare our results with different quantum memristor models that highlight different properties of this class of systems [6, 7]. [1] Chua, Leon. "Memristor-the missing circuit element." IEEE Transactions on circuit theory 18.5 (1971): 507-519. [2] Strukov, Dmitri B., et al. "The missing memristor found." nature 453.7191 (2008): 80-83. [3] Adhikari, Shyam Prasad, et al. "Memristor bridge synapse-based neural network and its learning." IEEE Transactions on neural networks and learning systems 23.9 (2012): 1426-1435. [4] Spagnolo, Michele, et al. "Experimental photonic quantum memristor." Nature Photonics 16.4 (2022): 318-323. [5] Sanz, Mikel, Lucas Lamata, and Enrique Solano. "Invited article: Quantum memristors in quantum photonics." APL Photonics 3.8 (2018). [6] Kumar, Shubham, et al. "Entangled quantum memristors." Physical Review A 104.6 (2021): 062605. [7] Kumar, S., et al. "Tripartite entanglement in quantum memristors." Physical Review Applied 18.3 (2022): 034004.
Authors: Alberto Ferrara, Rosario Lo Franco

Elusive phase transition in the replica limit of monitored systems

Guido Giachetti
CY Université PAris Cergy

Montiroed systems and Measurement-Induced Phase Transitions have sparked great enthusiasm in the last years. As a case of study, we introduce an exactly solvable model of monitored dynamics in a system of $N$ spin-$1/2$ particles with pairwise all-to-all noisy interactions, where each spin is constantly perturbed by weak measurements of the spin component in a random direction. We make use of the replica trick to account for the Born's rule weighting of the measurement outcomes in the study of purification and other observables, with an exact description in the large-$N$ limit. We find that the nature of the phase transition strongly depends on the number n of replicas used in the calculation, with the appearance of non-perturbative logarithmic corrections that destroy the disentangled/purifying phase in the relevant $n \rightarrow 1$ replica limit. Specifically, we observe that the purification time of a mixed state in the weak measurement phase is always exponentially long in the system size for arbitrary strong measurement rates

Magic of Matrix Product States

Guglielmo Lami
LPTM - Cergy Paris Université

Nonstabilizerness, or magic, is a critical quantum resource that, together with entanglement, characterizes the non-classical complexity of quantum states. Here, we address the problem of quantifying the magic of Matrix Product States (MPS) with bond dimension $\chi$. First, we show how Stabilizer Rényi Entropies (SRE) can be estimated by means of a simple perfect sampling of the MPS over the Pauli string configurations. Second, we consider random Matrix Product States (RMPS). We demonstrate that the $2$-SRE converges to that of Haar random states as $N/\chi^2$, where $N$ is the system size. This indicates that MPS with a modest bond dimension are as magical as generic states. Finally, we introduce the ensemble of Clifford enhanced Matrix Product States ($\mathcal{C}$MPS), built by the action of Clifford unitaries on RMPS. Leveraging our previous result, we show that $\mathcal{C}$MPS can approximate $4$-spherical designs with arbitrary accuracy. Our findings indicate that combining Clifford unitaries with polynomially complex tensor network states can generate highly non-trivial quantum states.

Fidelity optimized quantum surface codes with QGAN and CGAN decoders

Jiaxin Li
University of Palermo

Quantum generative adversarial networks (QGANs) have demonstrated superior performance when applied to image processing, financial analysis and other fields. We propose a quantum topological code decoder based on QGANs, which is applied to optimize fault-tolerant quantum teleportation systems. In this study, we first construct and test the quantum circuit of a QGAN algorithm, establishing a topological code decoder training model. Subsequently, algorithms are designed for the input and output of the topological code eigenvalue dataset, and an efficient decoder is trained. A topological-code-optimized quantum teleportation system with a QGAN decoder is then constructed, exhibiting better fault-tolerance performance compared to the original system. Decoding experiments with a code distance d = 3 and d = 5 show that the error correction success rate of this model reaches 99.887%. The QGAN decoder demonstrates a probability threshold of P = 0.1706, significantly higher than the classical decoder threshold which is approximately P = 0.1099. The quantum teleportation system, optimized for noise resistance under a topological code with d = 3, shows a noticeable fidelity improvement within the non-polarized noise threshold range of P < 0.0607. Differently, under a topological code optimization with d = 5, there is a significant fidelity improvement within the non-polarized noise threshold range of P < 0.0778. The proposed QGAN decoding model, combined with quantum teleportation methods, provides a novel approach for the application of quantum deep learning, whose principles can be applied to other areas of non-uniform noise processing. Finally, we discuss a classical generative adversarial network (CGAN) as a decoder for quantum error correction surface codes. In this CGAN decoder, two neural networks are used as generators and discriminators, respectively. Such a decoder is trained on a dataset of eigenvalues of surface codes that form trivial rings to achieve a higher error correction success rate.

Spectral characterization of a biphoton state through compressive stimulated emission tomography

Mylenne Manrique
Università degli Studi Roma Tre

Time and frequency aspects of light are either carefully controlled or given for granted. In quantum optics, the latter has been more customary, but in recent years considerable interest has been raised on the control and verification of spectral properties. In this talk, we will discuss on some recent progress in how the frequency domain can impact its metrology, by looking at how compressed sensing can be adopted for a full characterisation of photon pairs from down conversion. All these results point in the direction that an exhaustive control of spectral properties of quantum light is a demanding, but not a daunting task. New technological capabilities could be at reach.

Feasibility of quantum communication networks

Luca Mariani
Istituto di Calcolo e Reti ad Alte Prestazioni (ICAR-CNR)

In a world that heavily relies on the secrecy of digital data, the security of the ubiquitous public-key cryptography is undermined by the ongoing development of quantum computers, from both a hardware and software standpoint. On the other side, Quantum Key Distribution (QKD) is claimed to allow for unconditionally secure communication, but its practical implementation is hindered by the severe decay of key rates with distance. In an attempt to mitigate this drawback, one of the most frequently proposed use cases for QKD is the creation of a network on a metropolitan scale, to provide routes of trusted nodes between parties that would otherwise be disconnected. The question driving this work -- which combines fundamental concepts of complex network theory and quantum information theory -- is whether building such a network modelled after the existing Internet fiber infrastructure may represent a viable option. In this perspective, we will present the methods used to generate instances of real-world networks and adapt their topology to the limitations imposed by QKD, and we will discuss the connectivity properties of the resulting systems.

Readout in scalable superconducting quantum processors

Pasquale Mastrovito
Università di Napoli Federico II

Over the past decade, significant advancements in the optimization and engineering of superconducting qubits have driven remarkable improvements in their performance, enabling the continuous growth of quantum processors. However, this expansion is accompanied by a corresponding increase in architecture size and the number of decoherence channels, highlighting the necessity for alternative schemes and platforms that can effectively scale to large-scale architectures. Conventional readout approaches for superconducting qubits, which typically involve heterodyne detection at room temperature, do not scale efficiently with the increasing size and number of connections. In this study, we explore various methods to optimize qubit readout while enhancing the scalability of the entire architecture. Specifically, we analyze the implementation of diverse devices that can be integrated directly at cryogenic temperatures to improve the performance and scalability of superconducting quantum processors. These methods range from signal amplification to enhance the signal-to-noise ratio to novel techniques for mapping the qubit state that differ from state-of-the-art approaches.

Quantum Superresolution for two incoherent sources via multiphoton interference

Salvatore Muratore
university of portsmouth

One of the longstanding problems in a wide range of sensing and imaging applications is the estimation of the positions of two close incoherent sources. Indeed Rayleigh's criterion imposes a minimum separation between the two sources, below which it becomes impossible to distinguish them using classical methods. Recently a solution to this problem has been found by Tsang et al., who showed that the classical limit can be surpassed, achieving superresolution if the centroid of the two sources is known. However, it relies on the use of a multimode waveguide perfectly aligned with the centroid of the sources to decompose the incoming photons in the hermite-Gaussian spatial mode via spatial mode demultiplexing instead of direct imaging. This method is effective only for small distances between the sources. In this work we show a new technique based on multiphton quantum interference enabling superresolution without the need of spatial mode-multiplexing and independently of the value to be estimated of the distance between two incoherent sources. Remarkably, our technique only relies on correlation measurements in the far field which resolve the positions of the interfereing photons without the need of any additional optics. The advantages in experimental feasibility of this technique together with the possibility to monitor any change in the distance between two incoherent sources can pave the way to important applications in microscopy, astronomy and remote sensing.

Bounding Fidelity in Continuously Monitored Quantum Systems

Eoin O'Connor
Università degli Studi di Milano Statale

In the presence of environmental decoherence, achieving unit fidelity in quantum state preparation is often impossible. Monitoring the environment can enhance the maximum achievable fidelity, yet unit fidelity remains elusive in many scenarios. We derive a theoretical bound on the average fidelity in the ideal case of perfect environmental monitoring. The work focuses on preparing Dicke states under collective damping, employing machine learning techniques to identify optimal control protocols. These protocols are then compared against the theoretical bound, offering insights into the limits of fidelity in continuously monitored quantum systems.

Observation of the Quantum Zeno Effect on a NISQ Device

Simone Paganelli
Università dell'Aquila

We study the Quantum Zeno Effect (QZE) on a single qubit on IBM Quantum Experience devices under the effect of multiple measurements. We consider two possible cases: the Rabi evolution and the free decay. In both cases we observe the occurrence of the QZE as an increasing of the survival probability with the number of measurements.

Thermal density functional theory approach to quantum thermodynamics in quenched many-body systems

Antonio palamara
Università della Calabria

The time-independent density functional theory (DFT) [1] and time-dependent density functional theory (TDDFT) [2] stand as two of the most powerful methods to address the study of electronic properties, both ground and excited states, of interacting many-body systems at zero temperature. Mermin extended the proof to finite temperature of the Hohenberg and Kohn theorems [3], enabling the study of electronic properties of many-body systems under conditions where accounting for finite temperature effects is essential. On the other hand, quantum thermodynamics is a growing field of research, fueled by the increasing ability to prepare and control quantum systems on a microscopic scale. Quite recently, it has been been proved, in the context of quantum many-body systems, that interactions between particles may allow for a boost of the efficiency of heat engine [4-5]. However, from a theoretical point of view, addressing the study of a quantum many-body interacting system demands significant effort, often requiring the use of approximations to tackle the complexity of the problem. First steps in applying ideas from DFT to quantum thermodynamics problems have been taken in [6,7,8]. In this context in our work, by using the Mermin-Hohenberg-Kohn theorem, we show that the distribution of quantum work and the irreversible entropy production for a quenched many body system are functionals of the thermal densities. In particular, for the first moment of the two distributions it is possible to provide a simple analytical form for both as functionals of the densities and their derivatives. Through the Hubbard dimer [9], we have verified the correctness and applicability of our results. Specifically, it was possible to suggest how the Kohn-Sham (KS) scheme can be used to extrapolate thermodynamic quantities of interest. Given the advancements in quantum technologies and the interest in developing thermal machines that operate in the quantum regime, our results are important because the KS scheme, combined with the general results obtained, can be a valid method to study the thermodynamic properties of systems whose exact solution becomes extremely challenging. [1] P. Hohenberg and W. Kohn, Phys. Rev. \textbf{136}, B864 (1964). [2] E. Runge and E. K. Gross, Physical review letters 52, 997 (1984). [3] N. D. Mermin, Physical Review 137, A1441 (1965). [4] M. Herrera, J. H. Reina, I. D’Amico, and R. M. Serra, Phys. Rev. Res. 5, 043104 (2023). [5] V Mukherjee, U Divakaran, J. Phys. Condens. Matter 33 454001 (2021) [6] M. Herrera, R. M. Serra, and I. D’Amico, Scientific reports 7, 4655 (2017). [7] AH Skelt, et.al, Journal of Physics A: Mathematical and Theoretical 52, 485304 (2019). [8] K Zawadzki, AH Skelt, I D’Amico, Journal of Physics: Condensed Matter 34, 274002 (2022) [9] S. Murmann, A. Bergschneider, V. M. Klinkhamer, G. Zürn, T. Lompe, and S. Jochim, Phys. Rev. Lett. 114, 080402 (2015

Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group

Sunny Pradhan
University of the Basque Country

Motivated by quantum simulation, we consider Hamiltonians for lattice gauge theories with a finite non-Abelian group. We show that the electric Hamiltonian admits an interpretation as a certain natural Laplacian operator on the finite group. Independently of the chosen Hamiltonian, we provide a full explicit description of the physical, gauge-invariant Hilbert space using spin networks and derive a simple formula for computing its dimension. We illustrate the use of the gauge-invariant basis to diagonalise a dihedral gauge theory on a small periodic lattice.

Quantum dot based platform for multi-photon Quantum Information protocols

Giovanni Rodari
Sapienza Universita' di Roma

Quantum Dots (QDs) have recently emerged as one of the technologies that could enable the photon-based implementation of quantum information protocols of increasing complexity. Photon emitters based on QDs have indeed proven to be almost ideal sources of both single and entangled photons and offer a unique set of advantages: quasi-deterministic operation, high brightness, high single photon purity, and degree of pairwise photon indistinguishability; the latter being an essential element to enable linear-optics based quantum computing schemes. When paired with highly efficient time-to-spatial demultiplexing schemes, QD single-photon sources become promising building blocks for quantum information processing tasks requiring multi-photon resource states. In this contribution, I will give an overview of such technologies and an insight into the ongoing development of a versatile QD-based platform, which can be interfaced with both in-bulk and integrated reconfigurable linear optical interferometers for the experimental implementation of multi-photon quantum information protocols. To showcase the potential of such a hybrid photonic-based approach, I will then report on the use of this platform for the experimental investigation of the indistinguishability properties of multi-photon states, a central resource for quantum enhancement in both sensing and computation protocols [1]. Indeed, in order to develop and certify large-scale photonic devices a robust and accurate protocol to be able to characterize such multi-photon resource states is essential. We propose a set of reliable methods for the characterization of multiphoton indistinguishability, based on the measurement of both photon-bunching properties and photon-number variance at the output of a fully reconfigurable linear optical circuit. In particular, we show that such methods are effective even when the unitary evolution implemented in the interferometer is incorrectly dialed or only partly characterized; that is in a semi-device independent fashion. The results obtained show, on one side, how such semi-device independent methods can be applied in a practical setting and, on the other, provide a useful certification tool that could be scaled up to larger photonic implementations. [1] G. Rodari, L. Novo, R. Albiero, A. Suprano et al., “Semi-device independent characterization of multiphoton indistinguishability”, arXiv preprint, arXiv:2404.18636 (2024)

Entanglement Percolation in Quantum Networks

Alessandro Romancino
Università degli Studi di Palermo

Quantum information shows that entanglement is a crucial resource for applications that go beyond classical capabilities. Thanks to quantum correlations, protocols such as secure quantum cryptography, dense coding, and quantum teleportation are now possible to implement on various scales. However, entanglement at a distance remains a challenging experimental endeavor. To address this issue, entanglement distribution employs different methods like quantum repeaters and entanglement distillation. Another technique, inspired by statistical physics, exploits the features of a quantum network of partially entangled states. This protocol, called entanglement percolation, uses local operations and classical communication (LOCC) and entanglement swapping to create a maximally entangled state between two arbitrary nodes in the network. This problem can be perfectly mapped onto the problem of percolation theory and can be simulated effectively with classical network theory. The classical entanglement percolation (CEP) threshold measures the initial amount of entanglement needed at the beginning to ensure the creation of the desired singlet. This approach has been shown to be, in general, suboptimal, and an improvement called quantum entanglement percolation (QEP) has been developed by first preparing the quantum network using local quantum operations only. Still, it is already known that this protocol is also not optimal. Different aspects of the problem have also been tackled, such as multipartite entanglement and mixed states. A deterministic protocol based on concurrence has also shown promising results. We have generalized the problem by relaxing the original assumption that the initial states are fixed. By using random states and results from extreme value theory we have found out that only the average initial entanglement is important for entanglement distribution purposes and, in general, the QEP protocol can be worse than the CEP protocol in this more realistic scenario.

Coarse-graining discrete quantum dynamics

Antonio Rotundo
Università di Pavia

Quantum simulation is one of the most promising applications of quantum computers. One of its challenges is that most hardware platforms can only implement discrete dynamics, in both space and time, while the dynamics we would like to simulate is typically continuous. Therefore, it is important to understand discrete dynamics and how it effectively reproduces continuous dynamics at long wavelengths. Motivated by these considerations, we introduce a coarse-graining procedure for discrete dynamics. We do this by drawing a parallel with the physics of open quantum systems. The main idea is to split the degrees of freedom between a UV and an IR sector, of which only the latter can be observed. We can then treat the UV part as an unobserved environment that needs to be traced out. The dynamics of the IR degrees of freedom obtained in this way is typically non-unitary, as the original unitary evolution generates entanglement between UV and IR degrees of freedom. Our goal is to find the unitary that best approximates the IR dynamics. This situation is well studied for open quantum systems. In this case, the dynamics, after tracing out the environment, is governed by a quantum master equation that can be split in a Hamiltonian (unitary) and a dissipative (non-unitary) part. The Hamiltonian is usually chosen such that the dissipative term takes Lindblad form. Recently, it has been shown by Hayden and Source that this choice corresponds to minimising the size of the dissipative term according to a specific norm. We adapt this result to discrete dynamics and provide a prescription for finding the unitary that best approximates the IR dynamics. As an example, we apply this prescription to the Dirac quantum walk on the line.

Memory-Augmented Quantum Reservoir Computing

Luca Salatino
CNR-ICAR, University of Calabria

Traditional reservoir computing (RC) is an effective method for predicting chaotic systems due to its use of a high-dimensional dynamic system called the reservoir. This system processes information through a complex network with random weights internally fixed, however the learning phase remains linear, simplifying the training process and enhancing trainability. Quantum reservoir computing (QRC) utilizes quantum systems, whose Hilbert spaces expand exponentially with the number of qubits. The exponential dimension allows QRC to handle vastly more information, offering significant improvements in memory capacity and computational power. The original proposal of QRC by Fujii and Nakajima requires multiple copies of the reservoir system, posing challenges in practical implementation. We develop a simpler hybrid approach that leverages both quantum preprocessing and classical post-processing to solve tasks with high accuracy. Our approach is based on a classical manipulation of the output of the quantum measurements, enhancing the memory of the hybrid QRC. This helps to avoid the need for multiple system replicas while maintaining the benefits of quantum computational enhancements. In order to evaluate our proposed approach, we tested our QRC model with a well-known prediction problem related to the chaotic Mackey-Glass time series. In addition, to further evaluate the generality of this approach, we performed the tests on two different physical systems: a fully connected Ising model in a transverse field and a Rydberg atoms array. By optimizing the QRC model parameters, we obtained 700 predicted steps that is remarkably larger than the value reported in the literature.

Alternative architectures for optical quantum computing

Denis Stanev
GSSI - Gran Sasso Science Institute

Photonic processors are a promising platform candidate for the realization of quantum computers in the regime of quantum advantage. Quantum machine learning represents a promising approach to disclose novel possibilities for quantum information protocols. Thus, recent efforts have been dedicated to determine how to merge, or extend, machine learning approaches in the quantum domain. A relevant example is provided by the Quantum Optical Neural Network (QONN), a class of physical systems that aim to represent the quantum optical version of classical neural networks. We recently have demonstrated the potential of QONNs to achieve a deterministic optical quantum cloner. The employed architecture has been successfully trained to perform deterministic universal quantum cloning on a photonic platform, achieving a single copy fidelity of around 0.8269, meaning that we achieved a fidelity that is very close to that of an optimal universal quantum cloner, which is 5/6 = ~0.833. We have also verified numerically the robustness of this approach to experimental imperfections, and have quantified via numerical simulations how different levels of fabrication errors affect the performances of the trained networks. Even with significant levels of noise, well within the reach of current photonic technology, the QONN was capable of reaching high values of the operation fidelity, proving a significant resistance to noise. This result represents an essential feature for implementations of such an architecture based on NISQ technology. These results thus show the capabilities and flexibility of QONNs, which might prove important for designing even more complex optical circuits [For more details refer to: D. Stanev, N. Spagnolo, F. Sciarrino, Deterministic optimal quantum cloning via a quantum-optical neural network, Physical Review Research 5, 013139 (2023)] . Alternative architectures for quantum computing will also be briefly discussed, such as linear optics with internal feedforward.

Quantum optics with giant atoms in a structured photonic bath

Xuejian Sun
University of Palermo

We present a general framework to tackle quantum optics problems with giant atoms, i.e. quantum emitters each coupled non-locally to a structured photonic bath (typically a lattice) of any dimension. The theory encompasses the calculation and general properties of Green’s functions, atom-photon bound states (BSs), collective master equations and decoherence-free Hamiltonians (DFHs), and is underpinned by a formalism where a giant atom is formally viewed as a normal atom lying at a fictitious location. As a major application, we provide for the first time a general criterion to predict/engineer DFHs of giant atoms, which can be applied both in and out of the photonic continuum and regardless of the structure or dimensionality of the photonic bath. This is used to show novel DFHs in 2D baths such as a square lattice and photonic graphene.

An operational definition of entropy for post-quantum theories

Leonardo Vaglini
University of Pavia

In the last decade, several attempts have been made in order to generalise the notion of entropy within the broader context of Generalised Probabilistic Theories and Operational Probabilistic Theories (OPTs). Such generalisations exploit alternative characterisations of the Shannon's and von Neumann's entropy that refer to state preparations, measurements and their use in a communication scenario. In our work we adopt an alternative approach, and we define the entropy of a state as the optimal rate of a suitable compression task within the OPT framework, which can then be interpreted as the information content of the state which describes the source. We define a wide class of theories, named "digitisable", enjoying the following property: any system can be encoded on a finite array of a fixed type of system that we call operational bit, or o-bit. Classical and quantum theory are digitisable, the o-bit are given by the bit and the qubit respectively. We then consider the analog of the classical i.i.d. scenario, where the source is used many times and the message has the form of a factorised state. The information content is then defined as the smallest compression rate computed in the limit of long messages and vanishing error, namely the least number of o-bits per length of the message needed to reliably store the source. The distortion introduced by the compression protocol is evaluated by means of a function that generalises the entanglement fidelity of quantum theory. We then investigate the properties of the information content and, in particular, its relation with state purity: on the one hand, whenever the information content of a state is vanishing, the latter must be pure. On the other hand, if the parallel composition of systems is not purity-preserving, there must exist a pure state with a strictly positive information content. The latter fact is in contrast with the general understanding that pure states means perfect knowledge about the physical system at hand. Remarkably, it is also true that in a theory where all pure states have vanishing information content, the parallel composition operation must be purity-preserving. A natural question is if one of the aforementioned generalisations of entropy coincides with our definition. Given the operational nature of the notion of information content that we have proposed, this question is equivalent to asking whether one of such entropies plays the role of the Shannon's entropy (or of the von Neumann's one in the quantum setting) in a generalised noiseless coding theorem. We show that the answer to this question is negative by analyzing the behaviour of the information content in a toy-theory, called Bilocal Classical Theory (BCT). The difference with standard classical theory is that the parallel composition law of BCT is not purity-preserving, i.e., the independent preparation of two pure states does not correspond to a pure state of the composite system.

State estimation with quantum extreme learning machines beyond the scrambling time

Marco Vetrano
Università degli Studi di Palermo

Quantum extreme learning machines (QELMs) leverage untrained quantum dynamics to efficiently process information encoded in input quantum states, avoiding the high computational cost of training more complicated nonlinear models. On the other hand, quantum information scrambling (QIS) quantifies how the spread of quantum information into correlations makes it irretrievable from local measurements. Here, we explore the tight relation between QIS and the predictive power of QELMs. In particular, we show efficient state estimation is possible even beyond the scrambling time, for many different types of dynamics --- in fact, we show that in all the cases we studied, the reconstruction efficiency at long interaction times matches the optimal one offered by random global unitary dynamics. These results offer promising venues for robust experimental QELM-based state estimation protocols, as well as providing novel insights into the nature of QIS from a state estimation perspective.

Study on the quantum interference in Space to assess the relativistic effects

Paolo Villoresi
Università di Padova

Quantum interference is the most powerful tool for investigating the quantum states and then it is the candidate for the assessment of the transformation induced by a channel. We here study the effect of the crossing of the gravitation potential on photonics states, addressing the transformations occurring in a ground to satellite proposed experiment and the accessible information. 1. M. Mohageg, L. Mazzarella, C. Anastopoulos, J. Gallicchio, B.-L. Hu, T. Jennewein, S. Johnson, S.-Y. Lin, A. Ling, C. Marquardt, M. Meister, R. Newell, A. Roura, W. P. Schleich, C. Schubert, D. V. Strekalov, G. Val- lone, P. Villoresi, L. Worner, N. Yu, A. Zhai, and P. Kwiat, “The deep space quantum link: prospective funda- mental physics experiments using long-baseline quantum optics,” EPJ Quantum Technology 9, 25 (2022). 2. G. Vallone, D. Dequal, M. Tomasin, F. Vedovato, M. Schiavon, V. Luceri, G. Bianco, and P. Villoresi, “Inter- ference at the Single Photon Level Along Satellite-Ground Channels,” Physical Review Letters 116, 253,601 (2016). 3. D. R. Terno, G. Vallone, F. Vedovato, and P. Villoresi, “Large-scale optical interferometry in general space- times,” Physical Review D 101, 104,052 (2020). 4. D. R. Terno, F. Vedovato, M. Schiavon, A. R. H. Smith, P. Magnani, G. Vallone, and P. Villoresi, “Proposal for an optical interferometric measurement of the gravitational redshift with satellite systems,” Physical Review D 108, 084,063 (2023).

Magic and Entanglement Spectrum Anti-flatness in the 1D Quantum XY model

Michele Viscardi
Università degli studi di Napoli "Federico II"

A rigorous understanding of the relationship between non-stabilizerness and entanglement is essential for uncovering the origins of quantum complexity. In this work, we explore this relationship through an analysis of the ground state of the transverse field XY model. Specifically, we focus on two key quantities: the Stabilizer Rényi Entropy (SRE), a measure of how far a quantum state is from being a stabilizer, and the anti-flatness of the entanglement spectrum, which captures the structure of the entanglement spectrum and quantifies its deviation from a uniform distribution. By exploring the behavior of these quantities across different phases of the XY model, we provide new insights into the interplay between non-stabilizerness and entanglement, revealing how they evolve and influence the ground state complexity.