arXiv subjects

Leonardo Novo

Publications and source records attributed to Leonardo Novo.

At least 19 recordsLinked to original sources

arXiv2026

Optimal interferometric certification of multi-photon indistinguishability

Multiphoton indistinguishability is a key resource for photonic quantum technologies, yet its characterization typically relies on resource-intensive methods. In this work, we develop two efficient and experimentally friendly protocols to estimate or bound the fidelity $F_{\mathrm{ind}}$ of an $N$-photon state to the closest perfectly indistinguishable state. The first protocol applies to sources preparing separable states, uses a single Fourier interferometer together with photon-number-resolving detection, and yields tight two-sided bounds on $F_{\mathrm{ind}}$. The second protocol combines randomized implementations of linear-optical interferometers with photon counting, enabling direct estimation of $F_{\mathrm{ind}}$ for arbitrary $N$-photon states. Both protocols can certify $F_{\mathrm{ind}} = 1 - \mathcal{O}(ε)$ using provably optimal $\mathcal{O}(1/ε)$ samples, in contrast to previous approaches which required prior assumptions on the model of partial distinguishability. Our methods, based on a multiphoton generalization of the Hong-Ou-Mandel test, bring the rigorous and operationally meaningful certification of multiphoton indistinguishability within reach of current photonic technologies.

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arXiv2026

Efficient classical algorithm for estimating linear statistics of Boson Sampling

Boson Sampling is a prominent candidate for the demonstration of quantum computational advantage but it remains unclear whether a large-scale boson sampler can find useful computational applications. The challenge is that to use a boson sampler to estimate, for example, a physical observable, it is necessary to coarse grain the outcome distribution, owing to the exponential size of the outcome space and the anti-concentration properties of the Boson Sampling distribution. In this work, we analyse the complexity of a specific type of coarse-graining of Boson Sampling distributions based on linear functions of the output photon occupation numbers, which we refer to as linear statistics. We present an efficient classical algorithm for approximating linear statistics of boson samplers within additive error for different kinds of input states, such as Fock states and squeezed states. This allows us to unify in the same framework recent results on efficient quantum-inspired classical algorithms for simulating molecular vibronic spectra, or efficient classical approximations of coarse-grained distributions based on detector binning. Additionally, we show how our algorithm can be used to classically evaluate a proposed one-way function based on Boson Sampling, while other proposals for cryptographic applications escape our classical simulation techniques. We leave open the question of classical simulability of non-linear statistics and connect it to the problem of computing transition amplitudes of linear-optical circuits with one layer of interactions.

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arXiv2026

A unified framework for anomalous boson bunching

Anomalous bunching is a paradoxical quantum interferometric phenomenon in which partially distinguishable photons exhibit a higher probability of bunching into two or more modes than fully indistinguishable photons [Nat. Photonics 17, 702 (2023)]. While this effect is directly linked to violations of certain conjectures on matrix permanents, the mechanism underlying the anomaly is not yet fully understood. Here, we show that boson bunching is governed not by internal indistinguishability alone, but by the total indistinguishability of the postselected output state. Total indistinguishability combines the internal degrees of freedom, such as polarization or arrival time, with the spatial degrees of freedom of their wave functions restricted to the measured output modes of the interferometer. This reformulation preserves the expected connection between boson bunching and total indistinguishability, while clarifying how anomalous bunching can arise. It also reveals several additional facets of the same phenomenon, which are captured within a unified framework. In particular, we exhibit situations in which adding an independent source of distinguishability, either internal or spatial, can enhance multimode or even single-mode bunching probabilities, offering new insights into the subtle role of distinguishability in multiphoton interference.

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arXiv2026

Error Mitigation in Bosonic Systems via Virtual Distillation

Virtual distillation is a promising error-mitigation technique that exploits multiple copies of a noisy quantum state to estimate observables as if measured on a purified state. Although originally introduced in the context of bosonic many-body systems under the name of virtual cooling, its development and applications have largely focused on qubit-based quantum computation. Here, we establish a framework for virtual distillation in bosonic quantum information processing and continuous-variable quantum computing. Building on a diagonalization of cyclic shift operators implemented with passive linear-optical interferometers, we derive experimentally accessible protocols for estimating virtually distilled expectation values of observables relevant to bosonic architectures. In particular, we show how to recover noise-mitigated expectation values of number operators, phase-shift operators, and arbitrary quadratures from multi-copy measurements. For number operators, we further demonstrate the estimation of virtually distilled correlators of arbitrary order through the characteristic function of the photon-number distribution. We apply the framework to states affected by photon loss and dephasing, two of the dominant noise mechanisms in bosonic quantum computation, and quantify the resulting suppression of noise contributions. Our results extend virtual distillation beyond its original setting and provide a practical route toward error-mitigated measurements in bosonic quantum processors using experimentally available linear-optical resources.

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arXiv2026

Limits of multimode bunching for boson sampling validation: anomalous bunching induced by time delays

The multimode bunching probability is expected to provide a useful criterion for validating boson sampling experiments. Its applicability, however, is challenged by the existence of anomalous bunching, namely paradoxical situations in which partially distinguishable particles exhibit a higher bunching probability in two or more modes than perfectly indistinguishable ones. Using multimode bunching as a reliable criterion of genuine indistinguishability, therefore, requires a clear identification of the interferometric configurations in which anomalous bunching can or cannot occur. In particular, since uncontrolled small time delays between single-photon pulses constitute a common source of mode mismatch in current photonic platforms, it is essential to determine whether the resulting photon distinguishability might lead to anomalous bunching. Here, we first identify a broad class of interferometric configurations in which anomalous bunching is rigorously excluded, thereby establishing regimes where multimode bunching-based validation remains valid. Then, we find that, quite unexpectedly, temporal mode mismatch does not belong to this class. We exhibit a specific interferometric setup in which temporal distinguishability enhances multimode bunching, demonstrating that time delays can induce an anomalous behavior. These results help clarify the conditions under which multimode bunching remains a reliable validation tool.

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arXiv2026

Native linear-optical protocol for efficient multivariate trace estimation

The Hong-Ou-Mandel test estimates the overlap between spectral functions characterizing the internal degrees of freedom of two single photons. It can be viewed as a photon-native protocol that implements the well-known quantum SWAP test. Here, we propose a native linear-optical protocol that efficiently estimates multivariate traces of quantum states called Bargmann invariants, which are ubiquitous in quantum mechanics. Our protocol may be understood as a photon-native version of the cycle test in the circuit model, which encompasses many-photon multimode quantum states. We show the protocol is sample-efficient and discuss applications, such as generalized suppression laws, efficient quantum kernel estimation for quantum machine learning, eigenspectrum estimation, and the characterization of multiphoton indistinguishability.

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arXiv2025

An Elementary Characterization of Bargmann Invariants

Bargmann invariants, also known as multivariate traces of quantum states $\operatorname{Tr}(ρ_1 ρ_2 \cdots ρ_n)$, are unitary invariant quantities used to characterize weak values, Kirkwood-Dirac quasiprobabilities, out-of-time-order correlators (OTOCs), and geometric phases. Here we give a complete characterization of the set $B_n$ of complex values that $n$-th order invariants can take, resolving some recently proposed conjectures. We show that $B_n$ is equal to the range of invariants arising from pure states described by Gram matrices of circulant form. We show that both ranges are equal to the $n$-th power of the complex unit $n$-gon, and are therefore convex, which provides a simple geometric intuition. Finally, we show that any Bargmann invariant of order $n$ is realizable using either qubit states, or circulant qutrit states.

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arXiv2025

Optimal distillation of photonic indistinguishability

Imperfect photons' indistinguishability limits the performance of photonic quantum communication and computation . Distillation protocols, inspired by entanglement purification, enhance photons' indistinguishability by leveraging quantum interference in linear optical circuits. In this work, we present a three-photon distillation protocol optimized to achieve the maximum visibility gain, which requires consideration of multi-photon effects such as collective photonic phases. We employ interferometers with the minimum number of modes, optimizing also over the protocol's success probability. The developed protocol is experimentally validated with a platform featuring a demultiplexed quantum dot source interfaced with a programmable eight-mode laser-written integrated photonic processor. We achieve indistinguishability distillation with limited photonic resources and for several multi-photon distinguishability scenarios. This work helps to strengthen the role of distillation as a practical tool for photon-based quantum technologies.

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arXiv2025

Complexity of Gaussian quantum optics with a limited number of non-linearities

It is well known in quantum optics that any process involving the preparation of a multimode gaussian state, followed by a gaussian operation and gaussian measurements, can be efficiently simulated by classical computers. Here, we provide evidence that computing transition amplitudes of Gaussian processes with a single-layer of non-linearities is hard for classical computers. To do so, we show how an efficient algorithm to solve this problem could be used to efficiently approximate outcome probabilities of a Gaussian boson sampling experiment. We also extend this complexity result to the problem of computing transition probabilities of Gaussian processes with two layers of non-linearities, by developing a Hadamard test for continuous-variable systems that may be of independent interest. Given recent experimental developments in the implementation of photon-photon interactions, our results may inspire new schemes showing quantum computational advantage or algorithmic applications of non-linear quantum optical systems realizable in the near-term.

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arXiv2025

A logical implication between two conjectures on matrix permanents

We prove a logical implication between two old conjectures stated by Bapat and Sunder about the permanent of positive semidefinite matrices. Although Drury has recently disproved both conjectures, this logical implication yields a non-trivial link between two seemingly unrelated conditions that a positive semidefinite matrix may fulfill. As a corollary, the classes of matrices that are known to obey the first conjecture are then immediately proven to obey the second one. Conversely, we uncover new counterexamples to the first conjecture by exhibiting a previously unknown type of counterexamples to the second conjecture.

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arXiv2025

Unstructured Adiabatic Quantum Optimization: Optimality with Limitations

In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general statements can be made for adiabatic quantum optimization, as provable results regarding its performance are mostly unknown. Although a lower bound of $Ω(2^{n/2})$ has existed in such a setting for over a decade, a purely adiabatic algorithm with this running time has been absent. We show that adiabatic quantum optimization using an unstructured search approach results in a running time that matches this lower bound (up to a polylogarithmic factor) for a broad class of classical local spin Hamiltonians. For this, it is necessary to bound the spectral gap throughout the adiabatic evolution and compute beforehand the position of the avoided crossing with sufficient precision so as to adapt the adiabatic schedule accordingly. However, we show that the position of the avoided crossing is approximately given by a quantity that depends on the degeneracies and inverse gaps of the problem Hamiltonian and is NP-hard to compute even within a low additive precision. Furthermore, computing it exactly (or nearly exactly) is \#P-hard. Our work indicates a possible limitation of adiabatic quantum optimization algorithms, leaving open the question of whether provable Grover-like speed-ups can be obtained for any optimization problem using this approach.

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arXiv2025

Non-Interactive Oblivious Transfer and One-Time Programs from Noisy Quantum Storage

Few primitives are as intertwined with the foundations of cryptography as Oblivious Transfer (OT). Not surprisingly, with the advent of quantum information processing, a major research path has emerged, aiming to minimize the requirements necessary to achieve OT by leveraging quantum resources, while also exploring the implications for secure computation. Indeed, OT has been the target of renewed focus regarding its newfound quantum possibilities (and impossibilities), both towards its computation and communication complexity. For instance, non-interactive OT, known to be impossible classically, has been strongly pursued. In its most extreme form, non-interactive chosen-input OT (one-shot OT) is equivalent to a One-Time Memory (OTM). OTMs have been proposed as tamper-proof hardware solutions for constructing One-Time Programs -- single-use programs that execute on an arbitrary input without revealing anything about their internal workings. In this work, we leverage quantum resources in the Noisy-Quantum-Storage Model to achieve: 1. Unconditionally-secure two-message non-interactive OT -- the smallest number of messages known to date for unconditionally-secure chosen-input OT. 2. Computationally-secure one-shot OT/OTM, with everlasting security, assuming only one-way functions and sequential functions -- without requiring trusted hardware, QROM, or pre-shared entanglement. 3. One-Time Programs without the need for hardware-based solutions or QROM, by compiling our OTM construction with the [GKR08, GIS+10] compiler.

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arXiv2025

Experimental validation of boson sampling using detector binning

We experimentally demonstrate a testing strategy for boson samplers that is based on efficiently computable expressions for the output photon counting distributions binned over multiple optical modes. We apply this method to validate boson sampling experiments with three photons on a reconfigurable photonic chip, which implements a four-mode interferometer, analyzing 50 Haar-random unitary transformations while tuning photon distinguishability via controlled delays. We show that for high values of indistinguishability, the experiment accurately reproduces the ideal boson sampling binned-mode distributions, which exhibit variations that depend both on the specific interferometer implemented as well as the choice of bin, confirming the usefulness of the method to diagnose imperfections such as partial distinguishability or imperfect chip control. Finally, we analyze the behavior of Haar-averaged binned-mode distributions with partial distinguishability and demonstrate analytically that its variance is proportional to the average of the square of the photons' indistinguishability parameter. These findings highlight the central role of binning in boson sampling validation, offering a scalable and efficient framework for assessing multiphoton interference and experimental performance.

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arXiv2024

Experimental observation of counter-intuitive features of photonic bunching

Bosonic bunching is a term used to describe the well-known tendency of bosons to bunch together, and which differentiates their behaviour from that of fermions or classical particles. However, in some situations perfectly indistinguishable bosons may counter-intuitively bunch less than classical, distinguishable particles. Here we report two such counter-intuitive multiphoton bunching effects observed with three photons in a three-mode balanced photonic Fourier interferometer. In this setting, we show indistinguishable photons actually minimize the probability of bunching. We also show that any non-trivial value of the three-photon collective photonic phase leads to a decreased probability of all photons ending up in the same mode, even as we increase pairwise indistinguishability. Our experiments feature engineering of partial indistinguishability scenarios using both the time and the polarization photonic degrees of freedom, and a polarization-transparent 8-mode tunable interferometer with a quantum-dot source of single photons. Besides the foundational understanding, the observation of these counter-intuitive phenomena open news perspective in devising more efficient ways of routing photons for advantage in metrology and quantum computation.

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arXiv2024

Efficient validation of Boson Sampling from binned photon-number distributions

In order to substantiate claims of quantum computational advantage, it is crucial to develop efficient methods for validating the experimental data. We propose a test of the correct functioning of a boson sampler with single-photon inputs that is based on how photons distribute among partitions of the output modes. Our method is versatile and encompasses previous validation tests based on bunching phenomena, marginal distributions, and even some suppression laws. We show via theoretical arguments and numerical simulations that binned-mode photon number distributions can be used in practical scenarios to efficiently distinguish ideal boson samplers from those affected by realistic imperfections, especially partial distinguishability of the photons.

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arXiv2024

Anomalous bunching of nearly indistinguishable bosons

The commonly assumed straight link between boson bunching and particle indistinguishability in quantum interferometry has recently been challenged [Nat. Photon. 17, 702 (2023)]. Exploiting the connection between quantum optical interferences and matrix permanents, it appeared that bunching effects may arise that exceed the expected limit of fully indistinguishable particles by injecting peculiar polarization states of partially distinguishable photons in some interferometers. Surprisingly, all states giving rise to such an anomalous bunching were found to be far from the state of fully indistinguishable particles, raising the question of whether this intriguing phenomenon might even possibly exist with nearly indistinguishable particles. Here, we answer this question positively by relating it to a mathematical conjecture on matrix permanents dating from 1986, whose physical interpretation had not yet been unveiled. Using a recently found counterexample to this conjecture, we demonstrate that there is an optical interferometer involving 8 photons in 10 modes such that the probability that all photons bunch into two output modes can be enhanced by suitably perturbing the state of all photons having the same polarization. Such a finding reflects still another -- even less expected -- facet of anomalous boson bunching.

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arXiv2024

Advantages of multistage quantum walks over QAOA

Methods to find the solution state for optimization problems encoded into Ising Hamiltonians are a very active area of current research. In this work we compare the quantum approximate optimization algorithm (QAOA) with multi-stage quantum walks (MSQW). Both can be used as variational quantum algorithms, where the control parameters are optimized classically. A fair comparison requires both quantum and classical resources to be assessed. Alternatively, parameters can be chosen heuristically, as we do in this work, providing a simpler setting for comparisons. Using both numerical and analytical methods, we obtain evidence that MSQW outperforms QAOA, using equivalent resources. We also show numerically for random spin glass ground state problems that MSQW performs well even for few stages and heuristic parameters, with no classical optimization.

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arXiv2024

Semi-device independent characterization of multiphoton indistinguishability

Multiphoton indistinguishability is a central resource for quantum enhancement in sensing and computation. Developing and certifying large scale photonic devices requires reliable and accurate characterization of this resource, preferably using methods that are robust against experimental errors. Here, we propose a set of methods for the characterization of multiphoton indistinguishability, based on measurements of bunching and photon number variance. Our methods are robust in a semi-device independent way, in the sense of being effective even when the interferometers are incorrectly dialled. We demonstrate the effectiveness of this approach using an advanced photonic platform comprising a quantum-dot single-photon source and a universal fully-programmable integrated photonic processor. Our results show the practical usefulness of our methods, providing robust certification tools that can be scaled up to larger systems.

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