arXiv subjects

Leonardo Banchi

Publications and source records attributed to Leonardo Banchi.

At least 55 records · Page 3Linked to original sources

arXiv2021

Quantum Noise Sensing by generating Fake Noise

Noisy-Intermediate-Scale-Quantum (NISQ) devices are nowadays starting to become available to the final user, hence potentially allowing to show the quantum speedups predicted by the quantum information theory. However, before implementing any quantum algorithm, it is crucial to have at least a partial or possibly full knowledge on the type and amount of noise affecting the quantum machine. Here, by generalizing quantum generative adversarial learning from quantum states (Q-GANs) to quantum operations/superoperators/channels (here named as SuperQGANs), we propose a very promising framework to characterize noise in a realistic quantum device, even in the case of spatially and temporally correlated noise (memory channels) affecting quantum circuits. The key idea is to learn about the noise by mimicking it in a way that one cannot distinguish between the real (to be sensed) and the fake (generated) one. We find that, when applied to the benchmarking case of Pauli channels, the SuperQGAN protocol is able to learn the associated error rates even in the case of spatially and temporally correlated noise. Moreover, we also show how to employ it for quantum metrology applications. We believe our SuperQGANs pave the way for new hybrid quantum-classical machine learning protocols for a better characterization and control of the current and future unavoidably noisy quantum devices.

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arXiv2021

Optimal quantum spatial search with one-dimensional long-range interactions

Continuous-time quantum walks can be used to solve the spatial search problem, which is an essential component for many quantum algorithms that run quadratically faster than their classical counterpart, in $\mathcal O(\sqrt n)$ time for $n$ entries. However the capability of models found in nature is largely unexplored - e.g., in one dimension only nearest-neighbour Hamiltonians have been considered so far, for which the quadratic speedup does not exist. Here, we prove that optimal spatial search, namely with $\mathcal O(\sqrt n)$ run time and large fidelity, is possible in one-dimensional spin chains with long-range interactions that decay as $1/r^α$ with distance $r$. In particular, near unit fidelity is achieved for $α\approx 1$ and, in the limit $n\to\infty$, we find a continuous transition from a region where optimal spatial search does exist ($α<1.5$) to where it does not ($α>1.5$). Numerically, we show that spatial search is robust to dephasing noise and that, for realistic conditions, $α\lesssim 1.2$ should be sufficient to demonstrate optimal spatial search experimentally with near unit fidelity.

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arXiv2021

Ultimate Limits of Thermal Pattern Recognition

Quantum Channel Discrimination (QCD) presents a fundamental task in quantum information theory, with critical applications in quantum reading, illumination, data-readout and more. The extension to multiple quantum channel discrimination has seen a recent focus to characterise potential quantum advantage associated with quantum enhanced discriminatory protocols. In this paper, we study thermal imaging as an environment localisation task, in which thermal images are modelled as ensembles of Gaussian phase insensitive channels with identical transmissivity, and pixels possess properties according to background (cold) or target (warm) thermal channels. Via the teleportation stretching of adaptive quantum protocols, we derive ultimate limits on the precision of pattern classification of abstract, binary thermal image spaces, and show that quantum enhanced strategies may be used to provide significant quantum advantage over known optimal classical strategies. The environmental conditions and necessary resources for which advantage may be obtained are studied and discussed. We then numerically investigate the use of quantum enhanced statistical classifiers, in which quantum sensors are used in conjunction with machine learning image classification methods. Proving definitive advantage in the low loss regime, this work motivates the use of quantum enhanced sources for short-range thermal imaging and detection techniques for future quantum technologies.

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arXiv2021

Idler-free channel position finding

Entanglement is a powerful tool for quantum sensing, and entangled states can greatly boost the discriminative power of protocols for quantum illumination, quantum metrology, or quantum reading. However, entangled state protocols generally require the retention of an idler state, to which the probes are entangled. Storing a quantum state is difficult and so technological limitations can make protocols requiring quantum memories impracticable. One alternative is idler-free protocols that utilise non-classical sources but do not require any idler states to be stored. Here we apply such a protocol to the task of channel position finding. This involves finding a target channel in a sequence of background channels, and has many applications, including quantum sensing, quantum spectroscopy, and quantum reading.

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arXiv2021

Characterising port-based teleportation as a universal simulator of qubit channels

Port-based teleportation (PBT) is a teleportation protocol that employs a number of Bell pairs and a joint measurement to enact an approximate input-output identity channel. Replacing the Bell pairs with a different multi-qubit resource state changes the enacted channel and allows the PBT protocol to simulate qubit channels beyond the identity. The channel resulting from PBT using a general resource state is consequently of interest. In this work, we fully characterise the Choi matrix of the qubit channel simulated by the PBT protocol in terms of its resource state. We also characterise the PBT protocol itself, by finding a description of the map from the resource state to the Choi matrix of the channel that is simulated by using that resource state. Finally, we exploit our expressions to show improved simulations of the amplitude damping channel by means of PBT with a finite number of ports.

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arXiv2021

Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule

Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters, using feedback from measurements performed on the quantum device. Here we study the problem of estimating the gradient of the function to be optimized directly from quantum measurements, generalizing and simplifying some approaches present in the literature, such as the so-called parameter-shift rule. We derive a mathematically exact formula that provides a stochastic algorithm for estimating the gradient of any multi-qubit parametric quantum evolution, without the introduction of ancillary qubits or the use of Hamiltonian simulation techniques. The gradient measurement is possible when the underlying device can realize all Pauli rotations in the expansion of the Hamiltonian whose coefficients depend on the parameter. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy, for instance due to the coupling between the quantum device and an unknown environment.

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arXiv2020

How to enhance quantum generative adversarial learning of noisy information

Quantum Machine Learning is where nowadays machine learning meets quantum information science. In order to implement this new paradigm for novel quantum technologies, we still need a much deeper understanding of its underlying mechanisms, before proposing new algorithms to feasibly address real problems. In this context, quantum generative adversarial learning is a promising strategy to use quantum devices for quantum estimation or generative machine learning tasks. However, the convergence behaviours of its training process, which is crucial for its practical implementation on quantum processors, have not been investigated in detail yet. Indeed here we show how different training problems may occur during the optimization process, such as the emergence of limit cycles. The latter may remarkably extend the convergence time in the scenario of mixed quantum states playing a crucial role in the already available noisy intermediate scale quantum devices. Then, we propose new strategies to achieve a faster convergence in any operating regime. Our results pave the way for new experimental demonstrations of such hybrid classical-quantum protocols allowing to evaluate the potential advantages over their classical counterparts.

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arXiv2020

Quantum-enhanced barcode decoding and pattern recognition

Quantum hypothesis testing is one of the most fundamental problems in quantum information theory, with crucial implications in areas like quantum sensing, where it has been used to prove quantum advantage in a series of binary photonic protocols, e.g., for target detection or memory cell readout. In this work, we generalize this theoretical model to the multi-partite setting of barcode decoding and pattern recognition. We start by defining a digital image as an array or grid of pixels, each pixel corresponding to an ensemble of quantum channels. Specializing each pixel to a black and white alphabet, we naturally define an optical model of barcode. In this scenario, we show that the use of quantum entangled sources, combined with suitable measurements and data processing, greatly outperforms classical coherent-state strategies for the tasks of barcode data decoding and classification of black and white patterns. Moreover, introducing relevant bounds, we show that the problem of pattern recognition is significantly simpler than barcode decoding, as long as the minimum Hamming distance between images from different classes is large enough. Finally, we theoretically demonstrate the advantage of using quantum sensors for pattern recognition with the nearest neighbor classifier, a supervised learning algorithm, and numerically verify this prediction for handwritten digit classification.

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arXiv2020

Noise-Resilient Variational Hybrid Quantum-Classical Optimization

Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of a Hamiltonian or solving some machine-learning tasks. In these devices noise is unavoidable and impossible to error-correct, yet its role in the optimization process is not well understood, especially from the theoretical viewpoint. Here we consider a minimization problem with respect to a variational state, iteratively obtained via a parametric quantum circuit, taking into account both the role of noise and the stochastic nature of quantum measurement outcomes. We show that the accuracy of the result obtained for a fixed number of iterations is bounded by a quantity related to the Quantum Fisher Information of the variational state. Using this bound, we study the convergence property of the quantum approximate optimization algorithm under realistic noise models, showing the robustness of the algorithm against different noise strengths.

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arXiv2020

Convex optimization of programmable quantum computers

A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any finite-dimensional design of this model is known to be nonuniversal, meaning that the processor cannot perfectly simulate an arbitrary quantum channel over the input. Characterizing how close the simulation is and finding the optimal program state have been open questions for the past 20 years. Here, we answer these questions by showing that the search for the optimal program state is a convex optimization problem that can be solved via semidefinite programming and gradient-based methods commonly employed for machine learning. We apply this general result to different types of processors, from a shallow design based on quantum teleportation, to deeper schemes relying on port-based teleportation and parametric quantum circuits.

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arXiv2020

Training Gaussian Boson Sampling Distributions

Gaussian Boson Sampling (GBS) is a near-term platform for photonic quantum computing. Applications have been developed which rely on directly programming GBS devices, but the ability to train and optimize circuits has been a key missing ingredient for developing new algorithms. In this work, we derive analytical gradient formulas for the GBS distribution, which can be used to train devices using standard methods based on gradient descent. We introduce a parametrization of the distribution that allows the gradient to be estimated by sampling from the same device that is being optimized. In the case of training using a Kullback-Leibler divergence or log-likelihood cost function, we show that gradients can be computed classically, leading to fast training. We illustrate these results with numerical experiments in stochastic optimization and unsupervised learning. As a particular example, we introduce the variational Ising solver, a hybrid algorithm for training GBS devices to sample ground states of a classical Ising model with high probability.

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arXiv2019

Tight bounds for private communication over bosonic Gaussian channels based on teleportation simulation with optimal finite resources

Upper bounds for private communication over quantum channels can be derived by adopting channel simulation, protocol stretching, and relative entropy of entanglement. All these ingredients have led to single-letter upper bounds to the secret key capacity which can be directly computed over suitable resource states. For bosonic Gaussian channels, the tightest upper bounds have been derived by employing teleportation simulation over asymptotic resource states, namely the asymptotic Choi matrices of these channels. In this work, we adopt a different approach. We show that teleporting over an analytical class of finite-energy resource states allows us to closely approximate the ultimate bounds for increasing energy, so as to provide increasingly tight upper bounds to the secret-key capacity of one-mode phase-insensitive Gaussian channels. We then show that an optimization over the same class of resource states can be used to bound the maximum secret key rates that are achievable in a finite number of channel uses.

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arXiv2019

Optimal measurements for quantum fidelity between Gaussian states and its relevance to quantum metrology

Quantum fidelity is a measure to quantify the closeness of two quantum states. In an operational sense, it is defined as the minimal overlap between the probability distributions of measurement outcomes and the minimum is taken over all possible positive-operator valued measures (POVMs). Quantum fidelity has been investigated in various scientific fields, but the identification of associated optimal measurements has often been overlooked despite its great importance for practical purposes. We find here the optimal POVMs for quantum fidelity between multi-mode Gaussian states in a closed analytical form. Our general finding is specified for selected single-mode Gaussian states of particular interest and we identify three types of optimal measurements: a number-resolving detection, a projection on the eigenbasis of operator $\hat{x}\hat{p}+\hat{p}\hat{x}$, and a quadrature detection, each of which is applied to distinct types of single-mode Gaussian states. We also show the equivalence between optimal measurements for quantum fidelity and those for quantum parameter estimation, enabling one to easily find the optimal measurements for displacement, phase, squeezing, and loss parameter estimations using Gaussian states.

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arXiv2019

Multiphoton Tomography with Linear Optics and Photon Counting

Determining an unknown quantum state from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in quantum science. Here we study the number of measurement bases needed to fully characterize an arbitrary multi-mode state containing a definite number of photons, or an arbitrary mixture of such states. We show this task can be achieved using only linear optics and photon counting, which yield a practical though non-universal set of projective measurements. We derive the minimum number of measurement settings required and numerically show that this lower bound is saturated with random linear optics configurations, such as when the corresponding unitary transformation is Haar-random. Furthermore, we show that for N photons, any unitary 2N-design can be used to derive an analytical, though non-optimal, state reconstruction protocol.

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arXiv2019

Molecular Docking with Gaussian Boson Sampling

Gaussian Boson Samplers are photonic quantum devices with the potential to perform tasks that are intractable for classical systems. As with other near-term quantum technologies, an outstanding challenge is to identify specific problems of practical interest where these quantum devices can prove useful. Here we show that Gaussian Boson Samplers can be used to predict molecular docking configurations: the spatial orientations that molecules assume when they bind to larger proteins. Molecular docking is a central problem for pharmaceutical drug design, where docking configurations must be predicted for large numbers of candidate molecules. We develop a vertex-weighted binding interaction graph approach, where the molecular docking problem is reduced to finding the maximum weighted clique in a graph. We show that Gaussian Boson Samplers can be programmed to sample large-weight cliques, i.e., stable docking configurations, with high probability, even in the presence of photon loss. We also describe how outputs from the device can be used to enhance the performance of classical algorithms and increase their success rate of finding the molecular binding pose. To benchmark our approach, we predict the binding mode of a small molecule ligand to the tumor necrosis factor-$α$ converting enzyme, a target linked to immune system diseases and cancer.

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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.

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arXiv2018

Conditional channel simulation

In this work we design a specific simulation tool for quantum channels which is based on the use of a control system. This allows us to simulate an average quantum channel which is expressed in terms of an ensemble of channels, even when these channel-components are not jointly teleportation-covariant. This design is also extended to asymptotic simulations, continuous ensembles, and memory channels. As an application, we derive relative-entropy-of-entanglement upper bounds for private communication over various channels, including non-Gaussian mixtures of bosonic lossy channels. Among other results, we also establish the two-way quantum and private capacity of the so-called `dephrasure' channel.

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arXiv2018

Machine Learning Assisted Many-Body Entanglement Measurement

Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of quantum correlations in many-body systems. However, in an experiment, the only way of measuring entanglement in a generic mixed state is through reconstructive quantum tomography, requiring an exponential number of measurements in the system size. Here, we propose a machine learning assisted scheme to measure the entanglement between arbitrary subsystems of size $N_A$ and $N_B$, with $\mathcal{O}(N_A + N_B)$ measurements, and without any prior knowledge of the state. The method exploits a neural network to learn the unknown, non-linear function relating certain measurable moments and the logarithmic negativity. Our procedure will allow entanglement measurements in a wide variety of systems, including strongly interacting many body systems in both equilibrium and non-equilibrium regimes.

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