arXiv subjects

Jason Pereira

Publications and source records attributed to Jason Pereira.

5 recordsLinked to original sources

arXiv2024

Few measurement shots challenge generalization in learning to classify entanglement

The ability to extract general laws from a few known examples depends on the complexity of the problem and on the amount of training data. In the quantum setting, the learner's generalization performance is further challenged by the destructive nature of quantum measurements that, together with the no-cloning theorem, limits the amount of information that can be extracted from each training sample. In this paper we focus on hybrid quantum learning techniques where classical machine-learning methods are paired with quantum algorithms and show that, in some settings, the uncertainty coming from a few measurement shots can be the dominant source of errors. We identify an instance of this possibly general issue by focusing on the classification of maximally entangled vs. separable states, showing that this toy problem becomes challenging for learners unaware of entanglement theory. Finally, we introduce an estimator based on classical shadows that performs better in the big data, few copy regime. Our results show that the naive application of classical machine-learning methods to the quantum setting is problematic, and that a better theoretical foundation of quantum learning is required.

quant-ph↗

arXiv2021

Generalization in Quantum Machine Learning: a Quantum Information Perspective

Quantum classification and hypothesis testing are two tightly related subjects, the main difference being that the former is data driven: how to assign to quantum states $ρ(x)$ the corresponding class $c$ (or hypothesis) is learnt from examples during training, where $x$ can be either tunable experimental parameters or classical data "embedded" into quantum states. Does the model generalize? This is the main question in any data-driven strategy, namely the ability to predict the correct class even of previously unseen states. Here we establish a link between quantum machine learning classification and quantum hypothesis testing (state and channel discrimination) and then show that the accuracy and generalization capability of quantum classifiers depend on the (Rényi) mutual informations $I(C{:}Q)$ and $I_2(X{:}Q)$ between the quantum state space $Q$ and the classical parameter space $X$ or class space $C$. Based on the above characterization, we then show how different properties of $Q$ affect classification accuracy and generalization, such as the dimension of the Hilbert space, the amount of noise, and the amount of neglected information from $X$ via, e.g., pooling layers. Moreover, we introduce a quantum version of the Information Bottleneck principle that allows us to explore the various tradeoffs between accuracy and generalization. Finally, in order to check our theoretical predictions, we study the classification of the quantum phases of an Ising spin chain, and we propose the Variational Quantum Information Bottleneck (VQIB) method to optimize quantum embeddings of classical data to favor generalization.

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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.

quant-ph↗

arXiv2020

Hacking Alice's box in CV-QKD

Security analyses of quantum cryptographic protocols typically rely on certain conditions; one such condition is that the sender (Alice) and receiver (Bob) have isolated devices inaccessible to third parties. If an eavesdropper (Eve) has a side-channel into one of the devices, then the key rate may be sensibly reduced. In this paper, we consider an attack on a coherent-state protocol, where Eve not only taps the main communication channel but also hacks Alice's device. This is done by introducing a Trojan horse mode with low mean number of photons $\bar{n}$ which is then modulated in a similar way to the signal state. First we show that this strategy can be reduced to an attack without side channels but with higher loss and noise in the main channel. Then we show how the key rate rapidly deteriorates for increasing photons $\bar{n}$, being halved at long distances each time $\bar{n}+1$ doubles. Our work suggests that Alice's device should also be equipped with sensing systems that are able to detect and estimate the total number of incoming and outgoing photons.

quant-ph↗

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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