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Researcher profile

M. Cerezo

M. Cerezo contributes to research discovery and scholarly infrastructure.

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quant-phMachine Learningphysics.data-an

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Published work

12 published item(s)

preprint2026arXiv

Provable and scalable quantum Gaussian processes for quantum learning

Despite rapid recent advances in quantum machine learning, the field is in many ways stuck. Existing approaches can exhibit serious limitations, and we still lack learning frameworks that are simple, interpretable, scalable, and naturally suited to quantum data. To address this, here we introduce quantum Gaussian processes, a Bayesian framework for learning from quantum systems through priors over unknown quantum transformations. We show that, under suitable conditions, unitary quantum stochastic processes define Gaussian processes, thereby enabling regression, classification, and Bayesian optimization directly on quantum data. The key ingredient in this framework is sufficient knowledge of a quantum process's structure and symmetries to define an informative prior through its corresponding quantum kernel, effectively injecting a strong, physics-informed inductive bias into the learning model. We then prove that matchgate, or free-fermionic, evolutions give rise to provable and scalable quantum Gaussian processes, providing the first family in our framework where the unknown unitary acts non-trivially on all qubits. Finally, we demonstrate accurate long-range extrapolation, phase-diagram learning in many-body systems, and sample-efficient Bayesian optimization in a quantum sensing task. Our results identify quantum Gaussian processes as a promising route toward simpler and more structured forms of quantum learning.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Computable and operationally meaningful multipartite entanglement measures

Multipartite entanglement is an essential resource for quantum communication, quantum computing, quantum sensing, and quantum networks. The utility of a quantum state, $|ψ\rangle$, for these applications is often directly related to the degree or type of entanglement present in $|ψ\rangle$. Therefore, efficiently quantifying and characterizing multipartite entanglement is of paramount importance. In this work, we introduce a family of multipartite entanglement measures, called Concentratable Entanglements. Several well-known entanglement measures are recovered as special cases of our family of measures, and hence we provide a general framework for quantifying multipartite entanglement. We prove that the entire family does not increase, on average, under Local Operations and Classical Communications. We also provide an operational meaning for these measures in terms of probabilistic concentration of entanglement into Bell pairs. Finally, we show that these quantities can be efficiently estimated on a quantum computer by implementing a parallelized SWAP test, opening up a research direction for measuring multipartite entanglement on quantum devices.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Connecting ansatz expressibility to gradient magnitudes and barren plateaus

Parameterized quantum circuits serve as ansätze for solving variational problems and provide a flexible paradigm for programming near-term quantum computers. Ideally, such ansätze should be highly expressive so that a close approximation of the desired solution can be accessed. On the other hand, the ansatz must also have sufficiently large gradients to allow for training. Here, we derive a fundamental relationship between these two essential properties: expressibility and trainability. This is done by extending the well established barren plateau phenomenon, which holds for ansätze that form exact 2-designs, to arbitrary ansätze. Specifically, we calculate the variance in the cost gradient in terms of the expressibility of the ansatz, as measured by its distance from being a 2-design. Our resulting bounds indicate that highly expressive ansätze exhibit flatter cost landscapes and therefore will be harder to train. Furthermore, we provide numerics illustrating the effect of expressiblity on gradient scalings, and we discuss the implications for designing strategies to avoid barren plateaus.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Equivalence of quantum barren plateaus to cost concentration and narrow gorges

Optimizing parameterized quantum circuits (PQCs) is the leading approach to make use of near-term quantum computers. However, very little is known about the cost function landscape for PQCs, which hinders progress towards quantum-aware optimizers. In this work, we investigate the connection between three different landscape features that have been observed for PQCs: (1) exponentially vanishing gradients (called barren plateaus), (2) exponential cost concentration about the mean, and (3) the exponential narrowness of minina (called narrow gorges). We analytically prove that these three phenomena occur together, i.e., when one occurs then so do the other two. A key implication of this result is that one can numerically diagnose barren plateaus via cost differences rather than via the computationally more expensive gradients. More broadly, our work shows that quantum mechanics rules out certain cost landscapes (which otherwise would be mathematically possible), and hence our results are interesting from a quantum foundations perspective.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Generalization in quantum machine learning from few training data

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number $N$ of training data points. We show that the generalization error of a quantum machine learning model with $T$ trainable gates scales at worst as $\sqrt{T/N}$. When only $K \ll T$ gates have undergone substantial change in the optimization process, we prove that the generalization error improves to $\sqrt{K / N}$. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Non-trivial symmetries in quantum landscapes and their resilience to quantum noise

Very little is known about the cost landscape for parametrized Quantum Circuits (PQCs). Nevertheless, PQCs are employed in Quantum Neural Networks and Variational Quantum Algorithms, which may allow for near-term quantum advantage. Such applications require good optimizers to train PQCs. Recent works have focused on quantum-aware optimizers specifically tailored for PQCs. However, ignorance of the cost landscape could hinder progress towards such optimizers. In this work, we analytically prove two results for PQCs: (1) We find an exponentially large symmetry in PQCs, yielding an exponentially large degeneracy of the minima in the cost landscape. Alternatively, this can be cast as an exponential reduction in the volume of relevant hyperparameter space. (2) We study the resilience of the symmetries under noise, and show that while it is conserved under unital noise, non-unital channels can break these symmetries and lift the degeneracy of minima, leading to multiple new local minima. Based on these results, we introduce an optimization method called Symmetry-based Minima Hopping (SYMH), which exploits the underlying symmetries in PQCs. Our numerical simulations show that SYMH improves the overall optimizer performance in the presence of non-unital noise at a level comparable to current hardware. Overall, this work derives large-scale circuit symmetries from local gate transformations, and uses them to construct a noise-aware optimization method.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets

The no-free-lunch (NFL) theorem is a celebrated result in learning theory that limits one's ability to learn a function with a training data set. With the recent rise of quantum machine learning, it is natural to ask whether there is a quantum analog of the NFL theorem, which would restrict a quantum computer's ability to learn a unitary process (the quantum analog of a function) with quantum training data. However, in the quantum setting, the training data can possess entanglement, a strong correlation with no classical analog. In this work, we show that entangled data sets lead to an apparent violation of the (classical) NFL theorem. This motivates a reformulation that accounts for the degree of entanglement in the training set. As our main result, we prove a quantum NFL theorem whereby the fundamental limit on the learnability of a unitary is reduced by entanglement. We employ Rigetti's quantum computer to test both the classical and quantum NFL theorems. Our work establishes that entanglement is a commodity in quantum machine learning.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Trainability of Dissipative Perceptron-Based Quantum Neural Networks

Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we called dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer's output. We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits. Moreover, we provide quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths, and show that trainability is not always guaranteed.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Variational Quantum Algorithm for Estimating the Quantum Fisher Information

The Quantum Fisher information (QFI) quantifies the ultimate precision of estimating a parameter from a quantum state, and can be regarded as a reliability measure of a quantum system as a quantum sensor. However, estimation of the QFI for a mixed state is in general a computationally demanding task. In this work we present a variational quantum algorithm called Variational Quantum Fisher Information Estimation (VQFIE) to address this task. By estimating lower and upper bounds on the QFI, based on bounding the fidelity, VQFIE outputs a range in which the actual QFI lies. This result can then be used to variationally prepare the state that maximizes the QFI, for the application of quantum sensing. In contrast to previous approaches, VQFIE does not require knowledge of the explicit form of the sensor dynamics. We simulate the algorithm for a magnetometry setup and demonstrate the tightening of our bounds as the state purity increases. For this example, we compare our bounds to literature bounds and show that our bounds are tighter.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Noise Resilience of Variational Quantum Compiling

Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary $U$ is compiled into a short-depth gate sequence $V$. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence $V$ (i.e., the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation

Dynamical quantum simulation may be one of the first applications to see quantum advantage. However, the circuit depth of standard Trotterization methods can rapidly exceed the coherence time of noisy quantum computers. This has led to recent proposals for variational approaches to dynamical simulation. In this work, we aim to make variational dynamical simulation even more practical and near-term. We propose a new algorithm called Variational Hamiltonian Diagonalization (VHD), which approximately transforms a given Hamiltonian into a diagonal form that can be easily exponentiated. VHD allows for fast forwarding, i.e., simulation beyond the coherence time of the quantum computer with a fixed-depth quantum circuit. It also removes Trotterization error and allows simulation of the entire Hilbert space. We prove an operational meaning for the VHD cost function in terms of the average simulation fidelity. Moreover, we prove that the VHD cost function does not exhibit a shallow-depth barren plateau, i.e., its gradient does not vanish exponentially. Our proof relies on locality of the Hamiltonian, and hence we connect locality to trainability. Our numerical simulations verify that VHD can be used for fast-forwarding dynamics.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Variational Quantum Fidelity Estimation

Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity $F(ρ,σ)$ based on the "truncated fidelity" $F(ρ_m, σ)$, which is evaluated for a state $ρ_m$ obtained by projecting $ρ$ onto its $m$-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with $m$. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize $ρ$, (2) compute matrix elements of $σ$ in the eigenbasis of $ρ$, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where $σ$ is arbitrary and $ρ$ is low rank, which we call low-rank fidelity estimation, and we prove that a classical algorithm cannot efficiently solve this problem. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.

0 citations0 reviewsNo code linkedOpen access