Related papers: Quantum hardness of learning shallow classical cir…
We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…
One of the core challenges of research in quantum computing is concerned with the question whether quantum advantages can be found for near-term quantum circuits that have implications for practical applications. Motivated by this mindset,…
We present the first computationally-efficient algorithm for average-case learning of shallow quantum circuits with many-qubit gates. Specifically, we provide a quasi-polynomial time and sample complexity algorithm for learning unknown…
There is currently a large interest in understanding the potential advantages quantum devices can offer for probabilistic modelling. In this work we investigate, within two different oracle models, the probably approximately correct (PAC)…
Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can perform a task which constant-depth classical (i.e., AC$^0$) circuits cannot.…
Recently Brakerski, Christiano, Mahadev, Vazirani and Vidick (FOCS 2018) have shown how to construct a test of quantumness based on the learning with errors (LWE) assumption: a test that can be solved efficiently by a quantum computer but…
We study quantum-classical separations between classical and quantum supervised learning models based on constant depth (i.e., shallow) circuits, in scenarios with and without noises. We construct a classification problem defined by a…
Learning with Errors is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of post-quantum cryptography. In this work, we study the quantum sample complexity of Learning with…
The task of learning a probability distribution from samples is ubiquitous across the natural sciences. The output distributions of local quantum circuits form a particularly interesting class of distributions, of key importance both to…
We show that concrete hardness assumptions about learning or cloning the output state of a random quantum circuit can be used as the foundation for secure quantum cryptography. In particular, under these assumptions we construct secure…
In this work, we study the learnability of quantum circuits in the near term. We demonstrate the natural robustness of quantum statistical queries for learning quantum processes, motivating their use as a theoretical tool for near-term…
We study the complexity of PAC learning halfspaces in the presence of Massart noise. In this problem, we are given i.i.d. labeled examples $(\mathbf{x}, y) \in \mathbb{R}^N \times \{ \pm 1\}$, where the distribution of $\mathbf{x}$ is…
We study the quantum complexity class QNC^0_f of quantum operations implementable exactly by constant-depth polynomial-size quantum circuits with unbounded fan-out gates (called QNC^0_f circuits). Our main result is that the quantum OR…
We initiate the study of multi-party computation for classical functionalities (in the plain model) with security against malicious polynomial-time quantum adversaries. We observe that existing techniques readily give a polynomial-round…
In this work, we show that learning the output distributions of brickwork random quantum circuits is average-case hard in the statistical query model. This learning model is widely used as an abstract computational model for most generic…
Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…
Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework. More specifically we consider the following task: Given samples from some unknown…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…
Despite fundamental interests in learning quantum circuits, the existence of a computationally efficient algorithm for learning shallow quantum circuits remains an open question. Because shallow quantum circuits can generate distributions…
We consider quantum versions of two well-studied classical learning models: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples. We give…