Related papers: Quantum hardness of learning shallow classical cir…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
We show that the Learning with Errors (LWE) problem is classically at least as hard as standard worst-case lattice problems, even with polynomial modulus. Previously this was only known under quantum reductions. Our techniques capture the…
Large-scale quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model…
In this paper, we study the problem of learning an unknown quantum circuit of a certain structure. If the unknown target is an $n$-qubit Clifford circuit, we devise an efficient algorithm to reconstruct its circuit representation by using…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
Estimating the entropy of probability distributions and quantum states is a fundamental task in information processing. Here, we examine the hardness of this task for the case of probability distributions or quantum states produced by…
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…
In a companion paper it was shown that the class of constant-depth determinate k-ary recursive clauses is efficiently learnable. In this paper we present negative results showing that any natural generalization of this class is hard to…
Quantum algorithms have demonstrated promising speed-ups over classical algorithms in the context of computational learning theory - despite the presence of noise. In this work, we give an overview of recent quantum speed-ups, revisit the…
We investigate the relationship between two distinct classical approaches to quantum systems: direct simulation from a classical description and sample-based learning from measurement data. While both tasks ultimately aim to reproduce…
Security in machine learning is fragile when data are exfiltrated or perturbed, yet existing frameworks rarely connect the definition and analysis of the security to learnability. In this work, we develop a theory of secure learning…
Carmosino et al. (2016) demonstrated that natural proofs of circuit lower bounds for $\Lambda$ imply efficient algorithms for learning $\Lambda$-circuits, but only over \textit{the uniform distribution}, with \textit{membership queries},…
The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial…
We consider a new model for the testing of untrusted quantum devices, consisting of a single polynomial-time bounded quantum device interacting with a classical polynomial-time verifier. In this model we propose solutions to two tasks - a…
As quantum computing advances rapidly, guaranteeing the security of cryptographic protocols resistant to quantum attacks is paramount. Some leading candidate cryptosystems use the Learning with Errors (LWE) problem, attractive for its…
We prove the first hardness results against efficient proof search by quantum algorithms. We show that under Learning with Errors (LWE), the standard lattice-based cryptographic assumption, no quantum algorithm can weakly automate…
$\mathsf{QAC}^0$ is the class of constant-depth polynomial-size quantum circuits constructed from arbitrary single-qubit gates and generalized Toffoli gates. It is arguably the smallest natural class of constant-depth quantum computation…
Studies addressing the question "Can a learner complete the learning securely?" have recently been spurred from the standpoints of fundamental theory and potential applications. In the relevant context of this question, we present a…
Understanding the computational complexity of learning efficient classical programs in various learning models has been a fundamental and important question in classical computational learning theory. In this work, we study the…