Related papers: Quantum hardness of learning shallow classical cir…
Learning intersections of halfspaces is a central problem in Computational Learning Theory. Even for just two halfspaces, it remains a major open question whether learning is possible in polynomial time with respect to the margin $\gamma$…
Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…
Although a concept class may be learnt more efficiently using quantum samples as compared with classical samples in certain scenarios, Arunachalam and de Wolf (JMLR, 2018) proved that quantum learners are asymptotically no more efficient…
The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate…
Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions…
We present a lattice-based scheme for homomorphic evaluation of quantum programs and proofs that remains secure against quantum adversaries. Classical homomorphic encryption is lifted to the quantum setting by replacing composite-order…
Recent experiments demonstrated quantum computational advantage in random circuit sampling and Gaussian boson sampling. However, it is unclear whether these experiments can lead to practical applications even after considerable research…
The generation of certifiable randomness is the most fundamental information-theoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion…
While quantum computing can accomplish tasks that are classically intractable, the presence of noise may destroy this advantage in the absence of fault tolerance. In this work, we present a classical algorithm that runs in…
We consider the problem of decoding corrupted error correcting codes with NC$^0[\oplus]$ circuits in the classical and quantum settings. We show that any such classical circuit can correctly recover only a vanishingly small fraction of…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
In the universal blind quantum computation problem, a client wants to make use of a single quantum server to evaluate $C|0\rangle$ where $C$ is an arbitrary quantum circuit while keeping $C$ secret. The client's goal is to use as few…
In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with…
We continue the study of statistical/computational tradeoffs in learning robust classifiers, following the recent work of Bubeck, Lee, Price and Razenshteyn who showed examples of classification tasks where (a) an efficient robust…
The Learning with Errors (LWE) problem underlies modern lattice-based cryptography and is assumed to be quantum hard. Recent results show that estimating entanglement entropy is as hard as LWE, creating tension with quantum gravity and…
This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating…
We show a relation, based on parallel repetition of the Magic Square game, that can be solved, with probability exponentially close to $1$ (worst-case input), by $1D$ (uniform) depth $2$, geometrically-local, noisy (noise below a…
Recently a great deal of attention has focused on quantum computation following a sequence of results suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor's result that factoring and the…
A major concern of deep learning models is the large amount of data that is required to build and train them, much of which is reliant on sensitive and personally identifiable information that is vulnerable to access by third parties. Ideas…
Characterizing a quantum system by learning its state or evolution is a fundamental problem in quantum physics and learning theory with a myriad of applications. Recently, as a new approach to this problem, the task of agnostic state…