There are distributions that can be efficiently generated by a quantum learner with access to quantum samples, but not by a quantum learner with access to only classical samples, making progress to answering this question in the affirmative.
Abstract
Consider two PAC learning algorithms, both having access to quantum computation, but differing in the types of examples they obtain: one is provided with classical samples, while the other is given quantum samples. Are there any learning tasks that can be efficiently performed by the latter, but not by the former? This question, the focus of our work, is surprisingly still open. Our main result is to show that \emph{relative to an oracle}, there are distributions that can be efficiently generated by a quantum learner with access to quantum samples, but not by a quantum learner with access to only classical samples, making progress to answering this question in the affirmative.
The results show that forward-only access cannot provide an asymptotic query-complexity advantage over learning from classical data or quantum data copies in this worst-case setting, and establish the essential role of inverse access in the known realizable-setting improvement.
Natsuto Isogai, Satoshi Yoshida, M. Murao· 0 citations
The notion of meta-complexity of quantum relativization of oracles is introduced, and it is shown that this meta-complexity can be nontrivial by giving a complete classification, within the family of oracle pantheons defined in this paper, of which models can separate the complexity classes.
S. Aaronson, Adam Bouland, Jordan Docter et al.· 0 citations
A key challenge in quantum cryptography is to build quantum one-wayness and pseudorandomness without the use of (quantum computable) one-way functions. So far, this has turned out to be a difficult task, with only a few proposed candidates that are not directly built from one-way functions. Even within these few propos...
It is explained that the efficiently preparable states, device-generated distributions, variationally learned loading, and amortized preparation are required to get advantage from quantum machine learning and close with a checklist for evaluating input-dependent advantage claims.
Correlations that do not admit a deterministic explanation are a central feature of quantum theory and a key resource for quantum information processing. Identifying and certifying such correlations, however, remains a fundamental challenge. In this work, we advance on this problem by considering deterministic correlat...
Nicola d’Alessandro, Oliver Karlsson, C. R. I. Carceller· 1 citation· ⚡1
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