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Quantum learning algorithms imply circuit lower bounds
This result is optimal in both $\gamma$ and $T$, since it is not hard to learn any class $\mathfrak{C}$ of functions in (classical) time $T = 2^n$ (with no error), or in quantum time $T = \mathsf{poly}(n)$ with error at most $1/2 - \Omega(2^{-n/2})$ via Fourier sampling.
StoqMA vs. MA: the power of error reduction
StoqMA characterizes the computational hardness of stoquastic local Hamiltonians, which is a family of Hamiltonians that does not suffer from the sign problem.
Quantum Physics Computational Complexity
Quantum statistical query learning
Additionally, we show that in the private PAC learning setting, the classical and quantum sample complexities are equal, up to constant factors.
Quantum hardness of learning shallow classical circuits
The main technique in this result is to establish a connection between the quantum security of public-key cryptosystems and the learnability of a concept class that consists of decryption functions of the cryptosystem.
Learning with Errors is easy with quantum samples
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.
Quantum Physics Computational Complexity
