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Found 15 papers, 2 papers with code
On the Role of Entanglement and Statistics in Learning
We exhibit a class $C$ that gives an exponential separation between QSQ learning and quantum learning with entangled measurements (even in the presence of noise).
A survey on the complexity of learning quantum states
We survey various recent results that rigorously study the complexity of learning quantum states.
Private learning implies quantum stability
We then show information-theoretic implications between DP learning quantum states in the PAC model, learnability of quantum states in the one-way communication model, online learning of quantum states, quantum stability (which is our conceptual contribution), various combinatorial parameters and give further applications to gentle shadow tomography and noisy quantum state learning.
Positive spectrahedra: Invariance principles and Pseudorandom generators
Our main technical contributions are the following: We first prove an invariance principle for positive spectrahedra via the well-known Lindeberg method.
Computational Complexity Combinatorics
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.
A rigorous and robust quantum speed-up in supervised machine learning
Over the past few years several quantum machine learning algorithms were proposed that promise quantum speed-ups over their classical counterparts.
Sample-efficient learning of quantum many-body systems
In this work, we give the first sample-efficient algorithm for the quantum Hamiltonian learning problem.
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 Boosting
To this end, suppose we have a $\gamma$-weak quantum learner for a Boolean concept class $C$ that takes time $Q(C)$, we introduce a quantum boosting algorithm whose complexity scales as $\sqrt{VC(C)}\cdot poly(Q(C), 1/\gamma);$ thereby achieving a quadratic quantum improvement over classical AdaBoost in terms of $VC(C)$.
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.
Two new results about quantum exact learning
We present two new results about exact learning by quantum computers.
Optimizing quantum optimization algorithms via faster quantum gradient computation
We also show that in a continuous phase-query model, our gradient computation algorithm has optimal query complexity up to poly-logarithmic factors, for a particular class of smooth functions.
Quantum Physics Computational Complexity
A Survey of Quantum Learning Theory
This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers.
Optimal Quantum Sample Complexity of Learning Algorithms
This shows classical and quantum sample complexity are equal up to constant factors.
On the robustness of bucket brigade quantum RAM
We introduce a circuit model for the quantum bucket brigade architecture and argue that quantum error correction for the circuit causes the quantum bucket brigade architecture to lose its primary advantage of a small number of "active" gates, since all components have to be actively error corrected.
Quantum Physics
