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There is currently a large interest in understanding the potential advantages quantum devices can offer for probabilistic modelling. In this work we investigate, within two different oracle models, the probably approximately correct (PAC)…
Characterizing quantum nonlocality in networks is a challenging, but important problem. Using quantum sources one can achieve distributions which are unattainable classically. A key point in investigations is to decide whether an observed…
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…
Many combinatorial optimization problems admit a maximin fairness variant, where the aim is to find a distribution over possible solutions which maximizes an expected worst-case outcome. However, the support for an optimal distribution may…
We study the problem of learning k-juntas given access to examples drawn from a number of different product distributions. Thus we wish to learn a function f : {-1,1}^n -> {-1,1} that depends on k (unknown) coordinates. While the best known…
Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is…
Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its…
Generative models for quantum data pose significant challenges but hold immense potential in fields such as chemoinformatics and quantum physics. Quantum denoising diffusion probabilistic models (QuDDPMs) enable efficient learning of…
In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to develop efficient algorithms: - whose sample complexity…
Attempts to apply Neural Networks (NN) to a wide range of research problems have been ubiquitous and plentiful in recent literature. Particularly, the use of deep NNs for understanding complex physical and chemical phenomena has opened a…
Probabilistic power flow (PPF) plays a critical role in power system analysis. However, the high computational burden makes it challenging for the practical implementation of PPF. This paper proposes a model-based deep learning approach to…
Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…
At the interface of machine learning and quantum computing, an important question is what distributions can be learned provably with optimal sample complexities and with quantum-accelerated time complexities. In the classical case, Klivans…
Learning a hidden parity function from noisy data, known as learning parity with noise (LPN), is an example of intelligent behavior that aims to generalize a concept based on noisy examples. The solution to LPN immediately leads to decoding…
Quantum data access and quantum processing can make certain classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few in the near future. Thus, reliable schemes that allow…
Bayesian learning of model parameters in neural networks is important in scenarios where estimates with well-calibrated uncertainty are important. In this paper, we propose Bayesian quantized networks (BQNs), quantized neural networks…
In reinforcement learning, the classic objectives of maximizing discounted and finite-horizon cumulative rewards are PAC-learnable: There are algorithms that learn a near-optimal policy with high probability using a finite amount of samples…
We introduce quantum agents trained by episodic, reward-based reinforcement learning to autonomously rediscover several seminal quantum algorithms and protocols. In particular, our agents learn: efficient logarithmic-depth quantum circuits…