Related papers: Learning junta distributions, quantum junta states…

Cat states are an important resource for fault-tolerant quantum computing, where they serve as building blocks for a variety of fault-tolerant primitives. Consequently, the ability to prepare high-quality cat states at large fault distances…

We consider the problem of learning a discrete distribution in the presence of an $\epsilon$ fraction of malicious data sources. Specifically, we consider the setting where there is some underlying distribution, $p$, and each data source…

Given a dataset of input states, measurements, and probabilities, is it possible to efficiently predict the measurement probabilities associated with a quantum circuit? Recent work of Caro and Datta (2020) studied the problem of PAC…

A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of state-of-the-art classical computers,…

It has been known for almost 30 years that quantum circuits with interspersed depolarizing noise converge to the uniform distribution at $\omega(\log n)$ depth, where $n$ is the number of qubits, making them classically simulable. We show…

When experimentally learning the action of a continuous variable quantum process by probing it with inputs, there will often be some restriction on the input states used. One experimentally simple way to probe a quantum channel is using low…

Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups…

Recent work has shown that $n$-qubit quantum states output by circuits with at most $t$ single-qubit non-Clifford gates can be learned to trace distance $\epsilon$ using $\mathsf{poly}(n,2^t,1/\epsilon)$ time and samples. All prior…

Modeling joint probability distributions is an important task in a wide variety of fields. One popular technique for this employs a family of multivariate distributions with uniform marginals called copulas. While the theory of modeling…

Preparing large-qubit Dicke states is of broad interest in quantum computing and quantum metrology. However, the number of qubits available on a single quantum processing unit (QPU) is limited -- motivating the distributed preparation of…

We give an algorithm for learning $O(\log n)$ juntas in polynomial-time with respect to Markov Random Fields (MRFs) in a smoothed analysis framework where only the external field has been randomly perturbed. This is a broad generalization…

We propose several algorithms for learning unitary operators from quantum statistical queries with respect to their Choi-Jamiolkowski state. Quantum statistical queries capture the capabilities of a learner with limited quantum resources,…

Quantum circuits for loading probability distributions into quantum states are essential subroutines in quantum algorithms used in physics, finance engineering, and machine learning. The ability to implement these with high accuracy in…

We give the first super-polynomial (in fact, mildly exponential) lower bounds for tolerant testing (equivalently, distance estimation) of monotonicity, unateness, and juntas with a constant separation between the "yes" and "no" cases.…

Quantum state transfer protocols are a major toolkit in many quantum information processing tasks, from quantum key distribution to quantum computation. To assess performance of a such a protocol, one often relies on the average fidelity…

The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature…

Following [OW16], we continue our analysis of: (1) "Quantum tomography", i.e., learning a quantum state, i.e., the quantum generalization of learning a discrete probability distribution; (2) The distribution of Young diagrams output by the…

We examine the complexity of learning the distributions produced by finite-state quantum sources. We show how prior techniques for learning hidden Markov models can be adapted to the quantum generator model to find that the analogous state…

We prove a $k^{-\Omega(\log(\varepsilon_2 - \varepsilon_1))}$ lower bound for adaptively testing whether a Boolean function is $\varepsilon_1$-close to or $\varepsilon_2$-far from $k$-juntas. Our results provide the first superpolynomial…

Adaptive quantum circuits, leveraging measurements and classical feedback, significantly expand the landscape of realizable quantum states compared to their non-adaptive counterparts, enabling the preparation of long-range entangled states…