Related papers: Testing and learning structured quantum Hamiltonia…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
We give a $2^{\tilde{O}(\sqrt{n}/\epsilon)}$-time algorithm for properly learning monotone Boolean functions under the uniform distribution over $\{0,1\}^n$. Our algorithm is robust to adversarial label noise and has a running time nearly…
We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic…
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less…
Efficiently characterizing large quantum states and processes is a central yet notoriously challenging task in quantum information science, as conventional tomography methods typically require resources that grow exponentially with system…
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm…
As quantum simulators are scaled up to larger system sizes and lower noise rates, non-Markovian noise channels are expected to become dominant. While provably efficient protocols for Markovian models of quantum simulators, either closed…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
Estimating parameters of quantum systems is usually done by performing a sequence of predetermined experiments and post-processing the resulting data. It is known that online design, where the choice of the next experiment is based on the…
Hamiltonian neural networks (HNNs) represent a promising class of physics-informed deep learning methods that utilize Hamiltonian theory as foundational knowledge within neural networks. However, their direct application to engineering…
Modern quantum devices require high-precision Hamiltonian dynamics, but environmental noise can cause calibrated Hamiltonian parameters to drift over time, necessitating expensive recalibration. Detecting when recalibration is needed is…
Extracting information efficiently from quantum systems is a major component of quantum information processing tasks. Randomized measurements, or classical shadows, enable predicting many properties of arbitrary quantum states using few…
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…
Discrete and continuous variables oftentimes require different treatments in many learning tasks. Identifying the Hamiltonian governing the evolution of a quantum system is a fundamental task in quantum learning theory. While previous works…
In this work, we show, for the well-studied problem of learning parity under noise, where a learner tries to learn $x=(x_1,\ldots,x_n) \in \{0,1\}^n$ from a stream of random linear equations over $\mathrm{F}_2$ that are correct with…
Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an…
We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement nor classical communication. We characterize notions of simulation, and proceed to focus on…
A fundamental problem in quantum many-body physics is that of finding ground states of local Hamiltonians. A number of recent works gave provably efficient machine learning (ML) algorithms for learning ground states. Specifically, [Huang et…
We present an algorithm for sparse Hamiltonian simulation whose complexity is optimal (up to log factors) as a function of all parameters of interest. Previous algorithms had optimal or near-optimal scaling in some parameters at the cost of…
Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of…