Related papers: Quantum Glassiness From Efficient Learning

The theory of controlled quantum open systems describes quantum systems interacting with quantum environments and influenced by external forces varying according to given algorithms. It is aimed, for instance, to model quantum devices which…

For infinite-horizon average-cost criterion problems, there exist relatively few rigorous approximation and reinforcement learning results. In this paper, for Markov Decision Processes (MDPs) with standard Borel spaces, (i) we first provide…

We provide an adaptive learning algorithm for tomography of general quantum states. Our proposal is based on the simultaneous perturbation stochastic approximation algorithm and is applicable on mixed qudit states. The salient features of…

Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…

We introduce the Hidden Polynomial Function Graph Problem as a natural generalization of an abelian Hidden Subgroup Problem (HSP) where the subgroups and their cosets correspond to graphs of linear functions over the finite field F_p. For…

Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a…

Determining the ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and combinatorial optimization, yet it is often classically intractable due to the exponential growth of Hilbert space with system size.…

Quantum computing technology is advancing rapidly. Yet, even accounting for these trends, a quantum leap would be needed for quantum computers to meaningfully impact deep learning over the coming decade or two. We arrive at this conclusion…

We prove classical simulation hardness, under the generalized $\mathsf{P}\neq\mathsf{NP}$ conjecture, for quantum circuit families with applications in near-term chemical ground state estimation. The proof exploits a connection to particle…

By using a previously established exact characterization of the ground state of random potential systems in the thermodynamic limit, we determine the ground and first excited energy levels of quantum random energy models, discrete and…

The states accepted by a quantum circuit are known as the witnesses for the quantum circuit's satisfiability. The assumption BQP does not equal QMA implies that no efficient algorithm exists for constructing a witness for a quantum circuit…

Learning problems involving quantum data are natural candidates for demonstrating an advantage in quantum machine learning. Recent results indicate that, for certain tasks and under noiseless conditions, coherent processing of quantum data…

The preparation and computation of many properties of quantum Gibbs states is essential for algorithms such as quantum semidefinite programming and quantum Boltzmann machines. We propose a quantum algorithm that can predict $M$ linear…

In a quantum (inhomogeneous) Markov process $\rho_1:=\Gamma_1(\rho)$, $\rho_2:=\Gamma_1(\rho_1)$, ..., where $\Gamma_i$ are CPTP maps and $\rho$ is the initial state, the the state of the system is either oscillatory or convergent to a…

Classifying phase transitions is a fundamental and complex challenge in condensed matter physics. This work proposes a framework for identifying quantum phase transitions by combining classical shadows with unsupervised machine learning. We…

We experimentally demonstrate that a hybrid quantum-classical algorithm can outperform purely classical, off-the-shelf selected configuration interaction methods. First, we construct a class of local Hamiltonian problems with sparse ground…

Sensitivity to noise makes most of the current quantum computing schemes prone to error and nonscalable, allowing only for small proof-of-principle devices. Topologically-protected quantum computing aims at solving this problem by encoding…

We prove an algorithmic hardness result for finding low-energy states in the so-called \emph{continuous random energy model (CREM)}, introduced by Bovier and Kurkova in 2004 as an extension of Derrida's \emph{generalized random energy…

We study the power of quantum memory for learning properties of quantum systems and dynamics, which is of great importance in physics and chemistry. Many state-of-the-art learning algorithms require access to an additional external quantum…

Apprenticeship learning is a method commonly used to train artificial intelligence systems to perform tasks that are challenging to specify directly using traditional methods. Based on the work of Abbeel and Ng (ICML'04), we present a…