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Beyond computer science, quantum complexity theory can potentially revolutionize multiple branches of physics, ranging from quantum many-body systems to quantum field theory. In this paper, we investigate the relationship between the sample…
Sampling from Gibbs states -- states corresponding to system in thermal equilibrium -- has recently been shown to be a task for which quantum computers are expected to achieve super-polynomial speed-up compared to classical computers,…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
Given a Boolean formula $\phi(x)$ in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly $e$ clauses, for all values of $e$. Thus, the density of states is a histogram of the…
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…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be…
Quantum statistical mechanics allows us to extract thermodynamic information from a microscopic description of a many-body system. A key step is the calculation of the density of states, from which the partition function and all…
Adiabatic quantum computation starts from embedding a computational problem into a Hamiltonian whose ground state encodes the solution to the problem. This problem Hamiltonian, $H_{\rm p}$, is normally chosen to be diagonal in the…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
In this work, we consider a fundamental task in quantum many-body physics - finding and learning ground states of quantum Hamiltonians and their properties. Recent works have studied the task of predicting the ground state expectation value…
Computing electronic structures of quantum systems is a key task underpinning many applications in photonics, solid-state physics, and quantum technologies. This task is typically performed through iterative algorithms to find the energy…
We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a…
In a variety of physically relevant settings for learning from quantum data, designing protocols that can computationally efficiently extract information remains largely an art, and there are important cases where we believe this to be…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
We show that the two-dimensional (2D) local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete. We also prove similar results in 2D translation-invariant systems and for the 3D Heisenberg and…
In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a…