Related papers: Clustering in Hilbert space of a quantum optimizat…
Although most quantum systems thermalize locally on short time scales independent of initial conditions, recent developments have shown this is not always the case. Lattice geometry and quantum mechanics can conspire to produce constrained…
Magnetic systems with frustration often have large classical degeneracy. We show that their low-energy physics can be understood as dynamics within the space of classical ground states. We demonstrate this mapping in a family of quantum…
Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. Owing to the intimate…
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…
One-dimensional unitary scattering controlled by non-Hermitian (typically, ${\cal PT}$-symmetric) quantum Hamiltonians $H\neq H^\dagger$ is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
The Quantum Satisfiability problem (QSAT) is the generalization of the canonical NP-complete problem - Boolean Satisfiability. (k,s)-QSAT is the following variant of the problem: given a set of projectors of rank 1, acting non-trivially on…
Classical optimization problems can be solved by adiabatically preparing the ground state of a quantum Hamiltonian that encodes the problem. The performance of this approach is determined by the smallest gap encountered during the…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it allows to derive the ultimate bounds of the achievable precision. We show a relation between the statistical distance…
In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a…
We explore the flow of quantum correlations in cluster states defined on ladder type graphs as measurements are done on qubits located on the nodes of the cluster. We focus on three qubits at the end of the ladder and compute the…
We derive an exact expression for the quantumness of a Hilbert space (defined in quant-ph/0302092), and show that in composite Hilbert spaces the signal states must contain at least some entangled states in order to achieve such a…
Systems reaching thermal equilibrium are ubiquitous. For classical systems, this phenomenon is typically understood statistically through ergodicity in phase space, but translating this to quantum systems is a long-standing problem of…
We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $\alpha = m/n$ stays finite. Using exact but non-rigorous methods…
We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a…
We study the emergence of chaos in multilevel atoms with all-to-all interactions, inspired by cavity QED. Focusing on a 3-level Tavis-Cummings model in a far detuned limit, we detail its deep Hilbert space structure -- i.e. we enumerate all…
The promise of quantum computing lies in harnessing programmable quantum devices for practical applications such as efficient simulation of quantum materials and condensed matter systems. One important task is the simulation of…
In this work, we aim to solve a practical use-case of unsupervised clustering which has applications in predictive maintenance in the energy operations sector using quantum computers. Using only cloud access to quantum computers, we…
Measurement-based quantum computation has revolutionized quantum information processing, and the physical systems with which it can be implemented. One simply needs the ability to prepare a particular state, known as the cluster state, and…