Related papers: Geometric aspects of analog quantum search evoluti…

Quantum neural networks are promising for a wide range of applications in the Noisy Intermediate-Scale Quantum era. As such, there is an increasing demand for automatic quantum neural architecture search. We tackle this challenge by…

This paper examines the performance of spatial search where the Grover diffusion operator is replaced by continuous-time quantum walks on a class of interdependent networks. We prove that for a set of optimal quantum walk times and marked…

The problem of finding null geodesics in a stationary Lorentzian spacetime is known to to be equivalent to finding the geodsics of a Randers-Finlser structure. This latter problem is equivalent to finding the motion of charged particles…

We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…

Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schr\"odinger's equation. In the former, the…

We revisit well-known protocols in quantum metrology using collective spins and propose a unifying picture for optimal state preparation based on a semiclassical description in phase space. We show how this framework allows for quantitative…

This comment is to correct the proof of optimality of quantum spatial search for Erd\H{o}s-R\'enyi graphs presented in `Spatial Search by Quantum Walk is Optimal for Almost all Graphs' (https://doi.org/10.1103/PhysRevLett.116.100501). The…

Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…

We consider the quantum dynamical evolution of a fully-connected quantum system subjected to random projective measurements and study the first detection time of an extended subspace of the Hilbert space. Exact analytical expressions are…

High-fidelity quantum gates are an essential prerequisite for large-scale quantum computation. When manipulating practical quantum systems, environmentally and operationally induced errors are inevitable, and thus, in addition to being…

We study the time evolution of a PT-symmetric, non-Hermitian quantum system for which the associated phase space is compact. We focus on the simplest non-trivial example of such a Hamiltonian, which is linear in the angular momentum…

We study spatial search with continuous-time quantum walks on real-world complex networks. We use smaller replicas of the Internet network obtained with a recent geometric renormalization method introduced by Garc\'ia-P\'erez et al., Nat.…

Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum…

We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…

We propose a new variational quantum algorithm, which we refer to as TIMES-ADAPT, that prepares time-evolved states in a low-energy or symmetric subspace of a time-independent Hamiltonian on a quantum computer. Using a specially trained…

Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…

The unitary dynamics of quantum systems can be modeled as a trajectory on a Riemannian manifold. This theoretical framework naturally yields a purely geometric interpretation of computational complexity for quantum algorithms, a notion…

The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system with a complex projective Hilbert space as its phase space, thus equipped with a Riemannian metric in addition to a symplectic structure.…

Universal robust quantum control is essential for performing complex quantum algorithms and efficient quantum error correction protocols. Geometric phase, as a key element with intrinsic fault-tolerant feature, can be well integrated into…

A central feature of quantum mechanics is that a measurement is intrinsically probabilistic. As a result, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system…