相关论文: Operator Approach to Complexity : Excited States

The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis,…

We present results for the spectrum of excited mesons obtained from temporal correlations of spatially-extended single-hadron and multi-hadron operators computed in lattice QCD. The stochastic LapH algorithm is implemented on anisotropic,…

We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…

We study the complexity of Gaussian mixed states in a free scalar field theory using the 'purification complexity'. The latter is defined as the lowest value of the circuit complexity, optimized over all possible purifications of a given…

Variational calculations of excited electronic states are carried out by finding saddle points on the surface that describes how the energy of the system varies as a function of the electronic degrees of freedom. This approach has several…

The character of an electronically excited state is one of the most important descriptors employed to discuss the photophysics and photochemistry of transition metal complexes. In transition metal complexes, the interaction between the…

Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors of the local effective Hamiltonian that is constructed from…

We present two techniques that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations. The first technique realizes that to prepare the ground…

We extend the quantum geometric tensor from the state space to the operator level,and investigate its properties like the additivity for factorizable models and the splitting of two kinds contributions for the case of stationary reference…

We define and calculate versions of complexity for free fermionic quantum field theories in 1+1 and 3+1 dimensions, adopting Nielsen's geodesic perspective in the space of circuits. We do this both by discretizing and identifying…

Nielsen's geometric approach offers a powerful framework for quantifying the complexity of unitary transformations. In this formulation, complexity is defined as the length of the minimal geodesic in a suitably constructed geometric space…

We consider the Bose-Hubbard model in two and three spatial dimensions and numerically compute the quantum circuit complexity of the ground state in the Mott insulator and superfluid phases using a mean field approximation with additional…

Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its…

Optimum ground states are constructed in two dimensions by using so called vertex state models. These models are graphical generalizations of the well-known matrix product ground states for spin chains. On the hexagonal lattice we obtain a…

This work considers the open-loop control problem of steering a two level quantum system from an initial to a final condition. The model of this system evolves on the state space SU(2), having two inputs that correspond to the complex…

We study a model of strongly correlated electrons on the square lattice which exhibits charge frustration and quantum critical behavior. The potential is tuned to make the interactions supersymmetric. We establish a rigorous mathematical…

The energies of the excited states of the Nucleon, Delta and Omega are computed in lattice QCD, using two light quarks and one strange quark on anisotropic lattices. The calculations are performed at three values of the pion mass: 392(4),…

Quantum state preparation is a fundamental primitive in quantum algorithms for encoding classical data into quantum amplitudes. We compare the cost of preparing general $n$-qubit states with real amplitudes using two common paradigms:…

Quantum systems with geometrical frustration remain an outstanding challenge for numerical simulations due to the infamous numerical sign problem. Here, we overcome this obstruction via complex path integration in a geometrically frustrated…

It is known that ensembles of interacting oscillators or qubits can exhibit the phenomenon of quantum synchronization. In this work we consider a set of $N$ identical two-state systems that we call ``harmonic qubits'', because the kinetic…