Related papers: Quantum Adiabatic Evolution for Global Optimizatio…
We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum…
Experimental sciences have come to depend heavily on our ability to organize and interpret high-dimensional datasets. Natural laws, conservation principles, and inter-dependencies among observed variables yield geometric structure, with…
We develop a quantum topological data analysis (QTDA) protocol based on the estimation of the density of states (DOS) of the combinatorial Laplacian. Computing topological features of graphs and simplicial complexes is crucial for analyzing…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
We introduce a class of quantum adiabatic evolutions that we claim may be interpreted as the equivalents of the unitary gates of the quantum gate model. We argue that these gates form a universal set and may therefore be used as building…
We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonians in the same Hilbert space to be transformed into one another. The result is straightforward yet, for example, it lays the foundation to…
A central challenge in the successful implementation of adiabatic quantum algorithms is to maintain the quantum adiabaticity during the entire evolution. However, the energy gap between the ground and the excited states of interacting…
An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The…
Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…
This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically,…
Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution (H(epsilon…
Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand…
The application of quantum computing to data management has attracted growing interest, yet remains constrained by a limited understanding of how the physical behaviour of quantum devices relates to the structure and difficulty of database…
A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. This framework generalizes counterdiabatic driving to open quantum processes. Shortcuts to adiabaticity…
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass…
Nonadiabatic geometric phases are only dependent on the evolution path of a quantum system but independent of the evolution details, and therefore quantum computation based on nonadiabatic geometric phases is robust against control errors.…
In this paper we show that the performance of the quantum adiabatic algorithm is determined by phase transitions in underlying problem in the presence of transverse magnetic field $\Gamma$. We show that the quantum version of random…
Quantum-classical hybrid dynamics is crucial for accurately simulating complex systems where both quantum and classical behaviors need to be considered. However, coupling between classical and quantum degrees of freedom and the exponential…
The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables,…
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably…