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Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
The experimental realisation of the basic constituents of quantum information processing devices, namely fault-tolerant quantum logic gates, requires conditional quantum dynamics, in which one subsystem undergoes a coherent evolution that…
While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this work, we introduce the Quantum Laplace Transform (QLT),…
We analyze a new scheme for quantum information processing, with superconducting charge qubits coupled through a cavity mode, in which quantum manipulations are insensitive to the state of the cavity. We illustrate how to physically…
The strong coupling between individual optical emitters and propagating surface plasmons confined to a conducting nanotip make this system act as an ideal interface for quantum networks, through which a stationary qubit and a flying photon…
We investigate quantum computation with neutral atoms in optical microtraps where the qubit is implemented in the motional states of the atoms, i.e., in the two lowest vibrational states of each trap. The quantum gate operation is performed…
Quantum computing and quantum communication are remarkable examples of new information processing technologies that arise from the coherent manipulation of spins in nanostructures. We review our theoretical proposal for using electron spins…
If suitable quantum optical interactions were available, transforming optical field mode operators in a nonlinear fashion, the all-photonics platform could be one of the strongest contenders for realizing a quantum computer. Unlike other,…
While most approaches to geometric quantum computation is based on geometric phase in cyclic evolution, noncyclic geometric gates have been proposed to increase further the flexibility. While these gates remove the dynamical phase of the…
Geometric phase is a promising element to induce high-fidelity and robust quantum operations due to its built-in noise-resilience feature. Unfortunately, its practical applications are usually circumscribed by requiring complex interactions…
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic…
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…
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…
The universal quantum computation is obtained when there exists asymmetric anisotropic exchange between electron spins in coupled semiconductor quantum dots. The asymmetric Heisenberg model can be transformed into the isotropic model…
Quantum gates are crucial for processing quantum information, but implementing them in a photonic platform poses unique challenges due to the peculiar way photons propagate and interfere. Here, we examine quantum photonic gates that utilize…
Recently, nonadiabatic geometric quantum computation has been received much attention, due to its fast manipulation and intrinsic error-resilience characteristics. However, to obtain universal geometric quantum control, only limited and…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
We propose a theoretical protocol to implement multiqubit geometric gates (i.e., the M{\o}lmer-S{\o}rensen gate) using photonic cat-state qubits. These cat-state qubits stored in high-$Q$ resonators are promising for hardware-efficient…
Skyrmions in frustrated magnets have the helicity degree of freedom, where two different configurations of Bloch-type skyrmions are energetically favored by the magnetic dipole-dipole interaction and characterized by opposite helicities. A…
This paper introduces an efficient quantum computing method for reducing special graphs in the context of the graph coloring problem. The special graphs considered include both symmetric and non-symmetric graphs where the axis passes…