相关论文: Algebras and universal quantum computations with h…
Most quantum computing architectures to date natively support multi-valued logic, albeit being typically operated in a binary fashion. Multi-valued, or qudit, quantum processors have access to much richer forms of quantum entanglement,…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…
In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is…
Lie algebroids provide a natural medium to discuss classical systems, however, quantum systems have not been considered. In aim of this paper is to attempt to rectify this situation. Lie algebroids are reviewed and their use in classical…
In order to realize supersymmetric quantum mechanics methods on a four dimensional classical phase-space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal star-product in composing the components of…
We study the Chern-Simons approach to the topological quantum computing. We use quantum $\mathcal{R}$-matrices as universal quantum gates and study the approximations of some one-qubit operations. We make some modifications to the known…
We characterise a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and ancillary qubits. No additional access is…
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0\rangle$ computational basis. In addition, we allow the creation of a one-qubit ancilla in a…
Gauged PT quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan…
A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field…
We study Hamilton circuits of the Cayley graphs of the Weyl groupoids of the generalized quantum groups, or the quantum double of the Nichols algebras of diagonal-type, with finite root systems. We prove the existence of a Hamilton circuit…
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…
Quantum computers are the ideal platform for quantum simulations. Given enough coherent operations and qubits, such machines can be leveraged to simulate strongly correlated materials, where intricate quantum effects give rise to…
The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity, and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for…
The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with…
Quantum computing offers advantages over classical computation, yet the precise features that set the two apart remain unclear. In the standard quantum circuit model, adding a 1-qubit basis-changing gate -- commonly chosen to be the…
A fully optical method to perform any quantum computation with optical waveguide modes is proposed by supplying the prescriptions for a universal set of quantum gates. The proposal for quantum computation is based on implementing a quantum…
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the…
This dissertation explores quantum computation using qudits encoded into large spins, emphasizing the concept of quantum co-design to harness the unique capabilities of physical platforms for enhanced quantum information processing. First,…