Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

Search results for: qudit

3 A Novel Way to Create Qudit Quantum Error Correction Codes

Authors: Arun Moorthy

Abstract:

Quantum computing promises to provide algorithmic speedups for a number of tasks; however, similar to classical computing, effective error-correcting codes are needed. Current quantum computers require costly equipment to control each particle, so having fewer particles to control is ideal. Although traditional quantum computers are built using qubits (2-level systems), qudits (more than 2-levels) are appealing since they can have an equivalent computational space using fewer particles, meaning fewer particles need to be controlled. Currently, qudit quantum error-correction codes are available for different level qudit systems; however, these codes have sometimes overly specific constraints. When building a qudit system, it is important for researchers to have access to many codes to satisfy their requirements. This project addresses two methods to increase the number of quantum error correcting codes available to researchers. The first method is generating new codes for a given set of parameters. The second method is generating new error-correction codes by using existing codes as a starting point to generate codes for another level (i.e., a 5-level system code on a 2-level system). So, this project builds a website that researchers can use to generate new error-correction codes or codes based on existing codes.

Keywords: qudit, error correction, quantum, qubit

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2 Quantum Computing with Qudits on a Graph

Authors: Aleksey Fedorov

Abstract:

Building a scalable platform for quantum computing remains one of the most challenging tasks in quantum science and technologies. However, the implementation of most important quantum operations with qubits (quantum analogues of classical bits), such as multiqubit Toffoli gate, requires either a polynomial number of operation or a linear number of operations with the use of ancilla qubits. Therefore, the reduction of the number of operations in the presence of scalability is a crucial goal in quantum information processing. One of the most elegant ideas in this direction is to use qudits (multilevel systems) instead of qubits and rely on additional levels of qudits instead of ancillas. Although some of the already obtained results demonstrate a reduction of the number of operation, they suffer from high complexity and/or of the absence of scalability. We show a strong reduction of the number of operations for the realization of the Toffoli gate by using qudits for a scalable multi-qudit processor. This is done on the basis of a general relation between the dimensionality of qudits and their topology of connections, that we derived.

Keywords: quantum computing, qudits, Toffoli gates, gate decomposition

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1 Quantifying Parallelism of Vectors Is the Quantification of Distributed N-Party Entanglement

Authors: Shreya Banerjee, Prasanta K. Panigrahi

Abstract:

The three-way distributive entanglement is shown to be related to the parallelism of vectors. Using a measurement-based approach a set of 2−dimensional vectors is formed, representing the post-measurement states of one of the parties. These vectors originate at the same point and have an angular distance between them. The area spanned by a pair of such vectors is a measure of the entanglement of formation. This leads to a geometrical manifestation of the 3−tangle in 2−dimensions, from inequality in the area which generalizes for n− qubits to reveal that the n− tangle also has a planar structure. Quantifying the genuine n−party entanglement in every 1|(n − 1) bi-partition it is shown that the genuine n−way entanglement does not manifest in n− tangle. A new quantity geometrically similar to 3−tangle is then introduced that represents the genuine n− way entanglement. Extending the formalism to 3− qutrits, the nonlocality without entanglement can be seen to arise from a condition under which the post-measurement state vectors of a separable state show parallelism. A connection to nontrivial sum uncertainty relation analogous to Maccone and Pati uncertainty relation is then presented using decomposition of post-measurement state vectors along parallel and perpendicular direction of the pre-measurement state vectors. This study opens a novel way to understand multiparty entanglement in qubit and qudit systems.

Keywords: Geometry of quantum entanglement, Multipartite and distributive entanglement, Parallelism of vectors , Tangle

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