Quantum Gate Entangler and Entangling Capacity of a General Multipartite Quantum System

2008 ◽  
Vol 15 (03) ◽  
pp. 213-222 ◽  
Author(s):  
Hoshang Heydari
Keyword(s):  
Quantum System ◽  
Quantum Systems ◽  
Quantum Gate ◽  
Projective Varieties ◽  
Multipartite Quantum Systems ◽  
Higher Dimensional ◽  
Multipartite States ◽  
Complex Projective

We construct quantum gate entangler for general multipartite states based on the construction of complex projective varieties. We also discuss in detail the construction of quantum gate entangler for higher dimensional bipartite and multipartite quantum systems. Moreover, we construct and discuss entangling capacity of general multipartite quantum systems.

scholarly journals Selective Phase Rotation Quantum Gate Entangler

2009 ◽  
Vol 16 (04) ◽  
pp. 407-412
Author(s):  
Hoshang Heydari
Keyword(s):  
Integral Transform ◽  
Quantum Algorithms ◽  
Quantum Systems ◽  
Quantum Gate ◽  
Multipartite Quantum Systems ◽  
Phase Rotation ◽  
Quantum Integral ◽  
Qubit States

We construct a quantum gate entangler for multi-qubit states based on a selective phase rotation transform. In particular, we establish a relation between the quantum integral transform and the quantum gate entangler in terms of universal controlled gates for multi-qubit states. Our result gives an effective way of constructing topological and geometrical quantum gate entanglers for multipartite quantum systems, which could also lead to a construction of geometrical quantum algorithms.

scholarly journals ALGEBRAIC STRUCTURES OF MULTIPARTITE QUANTUM SYSTEMS

2011 ◽  
Vol 09 (01) ◽  
pp. 555-561
Author(s):  
HOSHANG HEYDARI
Keyword(s):  
Tensor Product ◽  
Quantum Systems ◽  
Algebraic Structures ◽  
Multipartite Quantum Systems ◽  
Multilinear Mapping ◽  
Multilinear Mappings ◽  
Multipartite States

We investigate the relation between multilinear mappings and multipartite states. We show that the isomorphism between multilinear mapping and tensor product completely characterizes decomposable multipartite states in a mathematically well-defined manner.

scholarly journals Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix Set

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jinli Xu ◽  
Baodong Zheng ◽  
Hongmei Yao
Keyword(s):  
Tensor Product ◽  
Quantum System ◽  
Quantum Systems ◽  
Hermitian Matrices ◽  
Linear Transformations ◽  
Multipartite Quantum Systems ◽  
Idempotent Matrix ◽  
Linear Maps

LetHnbe the set ofn×ncomplex Hermitian matrices and𝒫n(resp.,𝒯n) be the set of all idempotent (resp., tripotent) matrices inHn. Inl-partite quantum systemHm1Tml=⊗1lHmi,⊗1l𝒫mi(resp.,⊗1l𝒯mi) denotes the set of all decomposable elements⊗1lAisuch thatAi∈𝒫mi(resp.,Ai∈𝒯mi). In this paper, linear mapsϕfromHm1⋯mltoHnwithn≤m1⋯mlsuch thatϕ⊗1l𝒫mi∈𝒫nare characterized. As its application, the structure of linear mapsϕfromHm1⋯mltoHnwithn≤m1⋯mlsuch thatϕ⊗1l𝒯mi∈𝒯nis also obtained.

scholarly journals Simulating molecules on a cloud-based 5-qubit IBM-Q universal quantum computer

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
S. Leontica ◽  
F. Tennie ◽  
T. Farrow
Keyword(s):  
Quantum System ◽  
Energy Transport ◽  
Quantum Computer ◽  
Complex Molecule ◽  
Dissipative System ◽  
Quantum Simulation ◽  
Quantum Systems ◽  
Molecular Structures ◽  
Unitary Evolution ◽  
Universal Quantum

AbstractSimulating the behaviour of complex quantum systems is impossible on classical supercomputers due to the exponential scaling of the number of quantum states with the number of particles in the simulated system. Quantum computers aim to break through this limit by using one quantum system to simulate another quantum system. Although in their infancy, they are a promising tool for applied fields seeking to simulate quantum interactions in complex atomic and molecular structures. Here, we show an efficient technique for transpiling the unitary evolution of quantum systems into the language of universal quantum computation using the IBM quantum computer and show that it is a viable tool for compiling near-term quantum simulation algorithms. We develop code that decomposes arbitrary 3-qubit gates and implement it in a quantum simulation first for a linear ordered chain to highlight the generality of the approach, and second, for a complex molecule. We choose the Fenna-Matthews-Olsen (FMO) photosynthetic protein because it has a well characterised Hamiltonian and presents a complex dissipative system coupled to a noisy environment that helps to improve the efficiency of energy transport. The method can be implemented in a broad range of molecular and other simulation settings.

THE TRAPPED-ION QUBIT: COHERENT CONTROL IN INFINITE-DIMENSIONAL QUANTUM SYSTEMS

2009 ◽  
Vol 24 (32) ◽  
pp. 2565-2578
Author(s):  
C. RANGAN
Keyword(s):  
Quantum Computing ◽  
Quantum System ◽  
Quantum Control ◽  
Coherent Control ◽  
Quantum Information Processing ◽  
Quantum Systems ◽  
Infinite Dimensional ◽  
Trapped Ion ◽  
Rich Variety ◽  
Control Research

Theories of quantum control have, until recently, made the assumption that the Hilbert space of a quantum system can be truncated to finite dimensions. Such truncations, which can be achieved for most quantum systems via bandwidth restrictions, have enabled the development of a rich variety of quantum control and optimal control schemes. Recent studies in quantum information processing have addressed the control of infinite-dimensional quantum systems such as the quantum states of a trapped-ion. Controllability in an infinite-dimensional quantum system is hard to prove with conventional methods, and infinite-dimensional systems provide unique challenges in designing control fields. In this paper, we will discuss the control of a popular system for quantum computing the trapped-ion qubit. This system, modeled by a spin-half particle coupled to a quantized harmonic oscillator, is an example for a surprisingly rich variety of control problems. We will show how this infinite-dimensional quantum system can be examined via the lens of the Finite Controllability Theorem, two-color STIRAP, the generalized Heisenberg system, etc. These results are important from the viewpoint of developing more efficient quantum control protocols, particularly in quantum computing systems. This work shows how one can expand the scope of quantum control research to beyond that of finite-dimensional quantum systems.

scholarly journals USE OF THE WHIRLIGIG PRINCIPLE FOR STABILIZING THE INITIAL STATES OF SOME CLASSIC AND QUANTUM SYSTEMS

2020 ◽  
pp. 78-81
Author(s):  
V.A. Buts
Keyword(s):  
Quantum System ◽  
Excited States ◽  
Quantum Systems ◽  
Nuclear Systems ◽  
Initial States

It is shown that the whirligig principle can be used for stabilization of the initial states of some classical and quantum systems. This feature of the whirligig principle is demonstrated by simple examples. The most important result of this work is the proof of the fact that the stabilization of the excited states of quantum systems can be realized by acting not on the quantum system itself, but by acting on the states into which the system must go. Potentially, this result can be used to stabilize excited nuclear systems.

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