scholarly journals Various Constructions of Qudit SWAP Gate

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
S. Balakrishnan
Keyword(s):  
Arbitrary Dimension ◽  
Circuit Complexity ◽  
Quantum Systems ◽  
Swap Gate ◽  
Minimum Number ◽  
Swap Operation

It is known that SWAP operation for quantum systems of arbitrary dimension can be implemented using various qudit gates. In this paper, equivalence of some important qudit operations is demonstrated. Equivalence of the qudit operations is exploited to minimize the circuit complexity in the previously proposed qudit SWAP gate constructions. Further, constructions of qudit SWAP operation with minimum number of qudit gates are also proposed. Importantly, these circuit constructions of SWAP retain its properties like symmetry and simplicity.

LATTICE GAS MODELS ON SELF-SIMILAR APERIODIC TILINGS

1991 ◽  
Vol 03 (02) ◽  
pp. 163-221 ◽  
Author(s):  
C. P. M. GEERSE ◽  
A. HOF
Keyword(s):  
Lattice Gas ◽  
Arbitrary Dimension ◽  
Quantum Systems ◽  
Translation Invariance ◽  
Aperiodic Tilings ◽  
Mean Pressure ◽  
Lattice Gas Models ◽  
Self Similar ◽  
The Mean ◽  
Penrose Tilings

We discuss lattice gas models on the vertices of tilings in arbitrary dimension that are self-similar in the way Penrose tilings of the plane are self-similar. Among these, there are systems that fundamentally lack translation invariance. Under natural hypotheses on the interactions and the states, we prove the existence of thermodynaraic functions — the mean pressure, the mean energy and the mean entropy — and derive the variational principle. The relation between Gibbs states and tangent functionals to the mean pressure is investigated. Generalizations to quantum systems are also discussed. Our work extends results known for lattice gas models on periodic lattices.

Open quantum systems and thermal non-equilibrium processes

2020 ◽  
Vol 34 (17) ◽  
pp. 2050194
Author(s):  
Z. Rahdar ◽  
B. Lari
Keyword(s):  
Equilibrium Condition ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum ◽  
Equilibrium Processes ◽  
Swap Gate ◽  
Convexity And Concavity ◽  
Output Behavior ◽  
Environment Parameters ◽  
Non Equilibrium

In this paper, we investigate the effects of convexity and concavity of states on entanglement of the system under thermal non-equilibrium condition. In this regard, we consider a system consisting of two spin 1/2 particles with Dzyaloshinskii–Moriya (DM) interaction that follows the Tsallis statistics.Also, according to the desired statistics, the effect of environment parameters and the convexity or concavity of the input states on the output behavior of the SWAP gate is obtained.

scholarly journals Hamiltonian extensions in quantum metrology

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Julien Mathieu Elias Fraïsse ◽  
Daniel Braun
Keyword(s):  
Hilbert Space ◽  
Phase Shift ◽  
General Framework ◽  
Open Quantum Systems ◽  
Arbitrary Dimension ◽  
Quantum Fisher Information ◽  
Original System ◽  
Quantum Systems ◽  
Quantum Metrology ◽  
Shift Measurement

AbstractWe study very generally towhat extent the uncertainty with which a phase shift can be estimated in quantum metrology can be reduced by extending the Hamiltonian that generates the phase shift to an ancilla system with a Hilbert space of arbitrary dimension, and allowing arbitrary interactions between the original system and the ancilla. Such Hamiltonian extensions provide a general framework for open quantum systems, as well as for “non-linear metrology schemes” that have been investigated over the last few years. We prove that such Hamiltonian extensions cannot improve the sensitivity of the phase shift measurement when considering the quantum Fisher information optimized over input states.

scholarly journals Complexity from the reduced density matrix: a new diagnostic for chaos

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Arpan Bhattacharyya ◽  
S. Shajidul Haque ◽  
Eugene H. Kim
Keyword(s):  
Density Matrix ◽  
Quantum Chaos ◽  
Open Quantum Systems ◽  
Circuit Complexity ◽  
Quantum Systems ◽  
Harmonic Oscillators ◽  
Quantum Circuits ◽  
Reduced Density Matrix ◽  
Evolution Of Complexity ◽  
Reduced Density

Abstract We investigate circuit complexity to characterize chaos in multiparticle quantum systems. In the process, we take a stride to analyze open quantum systems by using complexity. We propose a new diagnostic of quantum chaos from complexity based on the reduced density matrix by exploring different types of quantum circuits. Through explicit calculations on a toy model of two coupled harmonic oscillators, where one or both of the oscillators are inverted, we demonstrate that the evolution of complexity is a possible diagnostic of chaos.

OPTIMAL STATE ESTIMATION AND CLONING FOR EQUATORIAL QUANTUM SYSTEMS WITH ARBITRARY DIMENSION

2005 ◽  
Vol 03 (01) ◽  
pp. 57-63
Author(s):  
C. MACCHIAVELLO
Keyword(s):  
State Estimation ◽  
Finite Dimension ◽  
Arbitrary Dimension ◽  
Optimal Estimation ◽  
Estimation Procedure ◽  
Quantum Systems ◽  
Optimal State ◽  
Optimal State Estimation

We review the problem of optimal estimation of multiple phases for systems with arbitrary finite dimension and derive the optimal estimation fidelity for equatorial states. We present optimal phase covariant cloning transformations for d-dimensional systems, relating these results to the optimal estimation procedure.

IMPROVED BOUNDS FOR GOSSIPING IN MESH BUS NETWORKS

2000 ◽  
Vol 01 (01) ◽  
pp. 1-19
Author(s):  
JEAN-CLAUDE BERMOND ◽  
SUSAN MARSHALL ◽  
MIN-LI YU
Keyword(s):  
Arbitrary Dimension ◽  
Minimum Number ◽  
One Step ◽  
Bus Network ◽  
Bus Networks

Improved bounds for the minimum gossiping time in mesh bus networks of arbitrary dimension for 1-port model are given. More precisely, the gossiping protocol consists of steps during which messages are sent via buses and at the end of the protocol, all the nodes should know all the information. Furthermore, during one step a bus can carry at most one message, and each node can either send or receive (not both) on at most one bus The minimum gossiping time of a bus network G is the minimum number of steps required to perform a gossip under this model. Here we determine almost exactly the minimum gossip time for 2-dimensional mesh bus networks and give tight bounds for d-dimensional mesh bus networks.

scholarly journals Self-testing quantum systems of arbitrary local dimension with minimal number of measurements

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Shubhayan Sarkar ◽  
Debashis Saha ◽  
Jędrzej Kaniewski ◽  
Remigiusz Augusiak
Keyword(s):  
Bell Inequality ◽  
Quantum Systems ◽  
Entangled State ◽  
Local Dimension ◽  
Maximally Entangled State ◽  
Testing Protocol ◽  
Self Testing ◽  
Minimum Number ◽  
Bell Nonlocality ◽  
Testing Protocols

AbstractBell nonlocality as a resource for device-independent certification schemes has been studied extensively in recent years. The strongest form of device-independent certification is referred to as self-testing, which given a device, certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit–qudit entangled states based on violation of a single d-outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, $${{{\mathrm{log}}}\,}_{2}d$$ log 2 d perfect random bits, while it requires only one random bit to encode the measurement choice.

scholarly journals Environment-Assisted Shortcuts to Adiabaticity

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1479
Author(s):  
Akram Touil ◽  
Sebastian Deffner
Keyword(s):  
Arbitrary Dimension ◽  
Quantum Systems ◽  
Unique Form ◽  
Shortcuts To Adiabaticity ◽  
Novel Method ◽  
Correlated Quantum Systems ◽  
The Cost

Envariance is a symmetry exhibited by correlated quantum systems. Inspired by this “quantum fact of life,” we propose a novel method for shortcuts to adiabaticity, which enables the system to evolve through the adiabatic manifold at all times, solely by controlling the environment. As the main results, we construct the unique form of the driving on the environment that enables such dynamics, for a family of composite states of arbitrary dimension. We compare the cost of this environment-assisted technique with that of counterdiabatic driving, and we illustrate our results for a two-qubit model.

scholarly journals A quantum Fredkin gate

2016 ◽  
Vol 2 (3) ◽  
pp. e1501531 ◽  
Author(s):  
Raj B. Patel ◽  
Joseph Ho ◽  
Franck Ferreyrol ◽  
Timothy C. Ralph ◽  
Geoff J. Pryde
Keyword(s):  
Quantum Computer ◽  
Logic Gates ◽  
Quantum Systems ◽  
Black Box ◽  
Quantum Computers ◽  
Fredkin Gate ◽  
Swap Gate ◽  
Quantum Analog ◽  
Photonic Qubit ◽  
Qubit Operation

Minimizing the resources required to build logic gates into useful processing circuits is key to realizing quantum computers. Although the salient features of a quantum computer have been shown in proof-of-principle experiments, difficulties in scaling quantum systems have made more complex operations intractable. This is exemplified in the classical Fredkin (controlled-SWAP) gate for which, despite theoretical proposals, no quantum analog has been realized. By adding control to the SWAP unitary, we use photonic qubit logic to demonstrate the first quantum Fredkin gate, which promises many applications in quantum information and measurement. We implement example algorithms and generate the highest-fidelity three-photon Greenberger-Horne-Zeilinger states to date. The technique we use allows one to add a control operation to a black-box unitary, something that is impossible in the standard circuit model. Our experiment represents the first use of this technique to control a two-qubit operation and paves the way for larger controlled circuits to be realized efficiently.

scholarly journals ON A GENERALIZED QUANTUM SWAP GATE

2012 ◽  
Vol 10 (03) ◽  
pp. 1250034 ◽  
Author(s):  
COLIN M. WILMOTT ◽  
PETER R. WILD
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Quantum Systems ◽  
Higher Dimensional ◽  
Swap Gate

The SWAP gate plays a central role in network designs for qubit quantum computation. However, there has been a view to generalize qubit quantum computing to higher dimensional quantum systems. In this paper we construct a generalized SWAP gate using only instances of the generalized controlled-NOT gate to cyclically permute the states of d qudits for d prime.

Sign in / Sign up

Export Citation Format

Share Document