scholarly journals Control aspects of quantum computing using pure and mixed states

2012 ◽  
Vol 370 (1976) ◽  
pp. 4651-4670 ◽  
Author(s):  
Thomas Schulte-Herbrüggen ◽  
Raimund Marx ◽  
Amr Fahmy ◽  
Louis Kauffman ◽  
Samuel Lomonaco ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Quantum Control ◽  
Open Quantum Systems ◽  
Jones Polynomial ◽  
Ion Traps ◽  
Quantum States ◽  
Nitrogen Vacancy ◽  
Quantum Circuits ◽  
State Transfer ◽  
Hard Problems

Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.

Quantum optics with nitrogen-vacancy centres in diamond

2017 ◽  
Author(s):  
Yiwen Chu ◽  
Mikhail D. Lukin
Keyword(s):  
Optical Properties ◽  
Quantum Information ◽  
Solid State ◽  
Quantum Optics ◽  
Quantum States ◽  
Nitrogen Vacancy ◽  
Common Theme ◽  
External Effects ◽  
Promising Candidate ◽  
Optical Photons

A common theme in the implementation of quantum technologies involves addressing the seemingly contradictory needs for controllability and isolation from external effects. Undesirable effects of the environment must be minimized, while at the same time techniques and tools must be developed that enable interaction with the system in a controllable and well-defined manner. This chapter addresses several aspects of this theme with regard to a particularly promising candidate for developing applications in both metrology and quantum information, namely the nitrogen-vacancy (NV) centre in diamond. The chapter describes how the quantum states of NV centres can be manipulated, probed, and efficiently coupled with optical photons. It also discusses ways of tackling the challenges of controlling the optical properties of these emitters inside a complex solid state environment.

scholarly journals Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 905
Author(s):  
Nina Megier ◽  
Manuel Ponzi ◽  
Andrea Smirne ◽  
Bassano Vacchini
Keyword(s):  
Quantum Dynamics ◽  
Open Quantum System ◽  
Open Quantum Systems ◽  
Phenomenological Approach ◽  
Quantum Systems ◽  
Renewal Processes ◽  
Continuous Part ◽  
Trace Distance ◽  
Open Quantum ◽  
And Control

Simple, controllable models play an important role in learning how to manipulate and control quantum resources. We focus here on quantum non-Markovianity and model the evolution of open quantum systems by quantum renewal processes. This class of quantum dynamics provides us with a phenomenological approach to characterise dynamics with a variety of non-Markovian behaviours, here described in terms of the trace distance between two reduced states. By adopting a trajectory picture for the open quantum system evolution, we analyse how non-Markovianity is influenced by the constituents defining the quantum renewal process, namely the time-continuous part of the dynamics, the type of jumps and the waiting time distributions. We focus not only on the mere value of the non-Markovianity measure, but also on how different features of the trace distance evolution are altered, including times and number of revivals.

scholarly journals Local Spin and Open Quantum Systems: Clarifying Misconceptions, Unifying Approaches

2020 ◽  
Author(s):  
Angel Martín Pendás ◽  
Evelio Francisco
Keyword(s):  
Quantum Control ◽  
Open Systems ◽  
Open Quantum Systems ◽  
Real Space ◽  
Quantum Systems ◽  
Spin Coupling ◽  
Molecular Systems ◽  
Open Quantum ◽  
Local Spin

<p>We now show that Clark and Davidson local spins operators are perfectly defined subsystem operators if a fragment is taken as an <i>open quantum system</i> (OQS). Open systems have become essential in quantum control and quantum computation, but have not received much attention in Chemistry. We have already shown (<i>J. Chem. Theory Comput</i>. <b>2018</b>, <i>15</i>, 1079) how real space OQSs can be defined in molecular systems and how they offer new insights relating quantum mechanical entaglement and chemical bonding. The OQS account of local spin that we offer yields a rigorous, yet easily accessible way to rationalize local spin values. A fragment is found in a mixed state direct sum of sectors characterized by different number of electrons that occur with different probabilities. The local spin is then a weighted sum of otherwise standard <i>S</i>(<i>S</i>+1) values. With OQS glasses, it is obvious that atomic or fragment spins should not vanish. Our approach thus casts doubts on any procedure used to annihilate them, like those used by Mayer and coworkers. OQS local spins allow for a fruitful use of models. One can propose easily sector probabilities for localized, covalent, ionic, zwitterionic, etc. situations, and examine their ideal local spins. We have mapped all 2c-2e cases, and shown how to do that in general multielectron cases. The role of electron correlation is also studied by tuning the Hubbard U/t parameter for H chains. Correlation induced localization changes the spin-coupling patterns even qualitatively, and show how the limiting antiferromagnet arises.</p>

scholarly journals Experimental implementation of precisely tailored light-matter interaction via inverse engineering

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Ying Yan ◽  
Chunyan Shi ◽  
Adam Kinos ◽  
Hafsa Syed ◽  
Sebastian P. Horvath ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Quantum Control ◽  
Quantum Information Processing ◽  
Rare Earth Ions ◽  
Adiabatic Process ◽  
Physical Constraints ◽  
Shortcuts To Adiabaticity ◽  
Experimental Implementation ◽  
Speed Up ◽  
Light Matter Interaction

AbstractAccurate and efficient quantum control in the presence of constraints and decoherence is a requirement and a challenge in quantum information processing. Shortcuts to adiabaticity, originally proposed to speed up the slow adiabatic process, have nowadays become versatile toolboxes for preparing states or controlling the quantum dynamics. Unique shortcut designs are required for each quantum system with intrinsic physical constraints, imperfections, and noise. Here, we implement fast and robust control for the state preparation and state engineering in a rare-earth ions system. Specifically, the interacting pulses are inversely engineered and further optimized with respect to inhomogeneities of the ensemble and the unwanted interaction with other qubits. We demonstrate that our protocols surpass the conventional adiabatic schemes, by reducing the decoherence from the excited-state decay and inhomogeneous broadening. The results presented here are applicable to other noisy intermediate-scale quantum systems.

scholarly journals State Transfer via On-Line State Estimation and Lyapunov-Based Feedback Control for a N-Qubit System

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 751 ◽  
Author(s):  
Sajede Harraz ◽  
Shuang Cong
Keyword(s):  
Feedback Control ◽  
State Estimation ◽  
Open Quantum Systems ◽  
State Feedback Control ◽  
Quantum Master Equation ◽  
Control Law ◽  
Control Laws ◽  
Quantum State Estimation ◽  
State Transfer ◽  
On Line

In this paper, we propose a Lyapunov-based state feedback control for state transfer based on the on-line quantum state estimation (OQSE). The OQSE is designed based on continuous weak measurements and compressed sensing. The controlled system is described by quantum master equation for open quantum systems, and the continuous measurement operators are derived according to the dynamic equation of system. The feedback control law is designed based on the Lyapunov stability theorem, and a strict proof of proposed control laws are given. At each sampling time, the state is estimated on-line, which is used to design the control law. The simulation experimental results show the effectiveness of the proposed feedback control strategy.

Dynamics of Interacting Classical and Quantum Systems

2011 ◽  
Vol 18 (04) ◽  
pp. 339-351 ◽  
Author(s):  
Dariusz Chruściński ◽  
Andrzej Kossakowski ◽  
Giuseppe Marmo ◽  
E. C. G. Sudarshan
Keyword(s):  
Characteristic Feature ◽  
Quantum Dynamics ◽  
Quantum Discord ◽  
Main Idea ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Quantum States ◽  
Algebra Of Observables ◽  
Classical Quantum ◽  
True Quantum

We analyze the dynamics of coupled classical and quantum systems. The main idea is to treat both systems as true quantum ones and impose a family of superselection rules which imply that the corresponding algebra of observables of one subsystem is commutative and hence may be treated as a classical one. Equivalently, one may impose a special symmetry which restricts the algebra of observables to the 'classical' subalgebra. The characteristic feature of classical-quantum dynamics is that it leaves invariant a subspace of classical-quantum states, that is, it does not create quantum correlations as measured by the quantum discord.

Quantum circuits for calculating the squared sum of the inner product of quantum states and its application

2019 ◽  
Vol 17 (05) ◽  
pp. 1950043
Author(s):  
Panchi Li ◽  
Jiahui Guo ◽  
Bing Wang ◽  
Mengqi Hao
Keyword(s):  
Quantum Circuit ◽  
Quantum States ◽  
Experimental Results ◽  
Quantum Circuits ◽  
Inner Product ◽  
Superposition State ◽  
Initial State ◽  
Control Rules ◽  
Control Qubit ◽  
Classical Computer

In this paper, we propose a quantum circuit for calculating the squared sum of the inner product of quantum states. The circuit is designed by the multi-qubits controlled-swapping gates, in which the initial state of each control qubit is [Formula: see text] and they are in the equilibrium superposition state after passing through some Hadamard gates. Then, according to the control rules, each basis state in the superposition state controls the corresponding quantum states pair to swap. Finally, the Hadamard gates are applied to the control qubits again, and the squared sum of the inner product of many pairs of quantum states can be obtained simultaneously by measuring only one control qubit. We investigate the application of this method in quantum images matching on a classical computer, and the experimental results verify the correctness of the proposed method.

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