scholarly journals An efficient quantum algorithm for the time evolution of parameterized circuits

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 512
Author(s):  
Stefano Barison ◽  
Filippo Vicentini ◽  
Giuseppe Carleo
Keyword(s):  
Variational Principle ◽  
Time Evolution ◽  
Quantum Dynamics ◽  
Quantum Algorithm ◽  
Quantum Systems ◽  
Small Time ◽  
Quantum Circuits ◽  
Time Step ◽  
Optimal Linear ◽  
Global Nature

We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected – Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time-step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principle to optimize all parameters at once. The global nature of our approach then significantly extends the scope of existing efficient variational methods, that instead typically rely on the iterative optimization of a restricted subset of variational parameters. Through numerical experiments, we also show that our approach is particularly advantageous over existing global optimization algorithms based on the time-dependent variational principle that, due to a demanding quadratic scaling with parameter numbers, are unsuitable for large parameterized quantum circuits.

scholarly journals Efficient simulation of sparse Markovian quantum dynamics

2017 ◽  
Vol 17 (11&12) ◽  
pp. 901-947 ◽  
Author(s):  
Andrew M. Childs ◽  
Tongyang Li
Keyword(s):  
Quantum Dynamics ◽  
Quantum Algorithms ◽  
Open Quantum Systems ◽  
Hamiltonian Dynamics ◽  
Quantum Algorithm ◽  
Quantum Systems ◽  
Efficient Simulation ◽  
Box Models ◽  
Short Time ◽  
Black Box Models

Quantum algorithms for simulating Hamiltonian dynamics have been extensively developed, but there has been much less work on quantum algorithms for simulating the dynamics of open quantum systems. We give the first efficient quantum algorithms for simulating Markovian quantum dynamics generated by Lindbladians that are not necessarily local. We introduce two approaches to simulating sparse Lindbladians. First, we show how to simulate Lindbladians that act within small invariant subspaces using a quantum algorithm to implement sparse Stinespring isometries. Second, we develop a method for simulating sparse Lindblad operators by concatenating a sequence of short-time evolutions. We also show limitations on Lindbladian simulation by proving a no–fast-forwarding theorem for simulating sparse Lindbladians in black-box models.

scholarly journals Fermionic duality: General symmetry of open systems with strong dissipation and memory

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Valentin Bruch ◽  
Konstantin Nestmann ◽  
Jens Schulenborg ◽  
Maarten Wegewijs
Keyword(s):  
Time Evolution ◽  
Quantum Dynamics ◽  
Open Systems ◽  
Broad Class ◽  
Open Quantum Systems ◽  
Causal Structure ◽  
Wide Band ◽  
Quantum Systems ◽  
Strong Interactions ◽  
General Symmetry

We consider the exact time-evolution of a broad class of fermionic open quantum systems with both strong interactions and strong coupling to wide-band reservoirs. We present a nontrivial fermionic duality relation between the evolution of states (Schrödinger) and of observables (Heisenberg). We show how this highly nonintuitive relation can be understood and exploited in analytical calculations within all canonical approaches to quantum dynamics, covering Kraus measurement operators, the Choi-Jamiołkowski state, time-convolution and convolutionless quantum master equations and generalized Lindblad jump operators. We discuss the insights this offers into the divisibility and causal structure of the dynamics and the application to nonperturbative Markov approximations and their initial-slip corrections. Our results underscore that predictions for fermionic models are already fixed by fundamental principles to a much greater extent than previously thought.

scholarly journals Symmetries and monotones in Markovian quantum dynamics

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 261
Author(s):  
Georgios Styliaris ◽  
Paolo Zanardi
Keyword(s):  
Time Evolution ◽  
Quantum Dynamics ◽  
Riemannian Metrics ◽  
Dynamical Evolution ◽  
Information Geometry ◽  
Quantum Systems ◽  
Conserved Quantities ◽  
Initial State ◽  
Markovian Dynamics ◽  
Special Case

What can one infer about the dynamical evolution of quantum systems just by symmetry considerations? For Markovian dynamics in finite dimensions, we present a simple construction that assigns to each symmetry of the generator a family of scalar functions over quantum states that are monotonic under the time evolution. The aforementioned monotones can be utilized to identify states that are non-reachable from an initial state by the time evolution and include all constraints imposed by conserved quantities, providing a generalization of Noether's theorem for this class of dynamics. As a special case, the generator itself can be considered a symmetry, resulting in non-trivial constraints over the time evolution, even if all conserved quantities trivialize. The construction utilizes tools from quantum information-geometry, mainly the theory of monotone Riemannian metrics. We analyze the prototypical cases of dephasing and Davies generators.

scholarly journals Unconditionally Stable Algorithm for Copolymer and Copolymer-Solvent Systems

2020 ◽  
Vol 12 ◽  
pp. 120001
Author(s):  
Aldo Pezzutti ◽  
Hugo Hernández
Keyword(s):  
Time Evolution ◽  
Simulation Method ◽  
Small Time ◽  
Dynamics Simulation ◽  
Time Step ◽  
Cell Dynamics ◽  
Unconditionally Stable ◽  
Stable Algorithm ◽  
Numerical Resolution ◽  
Solvent Systems

In the time evolution simulation of a copolymer system towards its equilibrium configuration, it is common to use the Otha-Kawasaki approach for free energy and time evolution by means of a Cahn-Hilliard diffusion equation. The conventional numerical resolution is to use the cell dynamics simulation method (CDS). Although this method gives an adequate response, it is limited since it needs very small time steps to present both appropriate resolution and stability. Recently, unconditionally stable methods have been used in gradient systems that provide adequate resolution and stability with a greater time step in solving Cahn-Hilliard equations. In this paper, we develop and implement unconditionally stable algorithms for copolymer-solvent systems and for the resolution of the time evolution of block copolymer systems under the Otha-Kawasaki functional.

scholarly journals Multiparticle quantum plasmonics

Nanophotonics ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. 1243-1269 ◽  
Author(s):  
Chenglong You ◽  
Apurv Chaitanya Nellikka ◽  
Israel De Leon ◽  
Omar S. Magaña-Loaiza
Keyword(s):  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Single Photon ◽  
Quantum Systems ◽  
Many Body ◽  
Statistical Fluctuations ◽  
Quantum Plasmonics ◽  
Control Of Quantum Systems ◽  
Multiparticle Systems ◽  
Quantum Photonics

AbstractA single photon can be coupled to collective charge oscillations at the interfaces between metals and dielectrics forming a single surface plasmon. The electromagnetic near-fields induced by single surface plasmons offer new degrees of freedom to perform an exquisite control of complex quantum dynamics. Remarkably, the control of quantum systems represents one of the most significant challenges in the field of quantum photonics. Recently, there has been an enormous interest in using plasmonic systems to control multiphoton dynamics in complex photonic circuits. In this review, we discuss recent advances that unveil novel routes to control multiparticle quantum systems composed of multiple photons and plasmons. We describe important properties that characterize optical multiparticle systems such as their statistical quantum fluctuations and correlations. In this regard, we discuss the role that photon-plasmon interactions play in the manipulation of these fundamental properties for multiparticle systems. We also review recent works that show novel platforms to manipulate many-body light-matter interactions. In this spirit, the foundations that will allow nonexperts to understand new perspectives in multiparticle quantum plasmonics are described. First, we discuss the quantum statistical fluctuations of the electromagnetic field as well as the fundamentals of plasmonics and its quantum properties. This discussion is followed by a brief treatment of the dynamics that characterize complex multiparticle interactions. We apply these ideas to describe quantum interactions in photonic-plasmonic multiparticle quantum systems. We summarize the state-of-the-art in quantum devices that rely on plasmonic interactions. The review is concluded with our perspective on the future applications and challenges in this burgeoning field.

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.

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