On GKLS dynamics for local operations and classical communication

We define a time continuous version of the concept of "local operations and classical communication" (LOCC), ubiquitous in quantum information theory. It allows us to construct GKLS master equations for particle systems that have (1) an arbitrary pair potential, and (2) local decoherence terms, but that do not entangle the constituents. The local decoherence terms take a particularly simple form if a principle of least decoherence is applied.Comment: 5pp. Submitted to special OSID volume "40 years of the GKLS equation

Thermodynamics of Markovian Open Quantum Systems with Application to Lasers

Goran Lindblad was one of the pioneers of what is called now Quantum Thermodynamics. From this vast and rapidly developing field we have selected a sample of results concerning quantum open systems described by Markovian Master Equations of the Lindblad (Gorini-Kossakowski-Sudarshan) type, which are applied to models of lasers. One can study their thermodynamics using the properties of quantum relative entropy, also introduced by Lindblad.Comment: 13 pages , 1 figure . To appear in the volume devoted to Goran Lindblad published by Open Systems and Information Dynamic

Quantum and classical dynamical semigroups of superchannels and semicausal channels

Quantum devices are subject to natural decay. We propose to study these decay processes as the Markovian evolution of quantum channels, which leads us to dynamical semigroups of superchannels. A superchannel is a linear map that maps quantum channels to quantum channels while satisfying suitable consistency relations. If the input and output quantum channels act on the same space, then we can consider dynamical semigroups of superchannels. No useful constructive characterization of the generators of such semigroups is known. We characterize these generators in two ways: First, we give an efficiently checkable criterion for whether a given map generates a dynamical semigroup of superchannels. Second, we identify a normal form for the generators of semigroups of quantum superchannels, analogous to the Gorini-Kossakowski-Lindblad-Sudarshan form in the case of quantum channels. To derive the normal form, we exploit the relation between superchannels and semicausal completely positive maps, reducing the problem to finding a normal form for the generators of semigroups of semicausal completely positive maps. We derive a normal for these generators using a novel technique, which applies also to infinite-dimensional systems. Our work paves the way for a thorough investigation of semigroups of superchannels: Numerical studies become feasible because admissible generators can now be explicitly generated and checked. Analytic properties of the corresponding evolution equations are now accessible via our normal form

Quantum Computing for Fusion Energy Science Applications

This is a review of recent research exploring and extending present-day quantum computing capabilities for fusion energy science applications. We begin with a brief tutorial on both ideal and open quantum dynamics, universal quantum computation, and quantum algorithms. Then, we explore the topic of using quantum computers to simulate both linear and nonlinear dynamics in greater detail. Because quantum computers can only efficiently perform linear operations on the quantum state, it is challenging to perform nonlinear operations that are generically required to describe the nonlinear differential equations of interest. In this work, we extend previous results on embedding nonlinear systems within linear systems by explicitly deriving the connection between the Koopman evolution operator, the Perron-Frobenius evolution operator, and the Koopman-von Neumann evolution (KvN) operator. We also explicitly derive the connection between the Koopman and Carleman approaches to embedding. Extension of the KvN framework to the complex-analytic setting relevant to Carleman embedding, and the proof that different choices of complex analytic reproducing kernel Hilbert spaces depend on the choice of Hilbert space metric are covered in the appendices. Finally, we conclude with a review of recent quantum hardware implementations of algorithms on present-day quantum hardware platforms that may one day be accelerated through Hamiltonian simulation. We discuss the simulation of toy models of wave-particle interactions through the simulation of quantum maps and of wave-wave interactions important in nonlinear plasma dynamics.Comment: 42 pages; 12 figures; invited paper at the 2021-2022 International Sherwood Fusion Theory Conferenc

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The last few years have seen a rapid evolution and expansion of the field. We review here recent progress in our understanding of the controllability of open quantum systems and in the development and application of quantum control techniques to quantum technologies. We also address key challenges and sketch a roadmap for future developments

Characterization and simulation of multipartite open quantum systems

Having a quick look at contemporary quantum mechanics, we immediately see that the study of open quantum systems is of great relevance both for fundamental reasons and for the development of quantum technologies that will be able to display quantum advantage. An open quantum system is defined in a very general way as a non-isolated quantum system that is interacting with one or more external environments. This picture can give us a valuable insight, for instance, into how a single superconducting qubit of a quantum computer that is subject to thermal fluctuations loses its coherences, or into the thermodynamics of an atom immersed in the electromagnetic field. Hence, improving our understanding of the dynamics and characterization of open quantum systems is a crucial challenge in the second quantum revolution, as well as a fascinating step forward in the study of the deepest concepts in Physics, such as the quantum to classical transition. Motivated by renewed studies on dissipative collective effects, by new dis- coveries about the features of noise in quantum computers, and by recent experiments focused on many-qubit systems, the interest in multipartite open quantum systems has recently risen. A dissipative collective effect may be defined as the coherent interference of the emissions (and/or absorptions) of many quantum particles interacting with external environments. Multipar- tite open quantum systems are open systems made of multiple subsystems, which can interact with each other and at the same time may be coupled to local and/or collective environments. This type of open quantum systems plays a crucial role, for instance, in the study of “crosstalk errors” in quantum information processors, in the thermodynamic analysis of spin or harmonic oscillator chains, as well as in the description of collective phenomena such as superradiance and quantum synchronization. The characterization and simu- lation of the dynamics of multipartite open quantum systems is the topic of this doctoral dissertation. This thesis consists of six original research articles and an introduction to their methodology, scope, and significance. The first two publications explore the validity and features of the so-called global and local master equations (i.e., the equations of motion for open quantum systems), which are widely employed in quantum thermodynamics. In particular, these papers are fo- cused on a particular type of master equation based on the “partial secular approximation”, which is shown to be accurate in all regimes of validity of the standard Markovian master equation. Moreover, the symmetry properties of these master equations are discussed. The third scientific article shows how the most common examples of multipartite open quantum systems can be simulated through a platform of superconducting qubits coupled to a resistor emitting thermal noise. The fourth publication studies how different collective effects, such as quantum synchronization, subradiance and entanglement gen- eration, can emerge in a model of two detuned qubits coupled to a common bath. The fifth research paper introduces a quantum algorithm based on a collision model that is able to simulate the most general Markovian multi- partite quantum dynamics, and proves that this algorithm can be efficiently simulated on a quantum computer. Finally, the sixth publication presents the experimental implementation of this algorithm on a near-term quantum com- puter, and assesses both theoretically and experimentally the features of noise on the algorithm. In conclusion, this thesis brings some relevant contributions to the field of multipartite open quantum systems, not only regarding methodological ques- tions, but also phenomenological predictions and experimental implementa- tions on a quantum computer. These contributions include the description and characterization of a general master equation for Markovian multipartite open quantum systems, and some new procedures for the analog and digital quantum simulation thereof.Kun tarkastellaan nopeasti nykyaikaista kvanttimekaniikkaa, huomaamme heti, että avoimien kvanttijärjestelmien tutkiminen on erittäin tärkeää sekä perustavanlaatuisista syistä että kvanttietujen näyttämisen mahdollistavien kvanttiteknologioiden kehittämisen kannalta. Avoin kvanttijärjestelmä määritellään yleisellä tavalla eristämättömäksi kvanttijärjestelmäksi, joka on vuorovaikutuksessa yhden tai useamman ulkoisen ympäristön kanssa. Tämä kuva voi antaa meille arvokkaan käsityksen esimerkiksi siitä, kuinka lämpövaihteluille riippuvainen suprajohtava kubitti kvanttitietokoneessa menettää koherenssinsa tai sähkömagneettiseen kenttään upotetun atomin termodynamiikasta. Näin ollen ymmärryksemme parantaminen avoimien kvanttijärjestelmien dynamiikan ja karakterisoinnin suhteen on ratkaiseva haaste toisessa kvanttivallankumouksessa sekä kiehtova edistysaskel fysiikan syvimpien käsitteiden, kuten kvanttimekaniikan ja klassisen mekaniikan rajan, tutkimisessa. Uusiutuneiden dissipatiivisten kollektiivisten vuorovaikutusten tutkimusten, kvanttitietokoneiden kohinan ominaisuuksista tehtyjen uusien löytöjen ja viimeaikaisten monikubittisiin järjestelmiin keskittyneiden kokeiden seurauksena kiinnostus moniosaisiin avoimiin kvanttijärjestelmiin kohtaan on viime aikoina lisääntynyt. Dissipatiivinen kollektiivinen vuorovaikutus voidaan määritellä monien ulkoisen ympäristön kanssa vuorovaikutuksessa olevien kvanttihiukkasten emission (ja/tai absorption) koherentiksi häiriöksi. Moniosaiset avoimet kvanttijärjestelmät ovat avoimia järjestelmiä, jotka koostuvat useista osajärjestelmistä, jotka voivat olla vuorovaikutuksessa toistensa kanssa ja samalla kytkeytyä paikallisiin ja/tai kollektiivisiin ympäristöihin. Tämän tyyppisillä avoimilla kvanttijärjestelmillä on ratkaiseva rooli esimerkiksi kvanttitietojen prosessorien “ylikuulumisvirheiden” tutkimuksessa, spin- tai harmonisten oskillaattoriketjujen termodynaamisessa analyysissä sekä kollektiivisten ilmiöiden, kuten supersäteilyn ja kvanttisynkronoinnin kuvauksessa. Moniosaisten avoimien kvanttijärjestelmien dynamiikan karakterisointi ja simulointi on tämän väitöskirjan aiheena. Tämä opinnäytetyö koostuu kuudesta alkuperäisestä tutkimusartikkelista ja johdannosta niiden metodologiaan, laajuuteen ja merkitykseen. Kaksi ensimmäistä julkaisua tutkivat niin kutsuttujen globaalien ja paikallisten pääyhtälöiden (eli avoimien kvanttijärjestelmien liikeyhtälöiden) pätevyyttä ja ominaisuuksia, joita käytetään laajalti kvanttitermodynamiikassa. Erityisesti nämä artikkelit keskittyvät tietyntyyppiseen pääyhtälöön, joka perustuu osittaiseen maalliseen approksimaatioon, joka on osoitettu olevan tarkka kaikissa standardin Markovin pääyhtälön kelpoisuusjärjestelmissä. Lisäksi käsitellään näiden pääyhtälöiden symmetriaominaisuuksia. Kolmas tieteellinen artikkeli osoittaa, kuinka yleisimpiä esimerkkejä moniosaisista avoimista kvanttijärjestelmistä voidaan simuloida suprajohtavien kubittien alustalla, joka on kytketty lämpökohinaa lähettävään vastukseen. Neljännessä julkaisussa tutkitaan, kuinka erilaiset kollektiiviset efektit, kuten kvanttisynkronointi, subradianssi ja takertuminen, voivat syntyä mallissa, jossa kaksi viritettyä kubittia on kytketty yhteiseen kylpyyn. Viides tutkimusartikkeli esittelee törmäysmalliin perustuvan kvanttialgoritmin, joka pystyy simuloimaan yleisintä Markovin moniosaista kvanttidynamiikkaa ja todistaa, että tämä algoritmi voidaan simuloida tehokkaasti kvanttitietokoneella. Lopuksi, kuudes julkaisu esittelee tämän algoritmin kokeellisen toteutuksen lähiajan kvanttitietokoneella ja arvioi sekä teoreettisesti että kokeellisesti algoritmin kohinan ominaisuuksia. Yhteenvetona voidaan todeta, että tämä opinnäytetyö tuo olennaisia panoksia moniosaisten avoimien kvanttijärjestelmien alaan ei pelkästään metodologisessa mielessä, mutta myös fenomenologisia ennusteita kokeellisille toteutuksille kvanttitietokoneella. Nämä panokset sisältävät yleisen pääyhtälön kuvauksen ja karakterisoinnin Markovin moniosaisille avoimille kvanttijärjestelmille ja uusia menetelmiä niiden analogisille ja digitaalisille kvanttisimulaatioille

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The last few years have seen a rapid evolution and expansion of the field. We review here recent progress in our understanding of the controllability of open quantum systems and in the development and application of quantum control techniques to quantum technologies. We also address key challenges and sketch a roadmap for future developments.Comment: this is a living document - we welcome feedback and discussio