Образование частиц при релятивистском столкновении тяжелых ядер на LHC с помощью GEANT4

В работе изучены корреляции тяжелых кварков, образующихся при ре- лятивистских столкновениях тяжелых ионов, которые достаточно чув- ствительны к воздействию среды и механизмам образования. Чтобы сде- лать количественное описание таких корреляций, в качестве первого шага анализируются азимутальные, поперечные импульсные и скоростные корреляции тяжелых кварк ‒ анти-кварковых пар QQ в столкновениях pp при 2 s O . Это создает предпосылки для выявления и изучения средовой модификации подобных корреляций при релятивистском столкновении тяжелых ядер на Большом адронном коллайдере. Далее изучается дополнительное образование кварков очарования в столкновениях тяжелых ионов из-за множественного рассеяния, а именно, реактивных столкновений, реактивно-тепловых столкновений и тепловых взаимодействий. Установлено, что они порождают азимутальные корреляции, которые совершенно отличаются от возникающих при быстром первоначальном производстве в ведущем порядке и в следующем за ведущим порядком

Interpolated Collision Model Formalism

The dynamics of open quantum systems (i.e., of quantum systems interacting with an uncontrolled environment) forms the basis of numerous active areas of research from quantum thermodynamics to quantum computing. One approach to modeling open quantum systems is via a Collision Model. For instance, one could model the environment as being composed of many small quantum systems (ancillas) which interact with the target system sequentially, in a series of "collisions". In this thesis I will discuss a novel method for constructing a continuous-time master equation from the discrete-time dynamics given by any such collision model. This new approach works for any interaction duration, $\delta t$, by interpolating the dynamics between the time-points $t = n\,\delta t$. I will contrast this with previous methods which only work in the continuum limit (as $\delta t\to 0$). Moreover, I will show that any continuum-limit-based approach will always yield unitary dynamics unless it is fine-tuned in some way. For instance, it is common to find non-unitary dynamics in the continuum limit by taking an (I will argue unphysical) divergence in the interaction strengths, $g$, such that $g^2 \delta t$ is constant as $\delta t \to 0$.Comment: 121 pages, 3 figures, Daniel Grimmer's PhD Thesis University of Waterloo 202

Fermion Sampling: a robust quantum computational advantage scheme using fermionic linear optics and magic input states

Fermionic Linear Optics (FLO) is a restricted model of quantum computation which in its original form is known to be efficiently classically simulable. We show that, when initialized with suitable input states, FLO circuits can be used to demonstrate quantum computational advantage with strong hardness guarantees. Based on this, we propose a quantum advantage scheme which is a fermionic analogue of Boson Sampling: Fermion Sampling with magic input states. We consider in parallel two classes of circuits: particle-number conserving (passive) FLO and active FLO that preserves only fermionic parity and is closely related to Matchgate circuits introduced by Valiant. Mathematically, these classes of circuits can be understood as fermionic representations of the Lie groups $U(d)$ and $SO(2d)$. This observation allows us to prove our main technical results. We first show anticoncentration for probabilities in random FLO circuits of both kind. Moreover, we prove robust average-case hardness of computation of probabilities. To achieve this, we adapt the worst-to-average-case reduction based on Cayley transform, introduced recently by Movassagh, to representations of low-dimensional Lie groups. Taken together, these findings provide hardness guarantees comparable to the paradigm of Random Circuit Sampling. Importantly, our scheme has also a potential for experimental realization. Both passive and active FLO circuits are relevant for quantum chemistry and many-body physics and have been already implemented in proof-of-principle experiments with superconducting qubit architectures. Preparation of the desired quantum input states can be obtained by a simple quantum circuit acting independently on disjoint blocks of four qubits and using 3 entangling gates per block. We also argue that due to the structured nature of FLO circuits, they can be efficiently certified.Comment: 65 pages, 13 figures, 1 table, v2: improved discussion and narrative, numerics about anticoncentration added, references updated, comments and suggestions are welcom

Normalizer Circuits and Quantum Computation

(Abridged abstract.) In this thesis we introduce new models of quantum computation to study the emergence of quantum speed-up in quantum computer algorithms. Our first contribution is a formalism of restricted quantum operations, named normalizer circuit formalism, based on algebraic extensions of the qubit Clifford gates (CNOT, Hadamard and $\pi/4$-phase gates): a normalizer circuit consists of quantum Fourier transforms (QFTs), automorphism gates and quadratic phase gates associated to a set $G$, which is either an abelian group or abelian hypergroup. Though Clifford circuits are efficiently classically simulable, we show that normalizer circuit models encompass Shor's celebrated factoring algorithm and the quantum algorithms for abelian Hidden Subgroup Problems. We develop classical-simulation techniques to characterize under which scenarios normalizer circuits provide quantum speed-ups. Finally, we devise new quantum algorithms for finding hidden hyperstructures. The results offer new insights into the source of quantum speed-ups for several algebraic problems. Our second contribution is an algebraic (group- and hypergroup-theoretic) framework for describing quantum many-body states and classically simulating quantum circuits. Our framework extends Gottesman's Pauli Stabilizer Formalism (PSF), wherein quantum states are written as joint eigenspaces of stabilizer groups of commuting Pauli operators: while the PSF is valid for qubit/qudit systems, our formalism can be applied to discrete- and continuous-variable systems, hybrid settings, and anyonic systems. These results enlarge the known families of quantum processes that can be efficiently classically simulated. This thesis also establishes a precise connection between Shor's quantum algorithm and the stabilizer formalism, revealing a common mathematical structure in several quantum speed-ups and error-correcting codes.Comment: PhD thesis, Technical University of Munich (2016). Please cite original papers if possible. Appendix E contains unpublished work on Gaussian unitaries. If you spot typos/omissions please email me at JLastNames at posteo dot net. Source: http://bit.ly/2gMdHn3. Related video talk: https://www.perimeterinstitute.ca/videos/toy-theory-quantum-speed-ups-based-stabilizer-formalism Posted on my birthda

Exploring new routes to decoherence-free quantum computing; and quantum thermodynamics for fermions

This thesis has two parts; the first part is a contribution to the research field of quantum measurement in quantum optics while the second part focuses on quantum thermodynamics for fermionic systems. The aim of the research on quantum optics is to detect and subsequently characterize quantum states of light. Specifically, we focus on characterizing 1) entanglement between a two-level atom and superposition of coherent states (known as Bell cat state) 2) quantum superposition of coherent states (Schr\"odinger cat states). The photon is the particle of light which carries quantum information; it is usually lost (destroyed) while being detected. Many physical implementations of quantum logic gate aim to encode quantum information processing into large registers of entangled qubits. However for these larger much distinguishable states, creating and preserving entanglement becomes difficult due to rapid onset of decoherence. Encoding quantum information on Schrodinger's cat states take advantage of a cavity resonators much larger Hilbert space, as compared with that of a two-level system. This architecture allows redundant qubit encodings that can simplify the operations needed to initialize, manipulate and measure the encoded information. For such a system to be viable as a quantum computing platform, efficient measurement of such encoded qubit observables must be possible. The concept of quantum non demolition measurement was introduced to evade the problem of decoherence. Researchers now know through quantum theory that it is indeed possible to count photons in a given state of light without destroying them. This nondestructive measurement scheme is coined in the term ``quantum non-demolition measurement". We can extend the ideas of quantum nondemolition measurement scheme to detect a system made up of two or more quantum states (not necessarily states of light) that are combined based on the superposition principle. An example is the Schr\"odinger's cat state which is a superposition of two coherent states of light of equal amplitudes but opposite phase. At this point, one is not only interested in counting photons, but in understanding the nature of the superposition, the possible problems and the different physical properties that follow. Ways to detect the Schr\"odinger cat states and subsequently a Bell cat state (Schr\"odinger cat entangled with a qubit) without significantly perturbing them are discussed. The method analyzed is the mode-invisibility measurement scheme earlier proposed to detect single Fock states and coherent states of light. The method gives a new insight to the known properties of Schr\"odinger cat states and contributes to our understanding of the quantum-classical boundary problem. The second part of the thesis falls in the research field of quantum thermodynamics and open quantum systems. Most problems in quantum thermodynamics have been explored in bosonic systems with little or less done in fermionic systems. Therefore the aim of this part of the thesis is to explore related quantum thermodynamical problems in fermionic systems. I begin by considering the problem of work extraction from noninteracting fermionic systems. For work to be extracted from the state of a quantum system, a unitary operation on the state must act to reduce the average energy of the system. Passive states are those states whose energy cannot be reduced through unitary transformation, that is work cannot be extracted via unitary transformations given only a single copy of the system. It follows that some passive states may have extractable work if several copies of the system is processed. Passive states for which no work can be extracted, no matter the number of available copies, are called completely passive states. An example is the thermal Gibbs state. Here, the limit for which multiple copies of passive states in fermionic systems can be activated for work extraction is studied. It was observed for n > 3 fermionic modes at the same frequency, the product state of n thermal states with different temperatures is not passive. This in principle implies that the construction of a heat engine in fermionic systems need access to three thermal baths at different temperature. This is unlike the bosonic system, where access to only two thermal baths are required. On the other hand, while the product state of three thermal states of three fermionic modes at the same frequency but different temperatures is not passive, the unitary transformation required to extract work from the state is difficult to realize. A set of operations that are easier to realize are Gaussian unitaries which are generated by Hamiltonian that are at most quadratic in the system's operators. One may consider extracting work via the restricted class of Gaussian unitaries. Hence fermionic Gaussian passive states for which energy cannot be extracted using only Gaussian operations are characterized. The last problem I investigate is that of understanding the dynamics of an open Markovian non-interacting fermionic system. I introduce a classification scheme for the generators of open fermionic Gaussian dynamics and simultaneously partition the dynamics along the following four lines: 1) unitary vs. non-unitary, 2) active vs. passive, 3) state-dependent vs. state-independent, and 4) single-mode vs. multi-mode. Unlike in the bosonic case where only eleven of these sixteen types of dynamics turn out to be possible, one observe only nine types of dynamics in the fermionic setting. Using this partition I discuss the consequences of imposing complete positivity on fermionic Gaussian dynamics. In particular, I show that completely positive dynamics must be either unitary (and so can be implemented without a quantized environment) or active (and so must involve particle exchange with an environment)