Introduction. In modern information theory, the idea of a fundamental connection between information, quantum mechanics and thermodynamics is becoming increasingly important. After the works of R. Landauer, the principle was formulated, which became the basis of a new field — information thermodynamics. On the other hand, the search for new ways of physical realization of qubits remains an urgent scientific problem. One of the potential quantum systems that has a natural two-state structure is the ortho- and para-states of the hydrogen molecule. The purpose. Hypothetical identification of the physical essence of the quantum-mechanical nature of information in the ortho/pair conversion of a hydrogen molecule, from the point of view of statistical mechanics and Landauer's thermodynamic principle as a fundamental energy limit for the legalization of information qubits. Results. From the point of view of quantum informatics, ortho/pair hydrogen molecules as quantum spin isomers can behave as different quantum components, because they have different statistical entropy. Therefore, they can be interpreted as two information configurations of one quantum system. Such a system is informationally and thermodynamically ordered in accordance with the Landauer principle and mathematically corresponding to the structure of a qubit or a logical two-level subsystem, isolated from the full four-dimensional Hilbert space of the two spins. The mathematical structure of this system corresponds to a two-level information space, which allows it to be interpreted as a potential model of an elementary quantum information carrier. Due to its antisymmetric structure, it shows increased adaptation in accordance with certain types of magnetic fluctuations, ions, chemical interactions and collective perturbations. The effective use of spin isomers as information carriers requires controlled quantum media, the creation of cryogenic and magnetic influences or isolated systems, and the synchronization of information operations with characteristic coherence times. Conclusions. The proposed conceptual and quantum-information analysis allows us to formulate a consistently consistent system of assumptions regarding a possible hypothesis about the interpretation of spin isomers of hydrogen as potential natural carriers of artificial quantum information. The practical implementation of this concept on the example of hydrogen requires further theoretical and experimental research aimed at studying the mechanisms of coordinated coherence, control of ortho/para-conversion and the possibilities of controlling the spin states of molecular systems. Keywords: quantum information, hydrogen isomer, qubit, entropy, spin conversion, ortho/pair transitions, quantum computer, Landauer's principle.
Introduction. In modern information theory, the idea of a fundamental connection between information, quantum mechanics and thermodynamics is becoming increasingly important. After the works of R. Landauer, the principle was formulated, which became the basis of a new field — information thermodynamics. On the other hand, the search for new ways of physical realization of qubits remains an urgent scientific problem. One of the potential quantum systems that has a natural two-state structure is the ortho- and para-states of the hydrogen molecule. The purpose. Hypothetical identification of the physical essence of the quantum-mechanical nature of information in the ortho/pair conversion of a hydrogen molecule, from the point of view of statistical mechanics and Landauer's thermodynamic principle as a fundamental energy limit for the legalization of information qubits. Results. From the point of view of quantum informatics, ortho/pair hydrogen molecules as quantum spin isomers can behave as different quantum components, because they have different statistical entropy. Therefore, they can be interpreted as two information configurations of one quantum system. Such a system is informationally and thermodynamically ordered in accordance with the Landauer principle and mathematically corresponding to the structure of a qubit or a logical two-level subsystem, isolated from the full four-dimensional Hilbert space of the two spins. The mathematical structure of this system corresponds to a two-level information space, which allows it to be interpreted as a potential model of an elementary quantum information carrier. Due to its antisymmetric structure, it shows increased adaptation in accordance with certain types of magnetic fluctuations, ions, chemical interactions and collective perturbations. The effective use of spin isomers as information carriers requires controlled quantum media, the creation of cryogenic and magnetic influences or isolated systems, and the synchronization of information operations with characteristic coherence times. Conclusions. The proposed conceptual and quantum-information analysis allows us to formulate a consistently consistent system of assumptions regarding a possible hypothesis about the interpretation of spin isomers of hydrogen as potential natural carriers of artificial quantum information. The practical implementation of this concept on the example of hydrogen requires further theoretical and experimental research aimed at studying the mechanisms of coordinated coherence, control of ortho/para-conversion and the possibilities of controlling the spin states of molecular systems. Keywords: quantum information, hydrogen isomer, qubit, entropy, spin conversion, ortho/pair transitions, quantum computer, Landauer's principle.
Landauer's principle sets fundamental thermodynamical constraints for classical and quantum information processing, thus affecting not only various branches of physics, but also of computer science and engineering. Despite its importance, this principle was only recently experimentally considered for classical systems. Here we employ a nuclear magnetic resonance set-up to experimentally address the information to energy conversion in a quantum system. Specifically, we consider a three nuclear spins [Formula: see text] (qubits) molecule-the system, the reservoir and the ancilla-to measure the heat dissipated during the implementation of a global system-reservoir unitary interaction that changes the information content of the system. By employing an interferometric technique, we were able to reconstruct the heat distribution associated with the unitary interaction. Then, through quantum state tomography, we measured the relative change in the entropy of the system. In this way, we were able to verify that an operation that changes the information content of the system must necessarily generate heat in the reservoir, exactly as predicted by Landauer's principle. The scheme presented here allows for the detailed study of irreversible entropy production in quantum information processors.
Standard CMOS circuits are expected to be no longer able to satisfy nowadays demand for higher performances and lower power consumption. This commits to look for new solutions. Quantum computation, whose fundamental quantity of information is the qubit, is a thoroughly new way of thinking to electronics. There are at least two main reasons for which quantum computing is expected to broaden computation horizons. First, specific algorithms can be engineered, manipulating the probability amplitudes of different states, to exploit the quantum superposition principle and achieve high parallelism. Second, it is expected to be spontaneously suitable to simulate complex quantum physical systems, as large molecules. Quantum computing requires the cooperation of several scientific fields. The leading idea has been to highlight the operations and algorithms a quantum computer must be able to perform and, then, to propose a hardware solution, providing the rigorous physical treatment mandatory for a deep understanding and for an appropriate modelling, something which is hard to find in nowadays literature. Thus, the first chapters address the quantum algorithms, focusing on Grover's search algorithm and deriving, from fundamentals, the corresponding circuit. The latter is then described in Quantum Assembly (QASM), which can be seen as the quantum equivalent of VHDL, and simulated on IBM Q Experience. The following chapters deal with a possible physical implementation of quantum processors: the encoding of qubits on nuclear spins in diamagnetic molecules. When a static magnetic field is applied to a spin-1/2 nucleus, two well-defined energy eigenstates arise, as a result of the Zeeman effect. Each of them can be associated with a qubit eigenstate. Thanks to nuclear magnetic resonance principles, the probability with which one of the two eigenstates is measured can be handled by the superposition of a radio frequency field at the resonance frequency of the nucleus. This can be interpreted as a rotation of the spin, and so of the qubit, about the RF field and enables the execution of single qubit quantum gates, since they are simple rotations of the state vector. The two-qubit CNOT gate is obtained through the interaction of spins via J-coupling. Considering that these gates constitute a universal set, every quantum algorithm can theoretically be run on an NMR processor. Different nuclei have different resonant frequencies, but the addressing of a specific spin can be achieved also in homonuclear molecules, since the resonant frequency depends also on the nuclear environment (nuclear shielding). While unwanted J-couplings can be removed thanks to refocusing, spin decoherence and relaxation phenomena force an upper limit to the allowed timescale. A main advantage of NMR is that this timescale is long, even at room temperature. Conversely, scalability is still an issue. A simple heteronuclear MATLAB model, based on the relations derived from first principles in the thesis, is proposed to prove the feasibility of NMR quantum processors. The input technological parameters, as chemical shielding and J-coupling, can be computed resorting on ORCA, or obtained from experimental data. The model, able to run a universal set of quantum gates and simple algorithms, can be useful to find an optimal operating point as a compromise between molecule physical properties and the quantities which can be controlled by nowadays NMR instrumentation.
The concept of quantum information is introduced as both normed superposition of two orthogonal subspaces of the separable complex Hilbert space and invariance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen.The separable complex Hilbert space is considered as the free variable of quantum information and any point in it (a wave function describing a state of a quantum system) as its value as the bound variable.A qubit is equivalent to the generalization of ‘bit’ from the set of two equally probable alternatives to an infinite set of alternatives. Then, that Hilbert space is considered as a generalization of Peano arithmetic where any unit is substituted by a qubit and thus the set of natural number is mappable within any qubit as the complex internal structure of the unit or a different state of it. Thus, any mathematical structure being reducible to set theory is representable as a set of wave functions and a subspace of the separable complex Hilbert space, and it can be identified as the category of all categories for any functor represents an operator transforming a set (or subspace) of the separable complex Hilbert space into another. Thus, category theory is isomorphic to the Hilbert-space representation of set theory & Peano arithmetic as above.Given any value of quantum information, i.e. a point in the separable complex Hilbert space, it always admits two equally acceptable interpretations: the one is physical, the other is mathematical. The former is a wave function as the exhausted description of a certain state of a certain quantum system. The latter chooses a certain mathematical structure among a certain category. Thus there is no way to be distinguished a mathematical structure from a physical state for both are described exhaustedly as a value of quantum information. This statement in turn can be utilized to be defined quantum information by the identity of any mathematical structure to a physical state, and also vice versa. Further, that definition is equivalent to both standard definition as the normed superposition and invariance of Hamilton and Lagrange interpretation of mechanical motion introduced in the beginning of the paper.Then, the concept of information symmetry can be involved as the symmetry between three elements or two pairs of elements: Lagrange representation and each counterpart of the pair of Hamilton representation. The sense and meaning of information symmetry may be visualized by a single (quantum) bit and its interpretation as both (privileged) reference frame and the symmetries 𝑈𝑈(1), 𝑆𝑆𝑆 (2), and 𝑆𝑆𝑆 (3) of the Standard model.
The thermodynamics of quantum processes is a recent field of study and it has been growing in recent years. Previously thought of as an emergent phenomenon for macroscopic systems, thermodynamics started being applied to quantum systems considering quantities such as heat and work as stochastics. The peculiarity of these systems is that, in addition to studying energetic resources, we must also take into account quantum informational resources such as entanglement and coherence. In this scenario, entropy becomes an important quantity, because in addition to being related to the irreversibility of a process, it can also be used as a measure of the amount of information in the system to which we have access. Entropy, unlike energy, is not a conserved quantity; that is, in a closed system, there is not only an entropy flow between it\'s parts, but also, in general, entropy production. According to the principle of Landauer [IBM Journal of Research and Development, vol. 5, no. 3, pp. 183191 (1961)], it is the entropy produced that causes the loss of information. Studying, then, the production of entropy becomes important for areas such as quantum computing, where you want to have control over information gains and losses. In quantum processes, entropy is produced due both to changes in the energy of the system and to fluctuations in coherence [Phys. Rev. E 99, 042105 (2019); npj Quantum Information 5, 23 (2019)], a purely quantum resource. In this project, we propose to study the statistics of entropy production due to coherence. For this, we will investigate two different splittings of the entropy production: the one proposed in [Phys. Rev. E, vol. 99, 042105 (2019); npj Quantum Information 5, 23 (2019)] and a most recent one proposed in [Phys. Rev. Research 2, 023377 (2020); New Journal of Physics 23, 063027 (2021)]. For simplicity, we will analyse a unitary quantum process, using the two-point measurement (TPM) scheme [Phys. Rev. E 75, 050102 (2007)]. We will apply both formalisms for two specific quantum systems: a macrospin model and the Lipkin-Meshkov-Glick (LMG) model [Nuclear Physics, vol. 62, no. 2, pp. 188 224 (1965)]. We will analyse, in these cases, how the distribution of coherence depends on parameters such as system dimension, temperature, evolution in time, etc.
Entropy is a fundamental concept which emerged along with other ideas during the development of thermodynamics and statistical mechanics Landau and Lifshitz (1978); Lieb and Yngvason (1999). Entropy has developed foremost out of phenomenological thermodynamical considerations such as the second law of thermodynamics in which it plays a prominent role Wehrl (1978). With the intense interest in the investigation of the physics of matter at the atomic and subatomic quantum levels, it maywell be askedwhether this concept can emerge out of the study of systems at a more fundamental level. In fact, it may be argued that a correct definition is only possible in the framework of quantum mechanics, whereas in classical mechanics, entropy can only be introduced in a rather limited and artificial way. Entropy relates macroscopic and microscopic aspects of nature, and ultimately determines the behavior of macroscopic systems. It is the intention here to present an introduction to this subject in a readable manner from the quantum point of view. There are many reasons for undertaking this. The intense interest in irreversible thermodynamics Grossing (2008), the statistical mechanics of astrophysical objects Padmanabhan (1990); Pathria (1977), quantum gravity and entropy of black holes Peres & al. (2004), testing quantum mechanics Ballentine (1970) and applications to condensed matter and quantum optics Haroche & al. (2006); Raimond & al. (2001) are just a few areas which are directly or indirectly touched on here. Let us begin by introducing the concept of entropy from the quantummechanical perspective, realizing that the purpose is to focus on quantum mechanics in particular. Quantum mechanics makes a clear distinction between observables and states. Observables such as position and momentum are mathematically described by self-adjoint operators in a Hilbert space. States, which are generally mixed, can be described by a density matrix, which is designated by ρ throughout. This operator ρ is Hermitean, has trace one and yields the expectation value of an observable A in the state ρ through the definition