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In order to prepare for the introduction of dynamical many-body and, eventually, field theoretical models, we show here that quantum mechanical exchange interactions in a three-spin chain can emerge from the deterministic dynamics of three classical Ising spins. States of the latter form an ontological basis, which will be discussed with reference to the ontology proposed in the Cellular Automaton Interpretation of Quantum Mechanics by ’tHooft. Our result illustrates a new Baker–Campbell–Hausdorff (BCH) formula with terminating series expansion.

The dissipative dynamics of a bistable Josephson cell in a transmission line resonator in a weakly dissipative regime was studied theoretically and numerically. The bistable cell consists of a quantronium qubit and a nonlinear bifurcation amplifier. Under the rotating wave approximation, the problem of the system evolution in a boson thermostat is reduced to the Pauli equation. Using the master equation, we have numerically studied the dissipative dynamics of the system. It was shown that the nonlinear bifurcation amplifier can determine the qubit states and the system can be used as a detector of single microwave photons.

The evolution of quantum coherence in a qubit is analyzed, over short and long times, in case the qubit interacts with a bosonic environment. The distribution of the frequency modes exhibits a low-frequency band gap. The initial conditions under study of the qubit and the bosonic environment are factorized or prepared with selective or nonselective measurements. The modulus of the coherence term of the reduced density matrix of the qubit evolves algebraically over short times and, due to the band gap, tends to the nonvanishing asymptotic value with damped oscillations. Depending on the measurement scheme, the nonselective preparation measurement can enhance quantum coherence or accelerate the decoherence process, over short times, according to dominant linear laws. Over long times, the nonselective preparation measurement produces the slowest-decaying envelope of the damped oscillations among the decoherence processes under study. Similar short- and long-time evolution is exhibited by the trace distance measure of two general states of the qubit.

The effects of the measurement apparatus on quantum coherence are studied by considering a purely dephasing model of a qubit. The initial state is prepared from a thermal state of the whole system by performing a nonselective measurement on the qubit. The magnitude of the initial postmeasurement coherence is bounded by the value $1∕2$, which is realized with special measurement schemes and in the low-temperature limit. The coherence magnitude identically vanishes, increases or decreases with an approximately constant rate over a determined short-time scale, according to the choice of the preparation measurement. The maximization of the short-time increasing or decreasing rate is favored by the choice of other special measurement schemes and the high-temperature limit. The measurement apparatus allows to manipulate the quantum coherence of the qubit over short times via nonselective preparation measurements.

In this work, the energies and eigenfunctions of ground state and first-excited states (GFES) of a strongly coupled polaron in a quantum pseudo-dot (QPD) were studied by using variational method of Pekar type (VMPT). A single qubit can be realized in this two-level quantum system. Then, we calculated the coherence time of a QPD qubit by employing the Fermi Golden Rule. The temperature effects on the coherence time are taken into account by using the quantum statistics theory (QST) and self-consistent calculation method. According to the obtained results, it is found that the coherence time increases with decreasing temperature. Also, this time is a decaying function of the chemical potential of the two-dimensional electron gas and the zero point of the PHP.

Cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its ontological states that evolve by permutations, in this way never creating would-be quantum mechanical superposition states. We review and illustrate this with a classical Ising spin chain. It is shown that it can be related to the Weyl equation in the continuum limit. Yet, the model of discrete spins or bits unavoidably becomes a model of qubits by generating superpositions, if only slightly deformed. We study modifications of its signal velocity which, however, do not relate to mass terms. To incorporate the latter, we consider the Dirac equation in 1+1 dimensions and sketch an underlying discrete deterministic “necklace of necklaces” automaton that qualifies as ontological.

The dynamics-from-permutations of classical Ising spins are studied for a chain of four spins. We obtain the Hamiltonian operator which is equivalent to the unitary permutation matrix that encodes assumed pairwise exchange interactions. It is shown how this can be summarized by an exact terminating Baker–Campbell–Hausdorff formula, which relates the Hamiltonian to a product of exponentiated two-spin exchange permutations. We briefly comment upon physical motivation and implications of this study.

The superposition of pure quantum states explicitly expressed in terms of a nonlinear addition rule of state density operators is reviewed. The probability representation of density matrices of qudit states is used to formulate the interference of the states as a combination of the probability distributions describing pure states. The formalism of quantizer–dequantizer operators is developed. Examples of spin-1/2 states and f-oscillator systems are considered.

The appearance of decoherence-recoherence events is analyzed in a dephasing model of a qubit which interacts with a bosonic environment. The initial condition is prepared from the thermal state of the whole system by performing a nonselective measurement on the qubit. Decoherence-recoherence events appear in the reduced dynamics of the qubit uniquely if special nonselective preparation measurements are adopted and the spectral density of the system fulfills determined conditions. General lower bounds are found for the number of decoherence-recoherence events in terms of the properties of the measurement scheme and of the spectral density. The number is finite for canonical spectral densities which are super-ohmic, perturbed super-ohmic, or ohmic at low frequencies and are arbitrarily tailored at high frequencies. The number is infinite in the sub-ohmic regime and for perturbations of the sub-ohmic or ohmic regime. Decoherence-recoherence times are evaluated, analytically and numerically, for ohmic-like spectral densities with exponential high-frequency cutoffs.

A key to achieving quantum computing is the qubit-entanglement. Nevertheless, real-life qubits cannot be isolated from the environment completely. As a result, the entanglement between qubits decoheres via their interaction with the environment. Therefore, it is essential to understand how the qubit-entanglement changes over time. In this work, we study the entanglement between qubits when placed in a bulk of dielectric material embedded with a nanosized metal particle. Most importantly, we focus on the effects of the unavoidable localized surface plasmons induced at the surface of the metal particle. We discuss how the distance between the metal particles affects the entanglement of the qubits and how various entangled states are affected by the localized surface plasmons.

American options are important financial products traded in enormous volumes across the world. Therefore, accurate and efficient valuation is of paramount importance for global financial markets. Due to the early exercise feature, the pricing of American options is significantly more complicated than European options, and an analytical closed-form solution is unavailable even for simple dynamic models. Practitioners employ various valuation methods to strike the balance: accurate valuation usually suffers inefficiency, while fast valuation likely leads to inaccuracy. In this paper, we provide an innovative solution to address both the accuracy and efficiency issues of pricing American options by applying quantum reinforcement learning. Meanwhile, the quantum part of the new approach would potentially speed up the calculation dramatically.

We have investigated decoherence mechanisms in a Josephson-junction flux qubit. Loss of the coherence due to energy relaxation and dephasing was studied by measurements of the time evolution of qubit states subjected to simple control pulse sequences. As a function of qubit bias parameters, the characteristic time scales of the decoherence as well as the decay envelope functions varied, from which information about the fluctuation spectrum of the environment were deduced.

The main topic of this paper is to introduce the Quantum Information theory, emphasizing its good properties, but also clarifying common misunderstandings. Quantum Information theories and technologies have indeed many positive and interesting features, and hold promises of great developments. However, there are also problems. At present time, we can count a very small number of quantum algorithms, for example Quantum Fourier Transform, Shor's and Grover's. Grover's Algorithm in particular is capable of accelerating the search of elements in a large database. In our opinion, future evolutions of such algorithms will be successfully applied to the world of data handling, for example to satisfy astronomical needs when its time resolution capabilities will be pushed toward Heisenberg quantum limit.

The qubit readout process with a Josephson bifurcation amplifier (JBA) is analyzed quantum-mechanically. We calculate and clarify the dynamics of the density operator of a driven nonlinear oscillator and a qubit coupled system during the measurement. In purely quantum-mechanical JBAs, the bifurcation is impossible. It requires finite decoherence. When the JBA is coupled to a qubit, that is initially in a superposition state, we can observe the entanglement formation between the qubit and the probe (JBA) and the projection into one of two separable states at the moment of the JBA transition begins. To readout the measurement result, however, we must wait until the two JBA states are macroscopically well separated. The waiting time is determined by the strength of the decoherence in the JBA. This would give a trade-off on the strength of the JBA decoherence for a precise readout.

Breather is an elementary excitation regarded as a bound state of a fluxon and an antifluxon in a long Josephson junction. In quantum-mechanical regime, the breather energy is quantized so that the breather can be considered as an artificial moving atom. We propose a new type of fluxon qubit that is constructed by quantum-mechanical superposition of the breather's states. We describe quantum logic gates of breather qubit required for constructing quantum computer. In addition, our qubit can move in the system so that transfer of quntum information is possible between mobile qubits as well as stationary qubits. Our talking qubits support the global information sharing in quantum information networks.

While the notion of complementarity in quantum systems goes back to the beginning of quantum theory, the concept of complementary subalgebras is quite new. Here we overview the recent developments of the field, characterizations of complementarity and complementary decompositions are reviewed, and we point to some still open questions.

We show that global geometric properties and gauge invariance play a non-trivial role in quantum computing and in quantum optics. The covariant derivative operator is constructed and related to free energy. Global geometric (Berry-like phase) characterization of the system and its gauge invariant behavior are described as properties emerging from the collective behavior of fluctuating quantum phases of qubit states.

We postulate bulk universal quantum computing (QC) cannot be achieved without surmounting the quantum uncertainty principle, an inherent barrier by empirical definition in the regime described by the Copenhagen interpretation of quantum theory - the last remaining hurdle to bulk QC. To surmount uncertainty with probability 1, we redefine the basis for the qubit utilizing a unique form of M-Theoretic Calabi-Yau mirror symmetry cast in an LSXD Dirac covariant polarized vacuum with an inherent ‘Feynman synchronization backbone’. This also incorporates a relativistic qubit (r-qubit) providing additional degrees of freedom beyond the traditional Block 2-sphere qubit bringing the r-qubit into correspondence with our version of Relativistic Topological Quantum Field Theory (RTQFT). We present a 3^rd generation prototype design for simplifying bulk QC implementation.