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Oriental Journal Of Chemistry

A Study of Quantum Information and Quantum Computers

Yadollah Farahmand, Zabialah Heidarnezhad, Fatemeh Heidarnezhad, Х. Х. Муминов, Fatemeh Heydari

Published Jun 29, 2014• 2 citations
Publisher

Abstract

In this article we will proceed to check of quantum computers structure i.e.qubits in different states by quantum theory principles and then we will express the qubits representation in different states by Bolch sphere in different aspects and we will achieve the density matrix and the expectation value in direction of z axis and finally we will proceed to collapse phenomena of quantum state in qubit measurement discussion.

DOI
10.13005/ojc/300227

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In this article we will proceed to check of quantum computers structure i.e.qubits in different states by quantum theory principles and then we will express the qubits representation in different states by Bolch sphere in different aspects and we will achieve the density matrix and the expectation value in direction of z axis and finally we will proceed to collapse phenomena of quantum state in qubit measurement discussion.
This presentation provides a comprehensive overview of the foundational principles of quantum computation. It begins by contrasting classical and quantum information, highlighting how quantum bits (qubits) leverage superposition, entanglement, and interference to process information in ways that surpass classical limits. The document explains the four postulates of quantum mechanics: state space (qubits as unit vectors in a Hilbert space), time evolution (via unitary operators), measurement (probabilistic collapse of the state), and composite systems (tensor products of subsystems). Key concepts such as the Bloch sphere representation, quantum gates (e.g., Hadamard, CNOT, Pauli gates), and quantum circuits are discussed, illustrating how quantum operations manipulate qubit states. The presentation also covers quantum evolution, the gate model for computation, and the universality of certain gate sets, emphasizing the potential for quantum parallelism and the transformative impact of quantum computing on fields like cryptography and optimization.
Present-day computers are essentially non-quantum mechanical in operation. The logic gates of a classical computer are irreversible in nature. For easy understanding, elementary quantum mechanics is reviewed including the Schrödinger’s equation, the particle-in-a-box problem, state superposition and collapsing. Bloch sphere representation of a quantum bit is explained. The qubits display interesting properties of quantum superposition, entanglement and interference, characteristic of atomic and subatomic particles. Measurements carried out on qubits cause their wave functions to collapse forcing them into a definite 0 or 1 state. Qubit decoherence on interaction with the environment is a major problem in quantum computing Three types of quantum computing devices are discussed including silicon, superconducting and trapped qubit devices. Among silicon devices, gate-controlled silicon quantum dots and phosphorous donor implanted Si substrates are considered. Superconducting qubit archetypes and their realization techniques are explained. The transmon qubit design is preferred for charge noise mitigation. Under the trapped ion qubit devices, construction and operation of Paul ion traps is discussed, and the types of trapped ion qubits are elucidated.
We use homodyne detection to monitor the radiative decay of a superconducting qubit. According to the classical theory of conditional probabilities, the excited-state population differs from an exponential decay law if it is conditioned upon a later projective qubit measurement. Quantum trajectory theory accounts for the expectation values of general observables, and we use experimental data to show how a homodyne detection signal is conditioned upon both the initial state and the finally projected state of a decaying qubit. We observe, in particular, how anomalous weak values occur in continuous weak measurement for certain pre- and postselected states. Subject to homodyne detection, the density matrix evolves in a stochastic manner, but it is restricted to a specific surface in the Bloch sphere. We show that a similar restriction applies to the information associated with the postselection, and thus bounds the predictions of the theory.
We argue that the usual Bloch sphere is insufficient in various aspects for the representation of qubits in quantum information theory. For example, spin flip operations with the quaternions I J K = e 2 π i 2 = − 1 and J I K = + 1 cannot be distinguished on the Bloch sphere. We show that a simple knot theoretic extension of the Bloch sphere representation is sufficient to track all unitary operations for single qubits. Next, we extend the Bloch sphere representation to entangled states using knot theory. As applications, we first discuss contextuality in quantum physics—in particular the Kochen-Specker theorem. Finally, we discuss some arguments against many-worlds theories within our knot theoretic model of entanglement. The key ingredients of our approach are symmetries and geometric properties of the unitary group.