The difference between a quantum computer and a classical computer is that the classical computer one bit has zero and one states with only 2^n states for n bits, while the quantum computer has the nature that phase and entanglement, so the quantum computer has more variations and can have nearly infinite possibilities. Therefore, the two principal axes of this paper are to observe the entangled state characteristics of multiple qubits (N=2 to N=7) on the IBM Q 53 qubit quantum computer and the influence of phase on the entangled state properties. The first part, which has been published in Quantum Engineering, is the GHZ-like states of multiple qubits (N = 2 to N = 7) in IBM Rochester, and compares the maximum violation values of Mermin orthogonal polynomials with the analytic results among each other. In another experiment, two qubits with different phase angles were used to analyze the phase trajectory, and the effect on the improved Mermin polynomial in the GHZ-like states was studied.
Our results in the first part show that the entanglement nature of IBM Rochester is fairly good when N ≤ 4, while for longer chains, entanglement is only valid for certain special connections. In the other experimental phase trajectory analysis, most of the trajectories are stable circular trajectories, and under certain circumstances the GHZ-like state and its excited state will produce the evolution of resurgence and reignition.
The difference between a quantum computer and a classical computer is that the classical computer one bit has zero and one states with only 2^n states for n bits, while the quantum computer has the nature that phase and entanglement, so the quantum computer has more variations and can have nearly infinite possibilities. Therefore, the two principal axes of this paper are to observe the entangled state characteristics of multiple qubits (N=2 to N=7) on the IBM Q 53 qubit quantum computer and the influence of phase on the entangled state properties. The first part, which has been published in Quantum Engineering, is the GHZ-like states of multiple qubits (N = 2 to N = 7) in IBM Rochester, and compares the maximum violation values of Mermin orthogonal polynomials with the analytic results among each other. In another experiment, two qubits with different phase angles were used to analyze the phase trajectory, and the effect on the improved Mermin polynomial in the GHZ-like states was studied.
Our results in the first part show that the entanglement nature of IBM Rochester is fairly good when N ≤ 4, while for longer chains, entanglement is only valid for certain special connections. In the other experimental phase trajectory analysis, most of the trajectories are stable circular trajectories, and under certain circumstances the GHZ-like state and its excited state will produce the evolution of resurgence and reignition.
Entanglement properties of IBM Q 53-qubit quantum computer are carefully examined with the noisy intermediate-scale quantum technology. We study Greenberger-Horne-Zeilinger-like states with multiple qubits (N = 2 to N = 7) on IBM Rochester and compare their maximal violation values of Mermin's polynomials with analytic results. A rule of N-qubits orthogonal measurements is taken to further justify the entanglement less than maximal values of local realism. The orthogonality of measurements is another reliable criterion for entanglement except the maximal values of LR. Our results indicate that the entanglement of IBM 53 qubits is reasonably good when N ≤ 4, while for the longer entangle chains, the entanglement is only valid for some special connectivity.
Violation of Mermin inequalities is tested on the five-qubit IBM quantum computer. For three, four, and five parties, quantum states that violate the corresponding Mermin inequalities are constructed using quantum circuits on superconducting qubits. Measurements on different bases are included as additional final gates in the circuits. The experimental results obtained using the quantum computer show violation of all Mermin inequalities, with a clear degradation of the results in the five-qubit case. Though this quantum computer is not competitive to test Mermin inequalities as compared to other techniques when applied to a few qubits, it does offer the opportunity to explore multipartite entanglement for four and five qubits beyond the reach of other alternative technologies.
Quantum computers have tremendous potential of simulating large quantum systems that classical computers can’t. In the theoretical verification of quantum non-locality principle, Bell’s and Mermin’s inequalities stood out, which proved to be valid in multiple empirical experiments. In this paper we report the tests of Bell and Mermin’s inequalities carried out on the 2- qubit and 3-qubit IBM quantum computer respectively. By comparing the result we obtained and the pattern predicted by the inequalities, our experimental results indicate clear violations of the two inequalities; thereby, we validate postulates in quantum mechanics and disprove the local realism argument in classical hidden variable theories proposed by Einstein, Podolsky, and Rosen on quantum circuits.
We analyze the basic aspects of the quantum information theory, namely the quantum version
of the theory that is behind all the classical implementations like computers and communications.
We focus on quantum computation, defining its fundamental unit: the qubit,
namely a quantum two-level system that will be described in detail in this thesis. We then
concentrate on the possible transformations gates that can be applied to qubits, both unitary
and non-unitary ones.
The challenges in the construction of qubits are impressive: in particular, it is difficult to
isolate the system from the environment. This interaction is modeled by non-unitary transformations.
The characteristic times connected to these processes are the relaxation time, the
time in which a state decays in another state, and the decoherence time, the time in which
quantum coherence is lost. These times are fundamental in quantum computing since they
quantify how many operations can be performed on qubits and still obtain reliable results.
We measure these characteristic times on the IBM quantum processor ’ibmq_16_melbourne’
performing three different experiments: one for the relaxation time and two for the decoherence
time, namely Ramsey and Echo experiments.
Finally, we implement a quantum algorithm, an algorithm that uses the resources of quantum
mechanics, like entanglement. We focus on finding a protocol to define the quantum
version of the elementary cellular automata, the quantum elementary cellular automata, and
run it on the IBM processor. They are dynamical systems defined on a lattice in which the
evolution is defined using simple local update rules.
Comparing the physical results with theoretical expectations and noise-affected simulations
we show the performance of the IBM processor.
The field of quantum computing is in the midst of a period of transformation as a result of the recent discovery of quantum entanglement. It is designed to perform computations that classical computers cannot handle since it is based on and operates in compliance with the rules of quantum mechanics. Because it operates on certain premises, it enables this to happen. Quantum bits, also known as qubits, have the unique ability to represent many states at once, unlike their conventional analogues. However, classical bits can only take on the values 0 or 1, and no other values in between. Quantum bits are capable of existing in a wide variety of states simultaneously. As a result of their unique ability to explore multiple solutions at once, quantum computers have the potential to dramatically boost the processing speed with which certain problems may be solved. Furthermore, qubits can show entanglement, in which the state of one qubit becomes intertwined with the state of another qubit, even if the qubits are separated by a great distance. Quantum entanglement describes this strange occurrence. This entanglement provides the way for the creation of new algorithms and enhanced computing power by simplifying the execution of complex interactions. Although difficulties like qubit stability and error correction must be overcome, quantum computing has the potential to revolutionize many different areas, including cryptography, optimization, and scientific discovery. Although significant strides have been made, the implementation of large-scale quantum computers remains in its infancy, necessitating ongoing research and development.
Bell-diagonal states are extremely important for understanding the dynamics and applications of some quantum resources. Quantum properties such as steering, entanglement, and coherence, among others, can be used as resources in quantum computing. Because of this, we believe it is necessary to understand the preparation of these states. We create an adjustable quantum circuit, which we implement on the International Business Machines (IBM) quantum computer. These computers are an excellent possibility for carrying out experiments like this. We implement the circuit on three different quantum chips that are available on the online platform. As an example, we measure non-locality, steering, entanglement, discord and non-local coherence for Werner states, which are a special type of the Bell-diagonal. We compare the theoretical results with the experimental data. We note the harmful effect that noise can have on quantum circuits, bringing undesirable decoherence effects to the system. We model noise in a simple way, using two quantum channels, amplitude damping and phase damping. We investigate the direct relationship between measures of discord and entanglement, as well as the sudden change of discord. But, even carrying out these tests on several quantum chips, it was not possible to carry out such verification with great clarity. On the other hand, the great importance of Bohr’s Complementarity Principle for Quantum Mechanics is well known. However, the search for quantifiers to measure wave or particle characteristics, in a quantum system, has always been very intense. Recently, a formalism was developed based on basic properties of the density matrix ( 0; Tr = 1). We use the IBM quantum computer to check the complementarity relationships based on these properties. We calculate quantum coherence, predictability and quantum correlations for a particular class of quantum states of one qubit and also for random quantum states of one, two and three qubits. We note that for both cases, the interaction of the system with the environment, and the consequent creation of correlation, generates a decrease in the sum of quantum coherence and predictability but which is compensated by the increase in quantum correlations between system and environment.