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Experimental study of quantum resources using IBM quantum computers

Mauro Buemo Pozzobom

Published Feb 26, 2021• 0 citations
OpenAlex

Abstract

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.

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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.
We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell diagonal states is generated, and several characteristic indicators, namely entanglement of formation and concurrence, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work, we also find a remarkable general inequality between "quantum discord" and "asymmetric relative entropy of discord": the former never exceeds the latter. We also prove that for all BDS the two coincide.
We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell diagonal states is generated, and several characteristic indicators, namely entanglement of formation and concurrence, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work, we also find a remarkable general inequality between “quantum discord” and “asymmetric relative entropy of discord”: the former never exceeds the latter. We also prove that for all BDS the two coincide.
Bohr's complementarity principle is of fundamental historic and conceptual importance for quantum mechanics (QM), and states that, with a given experimental apparatus configuration, one can observe either the wave-like or the particle-like character of a quantum system, but not both. However, it was eventually realized that these dual behaviors can both manifest partially in the same experimental setup, and, using ad hoc proposed measures for the wave and particle aspects of the quanton, complementarity relations were proposed limiting how strong these manifestations can be. Recently, a formalism was developed and quantifiers for the particleness and waveness of a quantum system were derived from the mathematical structure of QM entailed in the density matrix's basic properties ($\ensuremath{\rho}\ensuremath{\ge}0, \mathrm{Tr}\ensuremath{\rho}=1$). In this article, using IBM Quantum Experience quantum computers, we perform experimental tests of these complementarity relations applied to a particular class of one-qubit quantum states and also for random quantum states of one, two, and three qubits.
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.
Quantum discord is a more general measure of quantum correlations than entanglement and has been proposed as a resource in certain quantum information processing tasks. The computation of discord is mostly confined to two-qubit systems for which an analytical calculational scheme is available. The utilization of quantum correlations in quantum information-based applications is limited by the problem of decoherence, i.e., the loss of coherence due to the inevitable interaction of a quantum system with its environment. The dynamics of quantum correlations due to decoherence may be studied in the Kraus operator formalism for different types of quantum channels representing system-environment interactions. In this review, we describe the salient features of the dynamics of classical and quantum correlations in a two-qubit system under Markovian (memoryless) time evolution. The two-qubit state considered is described by the reduced density matrix obtained from the ground state of a spin model. The models considered include the transverse-field XY model in one dimension, a special case of which is the transverse-field Ising model, and the XXZ spin chain. The quantum channels studied include the amplitude damping, bit-flip, bit-phase-flip and phase-flip channels. The Kraus operator formalism is briefly introduced and the origins of different types of dynamics discussed. One can identify appropriate quantities associated with the dynamics of quantum correlations which provide signatures of quantum phase transitions in the spin models. Experimental observations of the different types of dynamics are also mentioned.
Abstract This laboratory work presents a practical introduction to the preparation and analysis of entangled quantum states (Bell pairs) using the Qiskit framework. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and is designed to provide hands-on experience with multi-qubit quantum circuits and entanglement generation. In Laboratory Work No. 3, participants construct and simulate a quantum circuit that prepares an entangled two-qubit state. As a representative example of multi-qubit operations in Qiskit, the circuit generates a Bell state by applying a Hadamard (H) gate to the first qubit q[0]q[0]q[0], followed by a controlled-NOT (CNOT) gate with q[0]q[0]q[0] as the control qubit and q[1]q[1]q[1] as the target qubit. This sequence creates a maximally entangled state, demonstrating the fundamental non-classical correlations characteristic of quantum systems. The laboratory exercise includes measurement operations applied to both qubits, illustrating how entanglement manifests in correlated classical outcomes. When the measurement operator is applied to the first qubit q[0]q[0]q[0], the corresponding classical bit records a definite value, and subsequent measurement of the second qubit q[1]q[1]q[1] yields a correlated result consistent with the structure of the Bell state. The probabilistic yet correlated outcomes provide direct evidence of quantum entanglement. The guide emphasizes the conceptual understanding of entanglement, circuit implementation in Qiskit, and the hybrid quantum-classical workflow underlying quantum computation. By bridging theoretical quantum mechanics with executable quantum circuits, this laboratory work enables students and researchers to experimentally explore one of the central phenomena of quantum information science using cloud-based quantum computing resources.