Dynamics of quantum correlations and their protection using novel dynamical decoupling sequences

Abstract

The core of this thesis focuses on the experimental demonstration of the dynamics of quantum resources, such as quantum correlations and quantum coherence, as well as their protection through the implementation of novel dynamical decoupling (DD) sequences. These sequences are applied to both nuclear spin-based nuclear magnetic resonance (NMR) quantum processors and superconducting qubit-based IBM quan tum processors. Quantum coherence and quantum correlation, particularly quantum entanglement as well as quantum discord are crucial quantum resources for a range of tasks in quantum computation, information processing, and communication. The study undertaken in this thesis primarily addresses two key areas: first, it experimentally demonstrates the enhancement of quantum discord (QD) and quantum coherence (QC) in a two-qubit entangled states through the application of quantum weak measurement operator and PT-symmetric Hamiltonian, respectively. The non-unitary characteristics of these operators pose significant challenges for their experimental implementation. To address these challenges, various dilation-based techniques have been proposed, including Stinespring dilation, the duality method, and Sz.-Nagy’s dilation techniques. In this thesis, the duality quantum algorithm based on dilation techniques is used to simulate a weak measurement operator where a three-qubit system is employed with the first two qubits serve as work qubits to generate a two-qubit entangled state, while the third qubit acts as an ancillary qubit. The weak measurement operator is applied to the first qubit of the two-qubit entangled state using the ancillary qubit, thereby reveal ing two weak variants of quantum discord: super quantum discord and weak quantum discord. As the name SQD suggests, QD increases with the strength of weak mea surement, thereby enhancing non-classical correlation. Conversely, WQD decreases with increasing measurement strength. Additionally, this thesis explores both theoreti cally and experimentally the dynamics of various types of quantum coherence, includ ing total coherence, local coherence, and global coherence, in multipartite entangled states. These dynamics are examined experimentally under the influence of a local PT-symmetric Hamiltonian, across regions of unbroken and broken phases, as well as at the exceptional point where the results demonstrate an enhancement in quantum co herence. Experimentally, PT-symmetric Hamiltonian is simulated through the duality vii 0. Abstract method. The second area of study delves into the experimental protection of quantum co herence and quantum entanglement from inherent environmental noise in a nuclear spin-based NMR quantum processor and a superconducting qubit-based IBM cloud quantum processor, respectively. Experimentally, various noisy multipartite entangled states are generated using superconducting qubits and are protected by applying newly proposed universally robust dynamical decoupling (URDD) sequences. The effective ness of the URDDsequencesisfurtherenhancedbyincorporatingphaserandomization (PR) and correlated phase randomization (CPR) techniques. In the IBM quantum pro cessor, URDD sequences are implemented using single-qubit gates, with identity gates employed to facilitate free evolution. The final section of the thesis focuses on the ex perimental protection of quantum states with various orders of coherence (first, second, and third order of coherence), generated using three nuclear spins in an NMR quan tum processor. First and third-order coherences are preserved using robust dynamical decoupling (DD) sequences, while second-order coherence is maintained with the im plementation of modified robust DD sequences. The content of this thesis has been divided into six chapters, which are briefly outlined as follows: Chapter 1 This chapter begins with an introduction to the basics of quantum computation and information processing. It then provides an overview of the general theory of NMR, highlighting key features such as the interaction of nuclear spins with both the static magnetic field and the radiofrequency field, as well as the relaxation processes. The chapter continues with a discussion of the physical realization of NMR as a quantum processor. Additionally, it provides a brief introduction to quantum correlation and coherence, non-unitary operations, and protection schemes. Finally, this chapter con cludes by outlining the aims and motivations behind the work presented in this thesis. Chapter 2 This chapter experimentally explores the effects of using a weak measurement opera tor, rather than a projective measurement, on evaluating quantum discord in two-qubit entangled states, specifically the Bell diagonal state and the Werner state. The results lead to the identification of two weak variants of quantum discord: super quantum discord (SQD) and weak quantum discord (WQD). In addition to it, the chapter also demonstrates how the behaviors of SQD and WQD change in both the Bell and Werner states as the strength of the weak measurement is increased. Their results are ex perimentally demonstrated using an NMR system involving three nuclear spins. The f irst two spins are used to generate entanglement, while the third spin simulates the viii weak measurement process on the first qubit of the entangled state. Further, the weak measurement process is found to be analogous to the phase damping (PD) channel in determining SQD and WQD. Consequently, the weak measurement process is experi mentally simulated using a PD channel, employing a quantum duality algorithm based on dilation techniques for the PD channel simulation, where the strength of the weak measurement is controlled by varying the strength of the PD channel. Chapter 3 This chapter demonstrates that quantum coherence (QC) is quantitatively enhanced under the influence of a local PT-symmetric Hamiltonian, where the quantification of QC is achieved using the relative entropy of coherence, which measures different types of QC in multipartite states. Consequently, this chapter focuses on the evolution of quantum coherence in bipartite and tripartite states-specifically, the two-qubit Bell state and the three-qubit GHZ state-when the first qubit in each state is subjected to a local PT-symmetric Hamiltonian across both the regions of unbroken and broken phase as well as at the exceptional point. Moreover, a local PT-symmetric Hamiltonian is experimentally simulated on an NMR quantum processor using a dilation technique of the quantum duality algorithm. This approach allows for the experimental verification of the dynamics of different types of QC in a two-qubit Bell state at three distinct strength of non-hermicity, covering both broken and unbroken regions, as well as the exceptional point. Chapter 4 This chapter focuses on newly developed protection techniques for dynamical decou pling (DD) sequences, specifically the universally robust DD (URDD) sequence, to address decoherence processes in IBM quantum processors based on superconducting qubits. Using a five-qubit manila IBM quantum processor, various noisy multipartite entangled states are generated on superconducting transmon qubits. An eighth-order URDDsequence is then experimentally applied simultaneously to each qubit involved in generating the entangled states, thereby protecting the multipartite entanglement. Moreover, phase randomization (PR) and correlated phase randomization (CPR) tech niques are independently integrated with the URDD sequence to further enhance its efficiency. The performance of the URDD sequence and its variants in protecting en tangled states is tracked by measuring the entanglement witness at various time points during free evolution and while implementing the protection scheme. ix 0. Abstract Chapter 5 This chapter focuses on the dynamics of quantum states with different orders of quan tumcoherence (zeroth, first, second, and third), created using a three-qubit NMR quan tum processor. These coherences of various orders are evolved in the presence of in herent environmental noise within the NMR system and are subsequently protected through the application of robust dynamical decoupling (DD) sequences such as XY8, UR12, XY16, and KDD20. The first-order coherences are preserved by applying a DDsequence to a single spin, while third-order coherences are protected by applying a DD sequence to all three qubits simultaneously. Similarly, zero and second-order coherences are protected by employing a modified DD sequence that acts on the two spins involved in their creation. Additionally, this chapter describes the generation of a three-qubit star state, where the entanglement within its two-qubit subsystems is protected using modified robust DD sequences. Chapter 6 This chapter summarizes the research conducted in this thesis and concludes with a discussion of potential future directions.