Ancilla Assisted Quantum Information Processing: General protocols and NMR implementations

Abstract

While a bit is the fundamental unit of binary classical information, a qubit is a fundamental unit of quantum information. In quantum information processing (QIP), it is customary to call the qubits under study as system qubits, and the additional qubits as ancillary qubits. In this thesis, I describe various schemes to exploit the ancillary qubits to e fficiently perform many QIP tasks and their experimental demonstrations in nuclear magnetic resonance (NMR) systems. Particularly, we have showed that, in the presence of suffi cient ancillary qubits, it is possible to completely characterize a general quantum state as well as a general quantum dynamics in a single measurement. In addition, it is also possible to exploit ancillary qubits for realizing noninvasive quantum measurements required for several experiments related to quantum physics. Finally, I will also illustrate some interesting applications of ancillary qubits in spectroscopy. The abstracts of individual chapters are given below. x Contents Chapter 1 is the introduction to this thesis. Here I describe about classical/quantum information, quantum information processing (QIP), nuclear magnetic resonance (NMR), NMR-QIP, and finally ancilla-assisted QIP. The standard method of Quantum State Tomography (QST) relies on the measurement of a set of noncommuting observables, realized in a series of independent experiments. Ancilla Assisted QST (AAQST) greatly reduces the number of independent measurements by exploiting an ancilla register in a known initial state. In suitable conditions AAQST allows mapping out density matrix of an input register in a single experiment. In chapter 2, I describe methods for explicit construction of AAQST experiments in multi-qubit registers. I also report NMR implementations of AAQST on certain qubit systems and the experimental results confirm the e ffectiveness of AAQST in such many-qubit registers. In chapter 3, I present a procedure to characterize a general quantum process in a single ensemble measurement. The standard procedure for quantum process tomography (QPT) requires a series of experiments. Each experiment involves initialization of the system to a particular basis state, applying the quantum process " on the system, and finally characterizing the output state by quantum state tomography (QST). The output states collected for a complete set of basis states enable us to calculate the matrix characterizing the process ". The standard procedure for QST itself requires independent experiments each involving measurement of a set of commuting observables. Thus QPT procedure demands a number of independent measurements, and moreover, this number increases rapidly with the size of the system. However in ensemble systems, the total number of independent measurements can be greatly reduced with the availability of ancilla qubits. Here we combine AAPT with AAQST to realize a ‘single-scan QPT’ (SSPT), a procedure to characterize a general quantum process in a single ensemble measurement. We demonstrate experimental SSPT by characterizing several single-qubit processes using a three-qubit NMR quantum register. Furthermore, using the SSPT procedure we experimentally characterize the twirling process and compare the results with theory. The measurement as described in quantum mechanics is in general invasive. An invasive measurement may aff ect subsequent dynamics of the quantum system. In chapter 4, I report use of ancilla assisted noninvasive measurement to study following two problems. In section 4.1, I describe violation of entropic Leggett-Garg inequality in nuclear spin ensembles. Entropic Leggett-Garg inequality (ELGI) places a bound on the statistical measurement outcomes of dynamical observables describing a macrorealistic system [1]. Such a bound is not necessarily obeyed by quantum systems and therefore provides an important way to distinguish quantumness from classical behaviour. We studied ELGI using a two-qubit NMR system and the experimental results showed a clear violation of ELGI by over four standard deviations. In section 4.2, I describe our experiments on retrieving joint probabilities by inversion of moments. Further, we studied sequential measurements of a single quantum system and investigated their moments and joint probabilities [2] and demonstrated that the moments and the probabilities are inconsistent with each other. The NOON state is a special multiple-quantum coherence that can be prepared easily using a star-topology spin-system. In chapter 5, I describe two important application of such systems: (i) measuring translational di ffusion constants in liquids and (ii) quantitative characterization of radio-frequency (RF) inhomogeneity of NMR probes. When compared with the standard single quantum method, the NOON state method requires shorter diff usion delays or weaker pulsed-field-gradients. Similarly, Torrey oscillations with NOON states decay at a faster rate than that of single quantum coherences and allow accurate characterization of RF inhomogeneity at higher RF powers. Chapter 6, contains an experimental study of the e fficiency of various dynamical decoupling sequences for suppressing decoherence of single as well as multiple quantum coherences (MQC) on large spin-clusters. The system involved crystallites of a powdered sample containing a large number of molecular protons interacting via long-range inter molecular dipole-dipole interaction. We invoked single as well as MQC using this interaction followed by an application of various DD sequences namely CPMG, UDD, and RUDD. The experiments reveal superior performance of RUDD sequences in suppressing decoherence. We have also analysed performances of CPMG, UDD, and RUDD sequences used in our experimental study via filter function analysis. The analysis confirms superior performance of RUDD and hence supports our experimental results.