This thesis focuses on implementing radio frequency (rf) reflectometry techniques for dispersive detection of charge and spin dynamics in nanoscale devices. I have investigated three aspects of rf reflectometry using state-of-the-art silicon (Si) complementary metal-oxide-semiconductor (CMOS) nanowire field effect transistors (NWFETs). First, a high-sensitivity capacitive gate-based charge sensor is developed by optimising the external matching circuit to detect capacitive changes in the high frequency resonator. A new circuit topology is used where superconducting niobium nitride (NbN) inductor is connected in parallel with a single-gate Si NWFET resulting in resonators with loaded Q-factors in the 400-800 range. For a resonator operating at 330 MHz, I have achieved a charge sensitivity of 7.7 $\mu e/\sqrt{\text{Hz}}$ and, when operating at 616 MHz, I get 1.3 $\mu e/\sqrt{\text{Hz}}$. This gate-based sensor can be used for fast, accurate and scalable techniques for quantum state readout in Si CMOS based quantum computing. Second, this new circuit topology for the resonator is used with a dual-gate Si NWFET. This dual-gate device geometry provides access to a double quantum dot (DQD) system in few electron regime. The spin-state of the two-electron DQD system is detected dispersively using Pauli spin blockade between joint singlet S(2,0) and triplet T$_-$(1,1) states in a finite magnetic field $B$. The singlet-triplet relaxation time $T_1$ at $B=4.5$~T is measured to be $\sim$1 ms using standard homodyne detection technique. Third, I expand the range of applications of gate-based sensing to accurate temperature measurements. I have experimentally demonstrated a primary thermometer by embedding a single-gate Si NWFET with the rf capacitive gate-based sensor. The thermometer, termed as gate-based electron thermometer (GET), relies on cyclic electron tunneling between discrete energy levels of a quantum dot and a single electron reservoir in the NWFET. I have found that the full-width-half-maximum (FWHM) of the resonator phase response depends linearly with temperature via well known physical law by using the ratio $k_\text{B}/e$ between the Boltzmann constant and the electron charge. The GET is also found to be magnetic field independent like other primary thermometers such as Coulomb blockade and shot noise thermometers.

acase@tulane.edu / In this dissertation we test our ability to implement linear entangling operations between small numbers of photons for application in quantum communication and computation. We begin by presenting a fast and highly parallelizable numerical algorithm for simulating linear optical circuits on classical hardware. Then, we apply this algorithm to three independent topics in quantum information: First, in Chapter 2, we determine the information capacity of an optical quantum channel and show that a linear encoding is generally sufficient to achieve this capacity. In Chapter 3 we introduce a computational encoding basis wherein qubits are stored in single-photon blocks and then test our ability to apply entangling operations between blocks. Finally, in Chapter 4, we use our algorithm to make progress in the long-standing problem of designing a near-perfect optical Bell state analyzer. We find a clear trend in state distinguishability as we incorporate unentangled pairs of ancilla photons. We also prove that if a measurement outcome in which all photons are bunched into only two output modes is possible, then perfect state discrimination is impossible. We then present a set of conditions that prevent this outcome. / 1 / Jake A Smith

This work presents Quantum Predicative Programming --- a theory ofquantum programming that encompasses many aspects of quantum computation and quantum communication. The theory provides a methodology to specify, implement, and analyse quantum algorithms, the paradigm of quantum non-locality, quantum pseudotelepathy games, computing with mixed states, and quantum communication protocols that use both quantum and classical communication channels.

This work presents Quantum Predicative Programming --- a theory ofquantum programming that encompasses many aspects of quantum computation and quantum communication. The theory provides a methodology to specify, implement, and analyse quantum algorithms, the paradigm of quantum non-locality, quantum pseudotelepathy games, computing with mixed states, and quantum communication protocols that use both quantum and classical communication channels.

This thesis describes the deployment of a free-space quantum key distribution system across the University of Waterloo campus. The quantum key distribution system has the ability to provide unconditionally secure communication between two parties: Alice and Bob. The system exploits the quantum mechanical property of entanglement in order to generate a key. Security is then guaranteed by the No-Cloning theorem and the laws of quantum mechanics which prevent a quantum system from being measured without disturbing it. Polarization-entangled photon pairs are created using the non-linear optical process of type-II spontaneous parametric down-conversion. A free-space link of approximately $\mathrm{580~m}$ is used to distribute one-half of the pairs to Alice at a distant location, while the other half of the pairs are locally detected by Bob. The details of the detection apparatus necessary to measure the polarization of the photons and the software used to process the measurement data according to the BBM92 protocol are described. An experimental violation of the CHSH inequality (a derivative of the original Bell inequality) is demonstrated to show that polarization-entangled photon pairs are in fact being distributed to the two parties. Finally, the full BBM92 protocol is performed using the entangled photon pairs to generate a secure key and transmit an encrypted message between Alice and Bob. Currently, the system can only be operated at night because background light saturates the detectors during the day; however, future work will focus on making daylight operation feasible.

This dissertation addresses the issue of noise in quantum information processing devices. It is common knowledge that quantum states are particularly fragile to the effects of noise. In order to perform scalable quantum computation, it is necessary to suppress effective noise to levels which depend on the size of the computation. Various theoretical proposals have discussed how this can be achieved, under various assumptions about properties of the noise and the availability of qubits. We discuss new approaches to the suppression of noise, and propose experimental protocols characterizing the noise. In the first part of the dissertation, we discuss a number of applications of teleportation to fault-tolerant quantum computation. We demonstrate how measurement-based quantum computation can be made inherently fault-tolerant by exploiting its relationship to teleportation. We also demonstrate how continuous variable quantum systems can be used as ancillas for computation with qubits, and how information can be reliably teleported between these different systems. Building on these ideas, we discuss how the necessary resource states for teleportation can be prepared by allowing quantum particles to be scattered by qubits, and investigate the feasibility of an implementation using superconducting circuits. In the second part of the dissertation, we propose scalable experimental protocols for extracting information about the noise. We concentrate on information which has direct practical relevance to methods of noise suppression. In particular, we demonstrate how standard assumptions about properties of the noise can be tested in a scalable manner. The experimental protocols we propose rely on symmetrizing the noise by random application of unitary operations. Depending on the symmetry group use, different information about the noise can be extracted. We demonstrate, in particular, how to estimate the probability of a small number of qubits being corrupted, as well as how to test for a necessary condition for noise correlations. We conclude by demonstrating how, without relying on assumptions about the noise, the information obtained by symmetrization can also be used to construct protective encodings for quantum states.

This thesis describes a linear-optical device for performing generalized quantum measurements on quantum bits (qubits) encoded in photon polarization, the implementation of said device, and its use in two diff erent but related experiments. The device works by coupling the polarization degree of freedom of a single photon to a `mode' or `path' degree of freedom, and performing a projective measurement in this enlarged state space in order to implement a tunable four-outcome positive operator-valued measure (POVM) on the initial quantum bit. In both experiments, this POVM is performed on one photon from a two-photon entangled state created through spontaneous parametric down-conversion. In the fi rst experiment, this entangled state is viewed as a two-qubit photonic cluster state, and the POVM as a means of increasing the computational power of a given resource state in the cluster-state model of quantum computing. This model traditionally achieves deterministic outputs to quantum computations via successive projective measurements, along with classical feedforward to choose measurement bases, on qubits in a highly entangled resource called a cluster state; we show that `virtual qubits' can be appended to a given cluster by replacing some projective measurements with POVMs. Our experimental demonstration fully realizes an arbitrary three-qubit cluster computation by implementing the POVM, as well as fast active feed-forward, on our two-qubit photonic cluster state. Over 206 diff erent computations, the average output delity is 0.9832 +/- 0.0002; furthermore the error contribution from our POVM device and feedforward is only of order 10^-3, less than some recent thresholds for fault-tolerant cluster computing. In the second experiment, the POVM device is used to implement a deterministic protocol for remote state preparation (RSP) of arbitrary photon polarization qubits. RSP is the act of preparing a quantum state at a remote location without actually transmitting the state itself. We are able to remotely prepare 178 diff erent pure and mixed qubit states with an average delity of 0.995. Furthermore, we study the the fidelity achievable by RSP protocols permitting only classical communication, without shared entanglement, and compare the resulting benchmarks for average fidelity against our experimental results. Our experimentally-achieved average fi delities surpass the classical thresholds whenever classical communication alone does not trivially allow for perfect RSP.

This thesis describes the deployment of a free-space quantum key distribution system across the University of Waterloo campus. The quantum key distribution system has the ability to provide unconditionally secure communication between two parties: Alice and Bob. The system exploits the quantum mechanical property of entanglement in order to generate a key. Security is then guaranteed by the No-Cloning theorem and the laws of quantum mechanics which prevent a quantum system from being measured without disturbing it. Polarization-entangled photon pairs are created using the non-linear optical process of type-II spontaneous parametric down-conversion. A free-space link of approximately $\mathrm{580~m}$ is used to distribute one-half of the pairs to Alice at a distant location, while the other half of the pairs are locally detected by Bob. The details of the detection apparatus necessary to measure the polarization of the photons and the software used to process the measurement data according to the BBM92 protocol are described. An experimental violation of the CHSH inequality (a derivative of the original Bell inequality) is demonstrated to show that polarization-entangled photon pairs are in fact being distributed to the two parties. Finally, the full BBM92 protocol is performed using the entangled photon pairs to generate a secure key and transmit an encrypted message between Alice and Bob. Currently, the system can only be operated at night because background light saturates the detectors during the day; however, future work will focus on making daylight operation feasible.

This dissertation addresses the issue of noise in quantum information processing devices. It is common knowledge that quantum states are particularly fragile to the effects of noise. In order to perform scalable quantum computation, it is necessary to suppress effective noise to levels which depend on the size of the computation. Various theoretical proposals have discussed how this can be achieved, under various assumptions about properties of the noise and the availability of qubits. We discuss new approaches to the suppression of noise, and propose experimental protocols characterizing the noise. In the first part of the dissertation, we discuss a number of applications of teleportation to fault-tolerant quantum computation. We demonstrate how measurement-based quantum computation can be made inherently fault-tolerant by exploiting its relationship to teleportation. We also demonstrate how continuous variable quantum systems can be used as ancillas for computation with qubits, and how information can be reliably teleported between these different systems. Building on these ideas, we discuss how the necessary resource states for teleportation can be prepared by allowing quantum particles to be scattered by qubits, and investigate the feasibility of an implementation using superconducting circuits. In the second part of the dissertation, we propose scalable experimental protocols for extracting information about the noise. We concentrate on information which has direct practical relevance to methods of noise suppression. In particular, we demonstrate how standard assumptions about properties of the noise can be tested in a scalable manner. The experimental protocols we propose rely on symmetrizing the noise by random application of unitary operations. Depending on the symmetry group use, different information about the noise can be extracted. We demonstrate, in particular, how to estimate the probability of a small number of qubits being corrupted, as well as how to test for a necessary condition for noise correlations. We conclude by demonstrating how, without relying on assumptions about the noise, the information obtained by symmetrization can also be used to construct protective encodings for quantum states.

This thesis describes a linear-optical device for performing generalized quantum measurements on quantum bits (qubits) encoded in photon polarization, the implementation of said device, and its use in two diff erent but related experiments. The device works by coupling the polarization degree of freedom of a single photon to a `mode' or `path' degree of freedom, and performing a projective measurement in this enlarged state space in order to implement a tunable four-outcome positive operator-valued measure (POVM) on the initial quantum bit. In both experiments, this POVM is performed on one photon from a two-photon entangled state created through spontaneous parametric down-conversion. In the fi rst experiment, this entangled state is viewed as a two-qubit photonic cluster state, and the POVM as a means of increasing the computational power of a given resource state in the cluster-state model of quantum computing. This model traditionally achieves deterministic outputs to quantum computations via successive projective measurements, along with classical feedforward to choose measurement bases, on qubits in a highly entangled resource called a cluster state; we show that `virtual qubits' can be appended to a given cluster by replacing some projective measurements with POVMs. Our experimental demonstration fully realizes an arbitrary three-qubit cluster computation by implementing the POVM, as well as fast active feed-forward, on our two-qubit photonic cluster state. Over 206 diff erent computations, the average output delity is 0.9832 +/- 0.0002; furthermore the error contribution from our POVM device and feedforward is only of order 10^-3, less than some recent thresholds for fault-tolerant cluster computing. In the second experiment, the POVM device is used to implement a deterministic protocol for remote state preparation (RSP) of arbitrary photon polarization qubits. RSP is the act of preparing a quantum state at a remote location without actually transmitting the state itself. We are able to remotely prepare 178 diff erent pure and mixed qubit states with an average delity of 0.995. Furthermore, we study the the fidelity achievable by RSP protocols permitting only classical communication, without shared entanglement, and compare the resulting benchmarks for average fidelity against our experimental results. Our experimentally-achieved average fi delities surpass the classical thresholds whenever classical communication alone does not trivially allow for perfect RSP.