A number of superconducting qubits, such as the transmon or the phase qubit, have an energy level structure with small anharmonicity. This allows for convenient access of higher excited states with similar frequencies. However, special care has to be taken to avoid unwanted higher-level populations when using short control pulses. Here we demonstrate the preparation of arbitrary three level superposition states using optimal control techniques in a transmon. Performing dispersive readout, we extract the populations of all three levels of the qutrit and study the coherence of its excited states. Finally we demonstrate full quantum state tomography of the prepared qutrit states and evaluate the fidelities of a set of states, finding on average 95%.
A number of superconducting qubits, such as the transmon or the phase qubit, have an energy level structure with small anharmonicity. This allows for convenient access of higher excited states with similar frequencies. However, special care has to be taken to avoid unwanted higher-level populations when using short control pulses. Here we demonstrate the preparation of arbitrary three level superposition states using optimal control techniques in a transmon. Performing dispersive readout, we extract the populations of all three levels of the qutrit and study the coherence of its excited states. Finally we demonstrate full quantum state tomography of the prepared qutrit states and evaluate the fidelities of a set of states, finding on average 95%.
This dissertation describes research to coherently control quantum states of superconducting devices. In the first project, the state of an 8 GHz 3D superconducting Al cavity at 20mK was manipulated to add a quantum of excitation. Preparing a harmonic resonator in a state with a well-defined number of excitations (Fock states) is not possible using one external classical drive. I generated Fock states by transferring a single excitation from a 5.5 GHz transmon qubit to a cavity using Stimulated Raman Adiabatic Passage (STIRAP). I also extended the STIRAP technique to put the cavity in higher Fock states, superpositions of Fock states, and Bell states between the qubit and the cavity. Master-equation simulations of the system’s density matrix were in good agreement with the data, and I obtained estimated fidelities of 89%, 68% and 43% for the first three Fock states, respectively. The second project involved implementing an entangling gate between two Al/AlOx/Al transmon qubits that were mounted in an Al cavity and cooled to 20mK. Pertinent system frequencies were as follows: one qubit was at 6.0 GHz, the other qubit at 6.8 GHz, the cavity at 7.7 GHz, and the qubit-qubit dispersive shift was -1MHz. By applying a specially-shaped pulse of duration tg = 907ns, I implemented a generalized CNOT gate using an all-microwave technique known as Speeding up Waveforms by Inducing Phases to Harmful Transitions (SWIPHT). Using quantum process tomography, I found that the gate fidelity was 80%–82%, close to the 87% fidelity expected from decoherence in the transmons during the gate time. Details of the device fabrication, device characterization, measurement techniques, and extensive modeling of device behavior are presented, along with chi-matrix characterization of single-qubit gates and SWIPHT gates.
Spin-1 systems, in comparison to spin-21 systems, offer a better security for encoding and transferring quantum information, primarily due to their larger Hilbert spaces. Superconducting artificial atoms possess multiple energy levels, thereby being capable of emulating higher-spin systems. Here I consider a one-dimensional lattice of nearest-neighbor-coupled superconducting transmon systems, and devise a scheme to transfer an arbitrary qutrit state (a state encoded in a three-level quantum system) across the chain. I assume adjustable couplings between adjacent transmons, derive an analytic constraint for the control pulse, and show how to satisfy the constraint to achieve a high-fidelity state transfer under current experimental conditions. My protocol thus enables enhanced quantum communication and information processing with promising superconducting qutrits.
We characterize control of a qutrit implemented in the lowest three energy levels of a capacitively shunted flux-biased superconducting circuit.Randomized benchmarking over the qutrit Clifford group yields an average fidelity of 98.89 ± 0.05%.For a selected subset of the Clifford group, we perform quantum process tomography and observe the behavior of repeated gate sequences.Each qutrit gate is generated using only two-state rotations via a method applicable to any unitary.We find that errors are due primarily to decoherence and have a significant contribution from level shifts.This work demonstrates high-fidelity qutrit control and outlines avenues for future work on the optimal control of superconducting qudits.
We have observed the Autler-Townes doublet in a superconducting Al/AlOX/Al transmon qubit that acts as an artificial atom embedded in a three-dimensional Cu microwave cavity at a temperature of 22 mK. Using pulsed microwave spectroscopy, the three lowest transmon levels are isolated, eliminating unwanted effects of higher qubit modes and cavity modes. The long coherence time ($\ensuremath{\sim}$$40\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{s}$) of the transmon enables us to observe a clear Autler-Townes splitting at drive amplitudes much smaller than the transmon level anharmonicity (177 MHz). Three-level density matrix simulations with no free parameters provide excellent fits to the data. At maximum separation, the fidelity of a dark state achieved in this experiment is estimated to be 99.6.
Abstract In quantum mechanics, although the no‐cloning theorem forbids us to clone an arbitrary quantum state ideally, it is still possible to partially reproduce an unknown quantum state by using a phase cloning machine. Since the no‐cloning theorem guarantees the safety of quantum key distribution (QKD), resulting in the famous Bennett–Brassard 1984 (BB84) protocol, phase cloning of BB84 states increases the probability to eavesdrop the transmitted information between correspondents, forcing us to recheck the security of the QKD protocol. In this work, we realize an optimal phase cloning machine for BB84 states in a superconducting quantum bit (qubit). The lowest three energy levels in this system are exploited as logical qubits to demonstrate this cloning procedure. Two microwaves are used to prepare and clone the states. In order to achieve the maximum fidelity, we use the state tomography to readout the experimental results. It is found that the state information is well preserved during this cloning process. The average fidelity between input and output states is 83.92%, making this a valid quantum cloning machine.
The potential of superconducting qubits as the medium for a scalable quantum computer has motivated the pursuit of improved interactions within this system. Two challenges for the field of superconducting qubits are measurement fidelity, to accurately determine the state of the qubit, and the efficient transfer of quantum states. In measurement, the current state-of-the-art method employs dispersive readout, by coupling the qubit to a cavity and reading the resulting shift in cavity frequency to infer the qubit's state; however, this is vulnerable to Purcell relaxation, as well as being modeled off a simplified two-level abstraction of the qubit. In state transfer, the existing proposal for moving quantum states is mostly untested against non-idealities that will likely be present in an experiment. In this dissertation, we examine three problems within these two areas.We first describe a new scheme for fast and high-fidelity dispersive measurement specifically designed to circumvent the Purcell Effect. To do this, the qubit-resonator interaction is turned on only when the resonator is decoupled from the environment; then, after the resonator state has shifted enough to infer the qubit state, the qubit-resonator interaction is turned off before the resonator and environment are recoupled. We also show that the effectiveness of this ``Catch-Disperse-Release'' procedure partly originates from quadrature squeezing of the resonator state induced by the Jaynes-Cummings nonlinearity.The Catch-Disperse-Release measurement scheme treats the qubit as a two-level system, which is a common simplification used in theoretical works. However, the most promising physical candidate for a superconducting qubit, the transmon, is a multi-level system. In the second work, we examine the effects of including the higher energy levels of the transmon. Specifically, we expand the eigenstate picture developed in the first work to encompass multiple qubit levels, and examine the resulting changes to the system. In particular, we analyze the population of the non-target eigenstates as a result of this expanded model, and provide an analytical form for these deviations from the simpler model in Catch-Disperse-Release (i.e., the dressed state approximation).Lastly, we assess the robustness of the existing quantum state transfer protocol, testing its performance under typical experimental deviations from the ideal case. We show that the procedure is resilient to almost all non-idealities, except frequency mismatch between the two cavities. We also demonstrate a method to compensate for one such error in frequency-matching.