## Dissertations - ALL

9-27-2022

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Physics

Plourde, Britton

#### Subject Categories

Physics | Quantum Physics

#### Abstract

Superconducting qubits are one of the leading approaches being investigated for building a scalable quantum computer. In the presence of external noise and perturbations plus local microscopic fluctuations and dissipation in the qubit environment, arbitrary quantum states will decohere, leading to bit-flip and phase-flip errors of the qubit. In order to build a fault-tolerant quantum computer that can preserve and process quantum information in the presence of noise and dissipation, one must implement some form of quantum error correction. Stabilizer operations are at the heart of quantum error correction and are typically implemented in software-controlled entangling gates and measurements of groups of qubits. Alternatively, qubits can be designed so that the Hamiltonian includes terms that correspond directly to a stabilizer for protecting quantum information. In this thesis, we demonstrate such a hardware implementation of stabilizers in a superconducting circuit composed of chains of $\pi$-periodic Josephson elements called a plaquette. Each plaquette consists of a superconducting loop with two conventional Josephson junctions and two inductors. We study the phase dependence of the plaquette by incorporating it into a resonant multi-loop circuit and measuring the resonator's frequency as a function of the external magnetic flux through each loop. To demonstrate the implementation of stabilizers in the Hamiltonian we made a superconducting circuit composed of a chain of three plaquettes shunted by a large capacitor. We map out the multidimensional flux space of the device by using on-chip bias lines to tune the magnetic flux through the three plaquettes independently. We measure the flux and charge dependence of the device's energy levels with microwave spectroscopy. We compare these measurements with numerical modeling of the energy level spectrum and obtain good agreement between theory and experiment for the designed and fabricated device parameters. We observe a softening of the energy band dispersion with respect to flux that is exponential in the number of frustrated plaquettes, this corresponds to the device being protected against errors caused by dephasing due to flux noise. The large shunt capacitor suppresses tunneling between the qubit logical states, and thus protects the device against bit-flip errors. A future qubit based on this design will exhibit simultaneous protection against bit-flip and phase-flip errors leading to gate errors that are significantly improved over the current state of the art.

Open Access

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