Geometric Phase of a Transmon in a Dissipative Quantum Circuit

Abstract

Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, we study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. We do so both for the case in which the evolution is unitary and when it is subjected to dissipative effects. These models offer a comprehensive quantum description of an anharmonic system interacting with a single mode of the electromagnetic field within a perfect or dissipative cavity, respectively. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment.

arXiv comment12 pages, 11 figures

References in corpus (34)

• Charge insensitive qubit design derived from the Cooper pair box
• Quantum state engineering with Josephson-junction devices
• Coherent control of macroscopic quantum states in a single-Cooper-pair box
• Circuit Quantum Electrodynamics
• Geometric quantum computation with NMR
• Fluxonium: single Cooper pair circuit free of charge offsets
• Geometric phases for mixed states in interferometry
• The Flux Qubit Revisited to Enhance Coherence and Reproducibility
• Non-adiabatic holonomic quantum computation
• Observation of Berry's Phase in a Solid State Qubit
• Experimental Realization of Non-Abelian Geometric Gates
• Kinematic approach to the mixed state geometric phase in nonunitary evolution
• Non-Adiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces
• Quantum logic gates for coupled superconducting phase qubits
• An experimental observation of geometric phases for mixed states using NMR interferometry
• Experimental implementation of universal nonadiabatic geometric quantum gates in a superconducting circuit
• Geometric phases for non-degenerate and degenerate mixed states
• Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit
• Multiplexed dispersive readout of superconducting phase qubits
• Vacuum induced Spin-1/2 Berry phase
• Transmon qubit readout fidelity at the threshold for quantum error correction without a quantum-limited amplifier
• Measurement scheme of the Berry phase in superconducting circuits
• Geometric phase with nonunitary evolution in presence of a quantum critical bath
• All-microwave leakage reduction units for quantum error correction with superconducting transmon qubits
• Connecting Berry's phase and the pumped charge in a Cooper pair pump
• A hardware-efficient leakage-reduction scheme for quantum error correction with superconducting transmon qubits
• Nonunitary geometric phases: a qubit coupled to an environment with random noise
• Geometric phases in superconducting qubits beyond the two-level-approximation
• Geometric quantum gates with superconducting qubits
• Measurement of a Vacuum-Induced Geometric Phase
• Cloaking a qubit in a cavity
• Corrections to the Berry phase in a solid-state qubit due to low-frequency noise
• Information Flow, Non-Markovianity and Geometric Phases
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness