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arXiv:cond-mat/0204153 · Quantum Information Processing

Quantum Codes for Simplifying Design and Suppressing Decoherence in Superconducting Phase-Qubits

Daniel A. Lidar, Lian-Ao Wu, Alexandre Blais

Published Jun 1, 2002• 15 citations
arXivHTMLPDF
DOI
10.1023/a:1019821008131

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This dissertation presents a theoretical analysis of protocols relevant for quantum information processing with superconducting qubits. The purpose of these protocols is decoherence suppression and quantum information transfer. Our analysis makes use of the standard density matrix formalism and Kraus operator (operator-sum) representation of quantum operations. We also use the mathematical trick of unravelling continuous evolution into discrete scenarios with corresponding probabilities.We show that decoherence due to zero-temperature energy relaxation can be almost completely suppressed, probabilistically, by weak measurement reversal (also known as quantum uncollapsing). To protect a qubit, a weak (partial) quantum measurement moves it towards the ground state, where it is kept during the storage period, while the second partial measurement restores the initial state. This procedure preferentially selects the cases without energy decay events. Stronger decoherence suppression requires smaller selection probability; a desired point in this trade-off can be chosen by varying the measurement strength.We also analyze several simple quantum error correction (QEC) and quantum error detection (QED) protocols, relevant to superconducting qubits. We show that for energy relaxation the repetitive N-qubit quantum codes cannot be used for QEC, but can be used for QED (also known as probabilistic error correction). Moreover, the repetitive code with only two qubits is sufficient for QED. We also present several other two-qubit algorithms realizable with the current technology of superconducting phase qubits; these algorithms can demonstrate QEC for intentional errors and QED for real decoherence.We also analyze a procedure designed to transfer the state of a microwave qubit from one superconducting resonator to another resonator via a transmission line; the emission and capture of the microwave energy is achieved using tunable couplers. The procedure is shown to be robust against experimental imperfections of required pulse shapes. Our results also indicate that a successful state transfer requires nearly equal resonator frequencies for the entire duration of the procedure.
The design of coupler-based superconducting two-qubit gates simplifies circuit layout and alleviate frequency crowding, thereby enhancing the scalability and flexibility of quantum chips. However, in such architectures, a trade-off often exists between suppressing crosstalk and reducing gate duration, and how to achieve synergistic optimization of both remains an open challenge. To address this, this paper proposes a coupler-assisted superconducting two-qubit geometric gate scheme oriented towards crosstalk robustness. By introducing additional parametric degrees of freedom, the scheme steers the system evolution along desired trajectories, thereby flexibly avoiding crosstalk-sensitive operational regions. Numerical simulations demonstrate that the proposed scheme can effectively suppress crosstalk errors while enabling fast gate operations, and exhibits strong robustness against typical experimental imperfections such as qubit frequency drift. Moreover, even when accounting for unavoidable high-frequency oscillation terms and qubit decoherence in realistic physical systems, our crosstalk-robust two-qubit geometric gates still achieve high fidelity. This work provides a feasible pathway toward robust and efficient two-qubit gate implementation in superconducting quantum computation.