Towards a Scalable Quantum Computing Platform in the Ultrastrong Coupling Regime by Thi Ha Kyaw

Author:Thi Ha Kyaw
Language: eng
Format: epub
ISBN: 9783030196585
Publisher: Springer International Publishing

After interacting with the collective resonator modes, the system evolution operator takes the form [11] (see Appendix A for the detailed derivation).

(4.17)

where is the displacement operator associated with the th bosonic mode within the manifold . In addition, with , M stands for the number of degenerate bosonic modes , and the unitary . After the evolution time , we have performed the desired controlled-phase gate operation between the qubits

(4.18)

where . The resultant state incurs an extra global phase due to the presence of , which is unavoidable since it is formidable by construction to tune a desired qubit frequency, via the external flux , without affecting the longitudinal and transversal coupling strengths (see Fig. 4.3a and b). To achieve maximum gate fidelity, we require both and . That means the two coupling strengths need to satisfy . The operational gate time is estimated to be ns if the collective mode frequency is , which implies a ratio operating at the USC regime. As soon as the two qubits are entangled, they are immediately detuned from the resonant frequency so that we may repeat the same procedure for other qubit pairs to arrive at a specific quantum error-correcting code, be it the five-qubit code (see Fig. 4.5) or the Steane code (see Fig. 4.6).

Fig. 4.5The five-qubit cluster state in a ring geometry. Each qubit represented by is prepared in state, and each black bond represents a controlled-phase gate operation

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