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arXiv:2408.17035 · Quantum Information Processing

Realization of commonly used quantum gates using perturbed harmonic oscillator

Kumar Gautam, Tarun Kumar Rawat, Harish Parthasarathy, Navneet Sharma

Published Jul 6, 2015• 16 citations
arXivHTMLPDF
DOI
10.1007/s11128-015-1059-0

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In order to be able to study dissipation, the interaction between a single system and their environment was introduced in quantum mechanics. Master and quantum Langeving equations was derived. Moreover, decoherence has been studied using this approach. One of the most commonly used model in this research field is a single harmonic oscillator interacting with a reservoir. In this work we analytically solve this model, in the resonance case, using the evolution operator method. Then, we use this result to study a quantum coupler, which is a particular case where there are a finite number of harmonic oscillators interacting with the single one. After that, we focuses in the analisis of the conditional quantum dynamics of the quantum coupler (using the computational basis of two qubits) by choosing a proper interaction time. This conditional dynamics provides a realization of a new quantum phase gate, which we call the relative phase gate. To the best of our knowledge, this phase gate has not been previously defined or proposed.
We investigate an approach to universal quantum computation based on the modulation of longitudinal qubit-oscillator coupling. We show how to realize a controlled-phase gate by simultaneously modulating the longitudinal coupling of two qubits to a common oscillator mode. In contrast to the more familiar transversal qubit-oscillator coupling, the magnitude of the effective qubit-qubit interaction does not rely on a small perturbative parameter. As a result, this effective interaction strength can be made large, leading to short gate times and high gate fidelities. We moreover show how the gate infidelity can be exponentially suppressed with squeezing and how the entangling gate can be generalized to qubits coupled to separate oscillators. Our proposal can be realized in multiple physical platforms for quantum computing, including superconducting and spin qubits.