Abstract
Continuous-variable (CV) systems are attracting increasing attention in the realization of universal quantum computation. Several recent experiments have shown the feasibility of using CV systems to, e.g., encode a qubit into a trapped-ion mechanical oscillator and perform logic gates [Nature 566, 513-517 (2019)]. The essential next step is to protect the encoded qubit from quantum decoherence, e.g., the motional decoherence due to the interaction between a mechanical oscillator and its environment. Here we propose a scheme to suppress quantum decoherence of a single-mode harmonic oscillator used to encode qubits by introducing a nonperturbative leakage elimination operator (LEO) specifically designed for this purpose. Remarkably, our nonperturbative LEO can be used to analytically derive exact equations of motion without approximations. It also allows us to prove that the effectiveness of these LEOs only depends on the integral of the pulse sequence in the time domain, while details of the pulse shape does not make a significant difference when the time period is chosen appropriately. This control method can be applied to a system at an arbitrary temperature and arbitrary system-bath coupling strength which makes it extremely useful for general open quantum systems.
Highlights
Decoherence, which is inevitable due to the coupling with the surrounding environment, is regarded as the main barrier to modern quantum technologies such as quantum computing
We propose a scheme to suppress quantum decoherence of a single-mode harmonic oscillator used to encode qubits by introducing a nonperturbative leakage elimination operator (LEO) designed for this purpose
We have found leakage elimination operators that suppress the decoherence of a single-mode harmonic oscillator coupled to a reservoir of many independent oscillators
Summary
Decoherence, which is inevitable due to the coupling with the surrounding environment, is regarded as the main barrier to modern quantum technologies such as quantum computing. An openloop quantum control method called dynamical decoupling, originating from the spin-echo effect in nuclear magnetic resonance experiments [3,4], provides a universal and effective method in suppressing decoherence The quantum control theory based on leakage elimination operation has remained out of reach for continuous-variable (CV) systems, such as a harmonic oscillator
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