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Bulletin of the American Physical Society

Floquet-engineered quantum state preparation in a noisy qubit

Eric Boyers, Mohit Pandey, David K Campbell, Anatoli Polkovnikov, Dries Sels, Alexander O. Sushkov

Published Mar 5, 2019• 0 citations
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Adiabatic evolution is a common strategy for manipulating quantum states and has been employed in diverse fields such as quantum simulation, computation, and annealing. However, adiabatic evolution is inherently slow and therefore susceptible to decoherence. Existing methods for speeding up adiabatic evolution require complex many-body operators or are difficult to construct for multilevel systems. Using the tools of Floquet engineering, we design a scheme for high-fidelity quantum state manipulation, utilizing only the interactions available in the original Hamiltonian. We apply this approach to a qubit and experimentally demonstrate its performance with the electronic spin of a nitrogen-vacancy center in diamond. Our Floquet-engineered protocol achieves state preparation fidelity of $0.994\ifmmode\pm\else\textpm\fi{}0.004$, on the same level as the conventional fast-forward protocol, but is more robust to external noise acting on the qubit. Floquet engineering provides a powerful platform for high-fidelity quantum state manipulation in complex and noisy quantum systems.
The conventional Floquet engineering scheme synthesizes a given target Hamiltonian with a deterministic temporal periodic driving field. In this work, we introduce the stochastic Floquet engineering scheme that can synthesize an arbitrary non-Hermitian target Hamiltonian using a time-periodic driving field with noisy amplitude. Our method is rooted in the Hermitian dynamics taking noise as a valuable quantum resource with no need for loss or gain in prior. We apply our method to engineer a cavity Hamiltonian with dissipative coupling between Fock states, and to prepare a given quantum state from a generally arbitrary quantum state. The stochastic Floqut engineering also provides a way to generate non-unitary quantum gates, which take advantage in certain tasks compared to unitary quantum computing, without the need for ancillae or state-dependent updating.
Counterdiabatic driving, which enforces adiabatic evolution in arbitrary timescales, can be realised by engineering a Floquet Hamiltonian which oscillates between the Hamiltonian and its derivative requiring no additional control terms. However, the coefficients of the Floquet Hamiltoinan require knowledge of the counterdiabatic terms, which can be difficult to derive outside of a limited set of examples. We introduce a new hybrid technique for the control of quantum systems, Counterdiabatic-influenced Floquet-engineering or CAFFEINE for short. CAFFEINE parameterises the Floquet Hamiltonian for counterdiabatic driving and utilises numerical quantum optimal control in order to obtain the desired target state. This removes the need to both obtain and implement counterdiabatic terms, however, it does require the ability to quickly oscillate each term in the Hamiltonian. If this oscillation is possible, then CAFFEINE provides a framework to implement quantum annealing protocols and general quantum state preparation. We illustrate this through optimisation of two numerical examples of preparing a Bell state with two qubits and performing annealing protocols for the one-dimensional Ising model. Beyond this, we also illustrate CAFFEINE's capabilities to learn the counterdiabatic terms, which can potentially be used as a probe of quantum chaos and the geometry of quantum dynamics.