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arXiv:2402.12807

Principle of least action for quasi-adiabatic state transfers with dissipation

Si Luo, Yinan Fang, Ying-Dan Wang, Stefano Chesi

Published Feb 20, 2024• 1 citation
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Abstract

We discuss a general formalism to optimize quasi-adiabatic state-transfer protocols, where high fidelity is achieved by maintaining the system in a dark subspace protected from the dominant dissipative channels. We cast the residual fidelity loss, induced by a combination of dissipation and non-adiabatic transitions, in the form of a classical action where the time-dependent control parameters act as coordinates. This allows us to apply the least action principle, yielding the fidelity upper-bound and the corresponding optimal transfer time. As an application, we analyze a system of two qubits subject to weak relaxation and dephasing, interacting through a strongly dissipative quantum bus. In this case, our formalism, we obtain a full characterization of the optimal state-transfer fidelity.

DOI
10.48550/arxiv.2402.12807

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We discuss a general formalism to optimize quasi-adiabatic state-transfer protocols, where high fidelity is achieved by maintaining the system in a dark subspace protected from the dominant dissipative channels. We cast the residual fidelity loss, induced by a combination of dissipation and non-adiabatic transitions, in the form of a classical action where the time-dependent control parameters act as coordinates. This allows us to apply the least action principle, yielding the fidelity upper-bound and the corresponding optimal transfer time. As an application, we analyze a system of two qubits subject to weak relaxation and dephasing, interacting through a strongly dissipative quantum bus. In this case, our formalism, we obtain a full characterization of the optimal state-transfer fidelity.
We quantify the influence of non-adiabatic leakage and system dissipation on the transfer fidelity with generic counter-intuitive pulses. By including the dissipation of all the parties, we find that the competition between non-adiabaticity and decoherence leads to an upper bound of the transfer fidelity. Using a systematic expansion valid in the desired high-fidelity limit, we derive the upper bound as a simple function of the system cooperativity. This approach also indicates how to reach the upper bound efficiently. Our results are widely applicable to quantum state engineering and are particularly significant for solid-state devices, which typically have non-negligible dissipation of the source and target systems.
Abstract We propose and analyze a robust quantum state transfer protocol through a scalable quantum data bus that consists of a network of controlled dissipative modules. In particular, we first demonstrate the ability to achieve perfect state transfer between two distinct quantum sites which are adiabatically coupled to the data bus in non-dissipative situation. We then consider the role of dissipation in adiabatic quantum state transfer via using Born–Markov master equation in the standard Lindblad form. Numerical simulation shows that the dissipation effect on the quality of transmission can be suppressed by engineering the network couplings of data bus properly.
Employing the scattering-Lindblad-Hamiltonian formalism description of quantum network theory, we model the general problem of quantum state transfer between two disparate quantum memory blocks in an open quantum system. We derive an analytical expression for the fidelity of quantum state transfer between the memory blocks under the action of a specific phase space trajectory for each of the relevant classical control fields. We find a set of trajectories that maximize the state transfer fidelity between asymmetric systems. We show that, for the example where the mechanical modes of two optomechanical oscillators act as the quantum memory blocks, their optical modes and a waveguide channel connecting them can be used to achieve a quantum state transfer fidelity of 96% with realistic parameters using our optimal control solution. The effects of the intrinsic losses and the asymmetries in the physical memory parameters are discussed quantitatively.
As quantum-computing platforms are susceptible to noise, the fidelity of quantum operations is limited by decoherence. Understanding this limitation is crucial for building utility-scale quantum processors. In previous works [Phys. Rev. Lett. 129, 150504 (2022); Quantum 9, 1684 (2025)], we presented analytical formulae for the average gate fidelity of multi-qubit operations under static Markovian noise processes, including operations that temporarily leave the computational subspace. However, some quantum-computing architectures dynamically modulate qubit or coupler frequencies to implement two-qubit gates, e.g., baseband flux gates; such modulation can lead to dissipation rates varying in time. In this Letter, we therefore generalize the fidelity-reduction formulae to encompass time-dependent dissipation. Applying our generalized formula, we obtain a fidelity bound for adiabatic operations and demonstrate that flux-dependent noise sensitivity, combined with qubit-coupler hybridization, significantly reduces the fidelity of adiabatic controlled-Z (CZ) gates in superconducting quantum computers. Our work thus provides essential theoretical tools for evaluating error budgets and optimizing the design of quantum operations in tunable quantum-computing architectures, and may also find applications in quantum-sensing and quantum-communication protocols that are affected by time-dependent dissipation.
Efficient adiabatic control schemes, where one steers a quantum system along an adiabatic path ensuring minimal excitations while achieving a desired final state, that enable fast, high-fidelity operations are essential for any practical quantum computation. However, current optimization protocols are not universally tractable due to stringent requirements imposed by the microscopic systems encoding the qubit, including complex energy level structures and unwanted transitions, and generally require a trade-off between speed and fidelity of the operation. Here, we address these challenges by developing a general framework for optimal control based on the quantum metric tensor. This framework allows for fast and high-fidelity adiabatic pulses, even for a dense energy spectrum, based solely on the Hamiltonian of the system instead of the time evolution propagator and independent of the size of the underlying Hilbert space. Furthermore, our framework suppresses diabatic transitions and state-dependent crosstalk effects without the need for additional control fields. As an example, we study the adiabatic charge transfer in a double quantum dot to find optimal control pulses with improved performance. We show that for the geometric protocol, the transfer fidelities are lower bounded F>99%\mathcal{F}>99\%F>99% for ultrafast $20~\mbox{ns}$ pulses, regardless of the size of the anti-crossing, while being robust against miscalibration errors and quasistatic noise.
We put forth a hitherto unexplored control strategy that enables high-fidelity fast transport of an unstable quantum wavepacket even in the presence of bath-induced dissipation. The wavepacket, which is confined within any shallow (anharmonic) potential trap is steered in acceleration, so as to maximize the transfer fidelity. This strategy can generally optimize any non-Markovian bath-dressed continuous-variable system dynamics. It can simultaneously cope with wavepacket leakage via non-adiabatic transitions and bath-induced dissipation in an optimal fashion. It can outperform methods based on counterdiabatic fields (shortcuts to adiabaticity) particularly for fast non-adiabatic transport. Transport fidelity is maximized even for trajectories exceeding the speed of bath-excitation propagation, e.g., for supersonic transfer through phonon baths. This general approach is illustrated for optimized transfer of impurities in Bose-Einstein condensates. It is applicable to both dissipative and non-dissipative transfer of trapped atoms and ions and molecular reaction products.