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arXiv:2107.12253 · Physical Review Research

Reservoir-engineering shortcuts to adiabaticity

Raphaël Menu, Josias Langbehn, Christiane P. Koch, Giovanna Morigi

Published Jul 5, 2022• 12 citations
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Abstract

We propose a protocol that achieves fast adiabatic transfer between two orthogonal states of a qubit by coupling with an ancilla. The qubit undergoes Landau-Zener dynamics, whereas the coupling realizes a time-dependent Hamiltonian, which is diagonal in the spin's instantaneous Landau-Zener eigenstates. The ancilla (or meter), in turn, couples to a thermal bath such that the overall dynamics is incoherent. We analyze the protocol's fidelity as a function of the strength of the coupling and of the relaxation rate of the meter. When the meter's decay rate is the largest frequency scale of the dynamics, the spin dynamics is encompassed by a master equation describing dephasing of the spin in the instantaneous eigenbasis. In this regime, the fidelity of adiabatic transfer improves as the bath temperature is increased. Surprisingly, the adiabatic transfer is significantly more efficient in the opposite regime, where the timescale of the ancilla dynamics is comparable to the characteristic spin timescale. Here, for low temperatures the coupling with the ancilla tends to suppress diabatic transitions via effective cooling. The protocol can be efficiently implemented by means of a pulsed, stroboscopic coupling with the ancilla and is robust against moderate fluctuations of the experimental parameters.

DOI
10.1103/physrevresearch.4.033005

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We propose a protocol that achieves fast adiabatic transfer between two orthogonal states of a qubit by coupling with an ancilla. The qubit undergoes Landau-Zener dynamics, whereas the coupling realizes a time-dependent Hamiltonian, which is diagonal in the spin's instantaneous Landau-Zener eigenstates. The ancilla (or meter), in turn, couples to a thermal bath such that the overall dynamics is incoherent. We analyze the protocol's fidelity as a function of the strength of the coupling and of the relaxation rate of the meter. When the meter's decay rate is the largest frequency scale of the dynamics, the spin dynamics is encompassed by a master equation describing dephasing of the spin in the instantaneous eigenbasis. In this regime, the fidelity of adiabatic transfer improves as the bath temperature is increased. Surprisingly, the adiabatic transfer is significantly more efficient in the opposite regime, where the timescale of the ancilla dynamics is comparable to the characteristic spin timescale. Here, for low temperatures the coupling with the ancilla tends to suppress diabatic transitions via effective cooling. The protocol can be efficiently implemented by means of a pulsed, stroboscopic coupling with the ancilla and is robust against moderate fluctuations of the experimental parameters.
The realization of quantum adiabatic dynamics is at the core of implementations of adiabatic quantum computers. One major issue is to efficiently compromise between the long time scales required by the adiabatic protocol and the detrimental effects of the environment, which set an upper bound to the time scale of the operation. In this work we propose a protocol which achieves fast adiabatic dynamics by coupling the system to an external environment by the means of a quantum-non-demolition (QND) Hamiltonian. We analyse the infidelity of adiabatic transfer for a Landau-Zener problem in the presence of QND measurement, where the qubit couples to a meter which in turn quickly dissipates. We analyse the protocol's fidelity as a function of the strength of the QND coupling and of the relaxation time of the meter. In the limit where the decay rate of the ancilla is the largest frequency scale of the dynamics, the QND coupling induces an effective dephasing in the adiabatic basis. Optimal conditions for adiabaticity are found when the coupling with the meter induces dissipative dynamics which suppresses unwanted diabatic transitions.
We analyze the efficiency of protocols for adiabatic quantum state transfer assisted by an engineered reservoir. The target dynamics is a quantum trajectory in the Hilbert space and is a fixed point of a time-dependent master equation in the limit of adiabatic dynamics. We specialize to quantum state transfer in a qubit and determine the optimal schedule for a class of time-dependent Lindblad equations. The speed limit on state transfer is extracted from a physical model of a qubit coupled to a reservoir, from which the Lindblad equation is derived in the Born-Markov limit. Our analysis shows that the resulting efficiency is comparable to the efficiency of the optimal unitary dynamics. Numerical studies indicate that reservoir-engineered protocols could outperform unitary protocols outside the regime of the Born-Markov master equation, namely, when correlations between the qubit and reservoir become relevant. Our study contributes to the theory of shortcuts to adiabaticity for open quantum systems and to the toolbox of protocols of the NISQ era.
The need for fast and robust quantum state transfer is an essential element in scalable quantum information processing, leading to widespread interest in shortcuts to adiabaticity for speeding up adiabatic quantum protocols. However, shortcuts to adiabaticity for systems with more than a few levels is occasionally challenging to compute in theory and frequently difficult to implement in experiments. In this paper, we develop a protocol for constructing shortcuts to adiabaticity through the multistate Landau-Zener approach and a stricter adiabatic condition. Importantly, our protocol only requires a few pieces of information about the energy spectrum and just adjusts the evolutionary rate of the system. It means that our protocol has broad applicability to theoretical models and does not require increasing the difficulty of the experiment. As examples, we apply our protocol to state transfer in the two-level Landau-Zener model, the non-Hermitian Su-Schrieffer-Heeger model, and the topological Thouless pump model and find that it can speed up the manipulation speed while remaining robust to Hamiltonian errors. Furthermore, based on the experimental friendliness of our findings, it can potentially be extended to many-body systems, dissipation cases, or Floquet processes. Overall, the proposed shortcut protocol offers a promising avenue for enhancing the efficiency and reliability of quantum state transfer protocols.
Based on shortcuts to adiabaticity and quantum Zeno dynamics, we present a protocol to implement quantum state transfer (QST) in a quantum spin-12\frac{1}{2}21​ chain. In the protocol, the complex Hamiltonian of an NNN-site system is simplified, and a simple effective Hamiltonian is present. It is shown that only the control of the coupling strengths between the boundary spins and the bulk spins are required for QST. Numerical simulations demonstrate that the protocol possesses high efficiency and is robust against the decay and the fluctuations of the control fields. The protocol might provide an alternative choice for transferring quantum states via spin chain systems.
Quantum adiabatic dynamics is the crucial element of adiabatic quantum computing and quantum annealing. Shortcuts to adiabaticity enable acceleration of the computational time by suppressing unwanted non-adiabatic processes with designed classical fields. Here, we consider quantum state transfer in the Landau-Zener model, which exemplifies the key elements of quantum adiabatic dynamics. We argue that non-adiabatic transitions can be suppressed by autonomous quantum dynamics, which involves coupling the Landau-Zener qubit to a second quantum system. By tuning the coupling strength, the composite quantum dynamics can reduce the probability of unwanted processes by more than two orders of magnitude. This is a prime example of control where the quantum properties of the control fields are key for implementing shortcuts to adiabaticity.
We propose an efficient qubit initialization protocol based on a dissipative environment that can be dynamically adjusted. Here the qubit is coupled to a thermal bath through a tunable harmonic oscillator. On-demand initialization is achieved by sweeping the oscillator rapidly into resonance with the qubit. This resonant coupling with the engineered environment induces fast relaxation to the ground state of the system, and a consecutive rapid sweep back to off resonance guarantees weak excess dissipation during quantum computations. We solve the corresponding quantum dynamics using a Markovian master equation for the reduced density operator of the qubit-bath system. This allows us to optimize the parameters and the initialization protocol for the qubit. Our analytical calculations show that the ground-state occupation of our system is well protected during the fast sweeps of the environmental coupling and, consequently, we obtain an estimate for the duration of our protocol by solving the transition rates between the low-energy eigenstates with the Jacobian diagonalization method. Our results suggest that the current experimental state of the art for the initialization speed of superconducting qubits at a given fidelity can be considerably improved.