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arXiv:2005.13062 · Physical Review Research

High-fidelity state transfer between leaky quantum memories

Daniel Soh, Eric Chatterjee, Matt Eichenfield

Published Jul 6, 2021• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevresearch.3.033027

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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.
Abstract In a quantum network, a key challenge is to minimize the direct reflection of flying qubits as they couple to stationary, resonator-based memory qubits, as the reflected amplitude represents state transfer infidelity that cannot be directly recovered. Optimizing the transfer fidelity can be accomplished by dynamically varying the resonator’s coupling rate to the flying qubit field. Here, we analytically derive the optimal coupling rate profile in the presence of intrinsic loss of the quantum memory using an open quantum systems method that can account for intrinsic resonator losses. We show that, since the resonator field must be initially empty, an initial amplitude in the resonator must be generated in order to cancel reflections via destructive interference; moreover, we show that this initial amplitude can be made sufficiently small as to allow the net infidelity throughout the complete transfer process to be close to unity. We then derive the time-varying resonator coupling that maximizes the state transfer fidelity as a function of the initial population and intrinsic loss rate, providing a complete protocol for optimal quantum state transfer between the flying qubit and resonator qubit. We present analytical expressions and numerical examples of the fidelities for the complete protocol using exponential and Gaussian profiles. We show that a state transfer fidelity of around 99.9% can be reached momentarily before the quantum information is lost due to the intrinsic loss in practical resonators used as quantum memories.
The realization of high-fidelity quantum control is crucial for quantum information processing, particularly in noisy environments where control strategies must simultaneously achieve precise manipulation and effective noise suppression. Conventional optimal control designs typically require numerical calculations of the system dynamics. Recent studies have demonstrated that long short-term memory neural networks (LSTM) can accurately predict the time evolution of open quantum systems. Based on LSTM predicted dynamics, we propose an optimal control framework for rapid and efficient optimal control design in open quantum systems. As illustrative examples, we apply the proposed framework to design optimal control for adiabatic speedup in a two-level system and for quantum state transfer in a spin chain, both under non-Markovian environments. For adiabatic speedup, our optimization procedure involves two steps: driving trajectory optimization and zero-area pulse optimization. Fidelity improvements for both steps have been obtained, demonstrating the effectiveness of the scheme. Furthermore, this effectiveness is validated for quantum state transfer in a spin chain, which is a high dimensional control problem. Our optimal control design scheme utilizes predicted dynamics to generate optimized controls, offering broad application potential in quantum computing, communication, and sensing.
We consider the transfer of continuous-variable entangled states in coupled oscillator chains embedded in a generic environment. We demonstrate high-fidelity transfer via optimal control in two configurations-a linear chain and an X-shaped chain. More specifically, we use the Krotov optimization algorithm to design control fields that achieve the desired state transfer. Under environmental memory effects, the Krotov algorithm needs to be modified, since the dissipative terms in non-Markovian dynamics are generally governed by the time-dependent system Hamiltonian. Remarkably, we can achieve high-fidelity transfer by simply tuning the frequencies of the oscillators while keeping the coupling strength constant, even in the presence of open-system effects. For the system under consideration, we find that quantum memory effects can aid in the transfer of entanglement and show improvement over the memoryless case. In addition, it is possible to target a range of entangled states, making it unnecessary to know the parameters of the initial state beforehand.
Quantum state transfer between distant nodes is essential for distributed quantum information processing. Existing protocols are typically optimized for specific coupling regimes, such as adiabatic dark-state transfer in the single-mode limit and pitch-and-catch schemes in the multimode regime, leaving the crossover between them without a simple and unified control strategy. Here we identify a minimal two-parameter control framework that enables high-fidelity quantum state transfer across this single-mode-to-multimode crossover in a multimode quantum channel. Using a pulse-shaped pitch-and-catch protocol controlled only by the pulse ramp rate and the emission-absorption delay, we achieve transfer fidelities exceeding 99.9%, extending pitch-and-catch protocols toward the single-mode limit without requiring dark-state protection or complex pulse design. We further demonstrate robustness against dissipation, disorder, detuning, and imperfect initialization under experimentally realistic conditions. These results provide a simple and broadly applicable framework for state transfer in multimode quantum channels, with relevance to circuit-QED and hybrid quantum-acoustic systems.
Quantum state transfer between distant nodes is at the heart of quantum processing and quantum networking. Stimulated by this, we propose a scheme where one can achieve quantum state transfer with a high fidelity between sites in a cavity quantum optomechanical network. In our lattice, each individual site is composed of a localized mechanical mode which interacts with a laser-driven cavity mode via radiation pressure, while photons hop between neighboring sites. After diagonalization of the Hamiltonian of each cell, we show that the system can be reduced to an effective Hamiltonian of two decoupled bosonic chains, and therefore we can apply the well-known results in quantum state transfer together with an additional condition on the transfer times. In fact, we show that our transfer protocol works for any arbitrary joint quantum state of a mechanical and an optical mode. Finally, in order to analyze a more realistic scenario we take into account the effects of independent thermal reservoirs for each site. By solving the standard master equation within the Born-Markov approximation, we reassure both the effective model and the feasibility of our protocol.