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arXiv:2011.05667 · Journal of Physics A Mathematical and Theoretical

Optimal quantum transfer from input flying qubit to lossy quantum memory

Eric Chatterjee, Daniel Soh, Matt Eichenfield

Published Jan 27, 2022• 3 citations

Abstract

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.

DOI: 10.1088/1751-8121/ac4fa6

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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.

Existing optimal control methods of open quantum systems rely on extensive numerical simulations of the dynamics in the presence of a bath, or alternatively ignore the exact bath dynamics. If the bath effects are to be treated properly on both Markovian and non-Markovian timescales using numerical simulations, the number of bath modes cannot be large. This may affect the ability to simulate realistic scenarios. Even if realistic, such simulations are hard to interpret physically. An alternative approach advocated here is to resort to a perturbative analysis provided the system–bath coupling is weak. This analysis would allow for the effects of any given bath (finite or infinite, Markovian or non-Markovian) and any control at our disposal. This poses the challenge of constructing a method for the optimization of various operations requiring proper manipulation of the system, based on a general perturbative treatment to second order in the system–bath coupling. This proposed treatment yields a universal tool for optimizing the fidelity of a given operation. It involves a fidelity-control matrix: a construct that allows us to prioritize the use of available control resources so as to maximize the operation fidelity in any given bath. As an analytically solvable example of this general method, we analyse quantum state-transfer optimization, from a ‘noisy’ (write-in) qubit to its ‘quiet’ counterpart (storage qubit). Intriguing interplay is revealed between our ability to avoid bath-induced errors that profoundly depend on the bath-memory time and the limitations imposed by leakage out of the operational subspace. Counterintuitively, under no circumstances is the fastest transfer optimal (for a given transfer energy).

Recent progress in quantum technologies enables the fabrication of large-scale qubit arrays, but their optimal control remains challenging. In our work, we present a protocol for perfect quantum state transfer in a nearest-neighbor coupled chain of qubits, achieving maximal fidelity and minimal transfer time simultaneously. We apply the quantum brachistochrone method and obtain a protocol for the transfer of Fock and Bell states. Our solution reaches the fundamental quantum speed limit in the lattices with time-varying couplings.

Abstract We put forward a proposal to construct a quantum network using a hybrid cavity–magnonics system as with two nodes. At each node, a cascade of the quantum system consists of cavity–magnonics and magnonic–qubit interactions, and the quantum interface between the flying qubit and superconducting qubit is mediated by a magnon. Considering the phase resulting from the distance between the two nodes, we derive a master equation for two superconducting qubits and show that, by adiabatically controlling the cavity–magnon coupling, perfect quantum state transfer between two qubits can be realized. We also consider the influence of intrinsic dissipation of the magnetic mode and the cavity mode. In an unideal case, the design time-dependent cavity–magnonics couplings obtained in the ideal case are still employed. Our results show that low intrinsic loss in the magnetic mode and the cavity mode is still welcome for the high fidelity of state transfer.

Abstract Finding minimal time and establishing the structure of the corresponding optimal controls which can transfer a given initial state of a quantum system into a given target state is a key problem of quantum control. In this work, this problem is solved for a basic component of various quantum technology processes—a qubit interacting with the environment and experiencing an arbitrary time-dependent coherent driving. We rigorously derive both upper and lower estimates for the minimal steering time. Surprisingly, we discover that the optimal controls have a very special form—they consist of two impulses, at the beginning and at the end of the control period, which can be assisted by a smooth time-dependent control in between. Moreover, an important for practical applications explicit almost optimal state transfer protocol is provided which only consists of four impulses and gives an almost optimal time of motion. The results can be directly applied to a variety of experimental situations for estimation of the ultimate limits of state control for quantum technologies.

Recent technological advances have allowed the fabrication of large arrays of coupled qubits, serving as prototypes for quantum processors. However, the optimal control of such systems remains notoriously challenging, limiting the potential of large-scale quantum systems. Here, we investigate a model problem of quantum state transfer in a large nearest-neighbor-coupled qubit array. We derive an optimal control strategy that simultaneously achieves maximal fidelity and minimal transfer time, reaching the quantum speed limit in a lattice with time-varying couplings.