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arXiv:2111.08977

Realization of a quantum perceptron gate with trapped ions

Patrick H. Huber, Johann Haber, Barthel, P., Juan José García‐Ripoll, E. Torrontegui, C. Wunderlich

Published Nov 17, 2021• 5 citations
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Abstract

We report the implementation of a perceptron quantum gate in an ion-trap quantum computer. In this scheme, a perceptron's target qubit changes its state depending on the interactions with several qubits. The target qubit displays a tunable sigmoid switching behaviour becoming a universal approximator when nested with other percetrons. The procedure consists on the adiabatic ramp-down of a dressing-field applied to the target qubit. We also use two successive perceptron quantum gates to implement a XNOR-gate, where the perceptron qubit changes its state only when the parity of two input qubits is even. The applicability can be generalized to higher-dimensional gates as well as the reconstruction of arbitrary bounded continuous functions of the perceptron observables.

DOI
10.48550/arxiv.2111.08977

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We report the implementation of a perceptron quantum gate in an ion-trap quantum computer. In this scheme, a perceptron's target qubit changes its state depending on the interactions with several qubits. The target qubit displays a tunable sigmoid switching behaviour becoming a universal approximator when nested with other percetrons. The procedure consists on the adiabatic ramp-down of a dressing-field applied to the target qubit. We also use two successive perceptron quantum gates to implement a XNOR-gate, where the perceptron qubit changes its state only when the parity of two input qubits is even. The applicability can be generalized to higher-dimensional gates as well as the reconstruction of arbitrary bounded continuous functions of the perceptron observables.
Gates acting on more than two qubits are appealing as they can substitute complex sequences of two-qubit gates, thus promising faster execution and higher fidelity. One important multiqubit operation is the quantum Toffoli gate that performs a controlled NOT operation on a target qubit depending on the state of two control qubits. Here we present the first experimental realization of the quantum Toffoli gate in an ion trap quantum computer, achieving a mean gate fidelity of 71(3)%. Our implementation is particularly efficient as the relevant logic information is directly encoded in the motion of the ion string.
The utility of classical neural networks as universal approximators suggests that their quantum analogues could play an important role in quantum generalizations of machine-learning methods. Inspired by the proposal in Torrontegui and Garc\'{\i}a-Ripoll [Europhys. Lett. 125, 30004 (2019)], we demonstrate a superconducting qubit implementation of a controlled gate, which generalizes the action of a classical perceptron as the basic building block of a quantum neural network. In a two-qubit setup we show full control over the steepness of the perceptron activation function, the input weight and the bias by tuning the gate length, the coupling between the qubits, and the frequency of the applied drive, respectively. In its general form, the gate realizes a multiqubit entangling operation in a single step, whose decomposition into single- and two-qubit gates would require a number of gates that is exponential in the number of qubits. Its demonstrated direct implementation as perceptron in quantum hardware may therefore lead to more powerful quantum neural networks when combined with suitable additional standard gates.
We demonstrate that it is possible to implement a quantum perceptron with a sigmoid activation function as an efficient, reversible many-body unitary operation. When inserted in a neural network, the perceptron's response is parameterized by the potential exerted by other neurons. We prove that such a quantum neural network is a universal approximator of continuous functions, with at least the same power as classical neural networks. While engineering general perceptrons is a challenging control problem —also defined in this work— the ubiquitous sigmoid-response neuron can be implemented as a quasi-adiabatic passage with an Ising model. In this construct, the scaling of resources is favorable with respect to the total network size and is dominated by the number of layers. We expect that our sigmoid perceptron will have applications also in quantum sensing or variational estimation of many-body Hamiltonians.
We demonstrate that it is possible to implement a quantum perceptron with a sigmoid activation function as an efficient, reversible many-body unitary operation. When inserted in a neural network, the perceptron's response is parameterized by the potential exerted by other neurons. We prove that such a quantum neural network is a universal approximator of continuous functions, with the same power as classical neural networks. While engineering general perceptrons is a challenging control problem --also defined in this work--, the ubiquitous sigmoid-response neuron can be implemented as a quasi-adiabatic passage with an Ising model. In this construct, the scaling of resources is favorable with respect to the total network size and is dominated by the number of layers. We expect that our sigmoid perceptron will have applications also in quantum sensing or variational estimation of many-body Hamiltonians.
A global race towards developing a gate-based, universal quantum computer that one day promises to unlock the never before seen computational power has begun and the biggest challenge in achieving this goal arguably is the quality implementation of a two-qubit gate. In a trapped-ion quantum computer, one of the leading quantum computational platforms, a two-qubit gate is typically implemented by modulating the individual addressing beams that illuminate the two target ions, which, together with others, form a linear chain. The required modulation, expectedly so, becomes increasingly more complex, especially as the quantum computer becomes larger and runs faster, complicating the control hardware design. Here, we develop a simple method to essentially remove the pulse-modulation complexity at the cost of engineering the normal modes of the ion chain. We demonstrate that the required mode engineering is possible for a three ion chain, even with a trapped-ion quantum computational system built and optimized for a completely different mode of operations. This indicates that a system, if manufactured to target specifically for the mode-engineering based two-qubit gates, would readily be able to implement the gates without significant additional effort.