Abstract
Quantum algorithms are designed to process quantum data (quantum bits) in a gate-based quantum computer. They are proven rigorously that they reveal quantum advantages over conventional algorithms when their inputs are certain quantum data or some classical data mapped to quantum data. However, in a practical domain, data are classical in nature, and they are very big in dimension, size, and so on. Hence, there is a challenge to map (embed) classical data to quantum data, and even no quantum advantages of quantum algorithms are demonstrated over conventional ones when one processes the mapped classical data in a gate-based quantum computer. For the practical domain of earth observation (EO), due to the different sensors on remote-sensing platforms, we can map directly some types of EO data to quantum data. In particular, we have polarimetric synthetic aperture radar (PolSAR) images characterized by polarized beams. A polarized state of the polarized beam and a quantum bit are the Doppelganger of a physical state. We map them to each other, and we name this direct mapping a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">natural embedding</i> , otherwise an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">artificial embedding</i> . Furthermore, we process our <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">naturally embedded</i> data in a gate-based quantum computer by using a quantum algorithm regardless of its quantum advantages over conventional techniques; namely, we use the QML network as a quantum algorithm to prove that we <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">naturally embedded</i> our data in input qubits of a gate-based quantum computer. Therefore, we employed and directly processed PolSAR images in a QML network. Furthermore, we designed and provided a QML network with an additional layer of a neural network, namely, a hybrid quantum-classical network, and demonstrate how to program (via optimization and backpropagation) this hybrid quantum-classical network when employing and processing PolSAR images. In this work, we used a gate-based quantum computer offered by an IBM Quantum and a classical simulator for a gate-based quantum computer. Our contribution is that we provided very specific EO data with a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">natural embedding</i> feature, the Doppelganger of quantum bits, and processed them in a hybrid quantum-classical network. More importantly, in the future, these PolSAR data can be processed by future quantum algorithms and future quantum computing platforms to obtain (or demonstrate) some quantum advantages over conventional techniques for EO problems.
Highlights
A quantum algorithm is an algorithm being processed in quantum computers, and a quantum ML (QML) network is the network of parameterized quantum gates in a gate-based quantum computer
The gate-based quantum computer itself is posing several new challenges, for instance, how to map classical data to qubits depending on the limited number of its input qubits, or how to use the specificity of the “qubits” to obtain quantum advantages over nonquantum computing techniques, while ubiquitous data in practical domains are of classical nature
The input data play an important role in a quantum algorithm to obtain quantum advantages, and for example, in scientific studies [9], [10], their authors implied that QML networks achieve quantum advantages over a conventional technique only if classical data are naturally embedded in their input qubits, or their input data are quantum data
Summary
R ECENT breakthroughs in building a gate-based quantum computer with very few quantum bits (qubits) [1]. The Jones vector is the Doppelganger of qubits (see Fig. 2), and the Stokes parameters have one-to-one correspondences with the qubits; a qubit (or a two-state qubit) |ψ ∈ C2, |ψ ∈ {|0, |1} is the quantum version of classical bits, and they can exist in superposition This one-to-one correspondence property allows us to employ and process the PolSAR images as the input data of a QML network. We demonstrate how to program a hybrid quantum-classical network when applying synthetic quantum data as its input, and we validate that the Stokes parameters convey information about polarization-changing targets in PolSAR images by training them on a hybrid quantum-classical network (see Sections V and VI).
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