Abstract
In this paper we present an approach to find quantum circuits suitable to mimic probabilistic and search operations on a physical NISQ device. We present both a gradient based and a non-gradient based machine learning approach to optimize the created quantum circuits. In our optimization procedure we make use of a cost function that differentiates between the vector representing the probabilities of measurement of each basis state after applying our learned circuit and the desired probability vector. As such our quantum circuit generation (QCG) approach leads to thinner quantum circuits which behave better when executed on physical quantum computers. Our approach moreover ensures that the created quantum circuit obeys the restrictions of the chosen hardware. By catering to specific quantum hardware we can avoid unforeseen and potentially unnecessary circuit depth, and we return circuits that need no further transpilation. We present the results of running the created circuits on quantum computers by IBM, Rigetti and Quantum Inspire.
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Notes
- 1.
Here the term ansatz refers to the initial layout of the quantum circuit in terms of which gate is applied to which qubit in each layer.
- 2.
An example of this is the Hadamard gate H. There are multiple textbook decompositions into rotation operations, all requiring 3 rotations, an example is \(H = e^{\frac{i\pi }{2}} R_Z \left( \frac{\pi }{2}\right) R_X \left( \frac{\pi }{2} \right) R_Z \left( \frac{\pi }{2} \right) \). When the application of H is followed by a measurement in the computational basis, however, it suffices to apply \(\tilde{H} = R_Z \left( \frac{\pi }{2}\right) R_X \left( \frac{\pi }{2}\right) \) to the qubits instead.
- 3.
The Hamming weight of a binary vector equals the amount of nonzero indices.
- 4.
An observable is a Hermitian matrix, multiplying a Hermitian matrix from both sides with some unitary V results in a Hermitian matrix \(Q = V^\dag \hat{Z}V\). In this case, since \(\hat{Z}_i = \mathinner {\left| {i}\right. \rangle }\mathinner {\left\langle {i}\right| }\) we get \(\hat{Q}_i=V^\dag \hat{Z}_iV = \mathinner {\left| {\xi }\right. \rangle }\mathinner {\left\langle {\xi }\right| }\), where \(\mathinner {\left| {\xi }\right. \rangle }\) is some quantum state.
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Acknowledgment
This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725. We also wish to express our gratitude to IBM and Quantum Inspire for making their quantum computers available online for public use. Furthermore the authors thank David de Laat for his useful ideas, fruitful discussions and valuable feedback on the manuscript.
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Schalkers, M.A., Möller, M. (2022). Learning Based Hardware-Centric Quantum Circuit Generation. In: Phillipson, F., Eichler, G., Erfurth, C., Fahrnberger, G. (eds) Innovations for Community Services. I4CS 2022. Communications in Computer and Information Science, vol 1585. Springer, Cham. https://doi.org/10.1007/978-3-031-06668-9_22
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