Quantum machine learning with indefinite causal order
Abstract: In a conventional circuit for quantum machine learning, the quantum gates used to encode the input parameters and the variational parameters are constructed with a fixed order. The resulting output function, which can be expressed in the form of a restricted Fourier series, has limited flexibility in the distributions of its Fourier coefficients. This indicates that a fixed order of quantum gates can limit the performance of quantum machine learning. Building on this key insight (also elaborated with examples), we introduce indefinite causal order to quantum machine learning. Because the indefinite causal order of quantum gates allows for the superposition of different orders, the performance of quantum machine learning can be significantly enhanced. Considering that the current accessible quantum platforms only allow to simulate a learning structure with a fixed order of quantum gates, we reform the existing simulation protocol to implement indefinite causal order and further demonstrate the positive impact of indefinite causal order on specific learning tasks. Our results offer useful insights into possible quantum effects in quantum machine learning.
- S. Lloyd, Universal quantum simulators, Science 273, 1073 (1996).
- D. P. DiVincenzo, Quantum computation, Science 270, 255 (1995).
- M. A. Nielsen and I. Chuang, Quantum computation and quantum information (2002).
- P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM review 41, 303 (1999).
- L. K. Grover, A fast quantum mechanical algorithm for database search, in Proceedings of the twenty-eighth annual ACM symposium on Theory of computing (1996) pp. 212–219.
- A. Montanaro, Quantum algorithms: an overview, npj Quantum Information 2, 1 (2016).
- Y. Liu, S. Arunachalam, and K. Temme, A rigorous and robust quantum speed-up in supervised machine learning, Nature Physics 17, 1013 (2021).
- I. Cong, S. Choi, and M. D. Lukin, Quantum convolutional neural networks, Nature Physics 15, 1273 (2019).
- M. Schuld and N. Killoran, Quantum machine learning in feature hilbert spaces, Physical review letters 122, 040504 (2019).
- T. Goto, Q. H. Tran, and K. Nakajima, Universal approximation property of quantum machine learning models in quantum-enhanced feature spaces, Physical Review Letters 127, 090506 (2021).
- M. Araújo, F. Costa, and Č. Brukner, Computational advantage from quantum-controlled ordering of gates, Physical review letters 113, 250402 (2014).
- S. Salek, D. Ebler, and G. Chiribella, Quantum communication in a superposition of causal orders, arXiv preprint arXiv:1809.06655 (2018).
- O. Oreshkov, F. Costa, and Č. Brukner, Quantum correlations with no causal order, Nature communications 3, 1092 (2012).
- O. Oreshkov, Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics, Quantum 3, 206 (2019).
- X. Zhao, Y. Yang, and G. Chiribella, Quantum metrology with indefinite causal order, Physical Review Letters 124, 190503 (2020).
- D. Felce and V. Vedral, Quantum refrigeration with indefinite causal order, Physical review letters 125, 070603 (2020).
- A. Feix, M. Araújo, and Č. Brukner, Quantum superposition of the order of parties as a communication resource, Physical Review A 92, 052326 (2015).
- D. Ebler, S. Salek, and G. Chiribella, Enhanced communication with the assistance of indefinite causal order, Physical review letters 120, 120502 (2018).
- M. Schuld, R. Sweke, and J. J. Meyer, Effect of data encoding on the expressive power of variational quantum-machine-learning models, Physical Review A 103, 032430 (2021).
- O. Koska, Simulation of the superposition of multiple temporal gates orders in quantum circuits (2021).
- Qiskit contributors, Qiskit: An open-source framework for quantum computing (2023).
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