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Instantaneous quantum polynomial quantum circuit Born machines (IQP-QCBMs) have been proposed as quantum generative models with a classically tractable training objective based on the maximum mean discrepancy (MMD) and a potential quantum advantage motivated by sampling-complexity arguments, making them an exciting model worth deeper investigation.
Temporally unstructured quantum computation
Dan Shepherd and Michael J. Bremner · 2008
Earlier work this paper cites.
Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
Michael J. Bremner, Richard Jozsa, and Dan J. Shepherd · 2010
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A kernel two-sample test
Arthur Gretton, Karsten M. Borgwardt, Malte J. Rasch, Bernhard Schölkopf, and Alexander Smola · 2012
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Average-case complexity versus approximate simulation of commuting quantum computations
Michael J. Bremner, Ashley Montanaro, and Dan J. Shepherd · 2016
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Achieving quantum supremacy with sparse and noisy commuting quantum computations
Michael J. Bremner, Ashley Montanaro, and Dan J. Shepherd · 2017
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Keisuke Fujii and Tomoyuki Morimae · 2017
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Kernel mean embedding of distributions: A review and beyond
Krikamol Muandet, Kenji Fukumizu, Bharath Sriperumbudur, Bernhard Schölkopf, et al · 2017
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Differentiable learning of quantum circuit born machines
Jin-Guo Liu and Lei Wang · 2018
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Limits of quantum generative models with classical sampling hardness, 2025
Sabrina Herbst, Ivona Brandić, and Adrián Pérez-Salinas · 2025
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Barren plateaus in variational quantum computing
Martín Larocca, Supanut Thanasilp, Samson Wang, Kunal Sharma, Jacob Biamonte, Patrick J. Coles, Lukasz Cincio, Jarrod R. McClean, Zoë Holmes, and M. Cerezo · 2025
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Erik Recio-Armengol, Shahnawaz Ahmed, and Joseph Bowles · 2025
Later among the works it cites.
Cost function dependent barren plateaus in shallow parametrized quantum circuits
M. Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J. Coles · 2041
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A lie algebraic theory of barren plateaus for deep parameterized quantum circuits
Michael Ragone, Bojko N. Bakalov, Frédéric Sauvage, Alexander F. Kemper, Carlos Ortiz Marrero, Martín Larocca, and M. Cerezo · 2041
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Manuel S Rudolph, Sacha Lerch, Supanut Thanasilp, Oriel Kiss, Oxana Shaya, Sofia Vallecorsa, Michele Grossi, and Zoë Holmes · 2024
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Noise-induced barren plateaus in variational quantum algorithms
Samson Wang, Enrico Fontana, M. Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J. Coles · 2041
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