Efficient classical simulation of continuous variable quantum information processes.

By Stephen D. Bartlett, Barry C. Sanders, Samuel L. Braunstein, Kae Nemoto. Physical Review Letters, 2001

373 citations recorded by the source corpus.

We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum information. For a collection of harmonic oscillators, any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators (including finite losses) and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/e353792b9a71552bd99d34ab5a86ad4860fe2575

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Citations in the corpus

Graphical calculus for Gaussian pure states (2010, methodology): “The mathematics behind this generalization is not new [44, 45, 53, 62].”
Wigner Function Negativity and Contextuality in Quantum Computation on Rebits (2014, background): “Indeed, there exists [3] an equivalent of the GottesmanKnill theorem for continuous variables.”
Entanglement distillation from Gaussian input states (2010, background): “Triggered by this new paradigm of non-Gaussian QIP, the research field extending to the non-Gaussian regime has rapidly developed [18–20].”
Sufficient Conditions for Efficient Classical Simulation of Quantum Optics (2015, background): “input states to a LON and Gaussian measurements at the output [31].”
Quantum computational advantage with a programmable photonic processor (2022, background): “Although groundbreaking, these demonstrations have remained well outside the domain of quantum computational advantage, as they lacked non-Gaussian elements and were unable to synthesize states of sufficient complexity to evade efficient classical simulation 27 .”
Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer (2020, background): “In analogy to the qubit and qudit stabilizer formalisms [51–53], CV quantum computation also possesses an efficiently simulable sub-theory, Gaussian computation [44].”
Strawberry Fields: A Software Platform for Photonic Quantum Computing (2018, methodology): “This result is the CV version [69] of the Gottesman-Knill theorem of discrete-variable quantum information [49].”
Quantum interface between light and atomic ensembles (2008, background): “…of entanglement from Gaussian states (Eisert et al., 2002; Fiurasek, 2002; Giedke and Cirac, 2002) and that algorithms for efficient classical simulation of any evolution involving only Gaussian operation and Gaussian initial states exist (Bartlett et al., 2002; Lloyd and Braunstein, 1999).”
Modes and states in quantum optics (2019, background): “, 2012), which cannot lead to quantum advantage (Bartlett et al., 2002), a property which can be extended to any positive Wigner function state (Mari and Eisert, 2012).”