Time-Domain Universal Linear-Optical Operations for Universal Quantum Information Processing

Yonezu, Kazuma; Enomoto, Y.; Yoshida, Takato O.; Takeda, Shuntaro

doi:10.1103/physrevlett.131.040601

Cited by 7 publications

(2 citation statements)

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“…Note that there are many non-generic instances of U (but commonly encountered in actual devices) where this algorithm would terminate in the first junta set update. For instance, consider U being a tensor product of generalized beamsplitters on modes (1, 2), (3,4), . .…”

Section: K-loj Learning Algorithmmentioning

confidence: 99%

“…For instance, after the initial generation of nonclassical resource states using optical nonlinearities or heralded entanglement, a set of linear optical layers creates the necessary complexity for the production of photonic or continuous-variable (CV) cluster states, which are the central resources for optical implementations of measurementbased quantum computation. However, specific architectures for implementing many-mode linear optical circuits range from free space temporal modes [3], to on-chip programmable couplings [4], to switchable fiber demultiplexing [5]. The Borealis device [6] provides a striking example of the latter, in which 216 pulses (of temporal duration τ ) of single temporal mode CV squeezed states are sequentially routed through fiber-based time-delay loops of length τ , 6τ , and 36τ .…”

Section: Introductionmentioning

confidence: 99%

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Learning linear optical circuits with coherent states

Volkoff,

Sornborger

2024

J. Phys. A: Math. Theor.

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We analyze the energy and training data requirements for supervised learning of an $M$-mode linear optical circuit by minimizing an empirical risk defined solely from the action of the circuit on coherent states. When the linear optical circuit acts non-trivially only on $k<M$ unknown modes (i.e., a linear optical $k$-junta), we provide an energy-efficient, adaptive algorithm that identifies the junta set and learns the circuit. We compare two schemes for allocating a total energy, $E$, to the learning algorithm. In the first scheme, each of the $T$ random training coherent states has energy $E/T$. In the second scheme, a single random $MT$-mode coherent state with energy $E$ is partitioned into $T$ training coherent states. The latter scheme exhibits a polynomial advantage in training data size sufficient for convergence of the empirical risk to the full risk due to concentration of measure on the $(2MT-1)$-sphere. Specifically, generalization bounds for both schemes are proven, which indicate that for $\epsilon$-approximation of the full risk by the empirical risk with high probability, $O(E^{2/3}M^{2/3}/\epsilon^{2/3})$ training states are sufficient for the first scheme and $O(E^{1/3}M^{1/3}/\epsilon^{2/3})$ training states are sufficient for the second scheme.

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Section: K-loj Learning Algorithmmentioning

confidence: 99%