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Measurement-based acceleration of optical computations

I. V. Vovchenko, A. A. Zyablovsky, A. A. Pukhov, E. S. Andrianov

TL;DR

This work proposes a measurement-based approach to accelerate optical linear computations by exploiting collective, Rabi-like oscillations in a central resonator coupled to $N$ side resonators. By averaging the central-mode occupancy over a time window, the output encodes a dot-product between a matrix of squared couplings and a vector of initial side-mode occupancies, enabling matrix-vector multiplication with a matrix formed by the couplings and an input vector from the initial occupancies. The key findings show that the collective oscillation frequency scales as $\Omega_R=\sqrt{(\Delta/2)^2+(\vec{\Omega},\vec{\Omega})}$, and for zero detuning, $\Omega_R\sim\sqrt{N}$, leading to a reduction in computation time as $t_0\propto 1/\Omega_R$. The paper also analyzes limits from non-resonant cross-talk in a restricted optical frequency band, providing estimates such as a per-frequency rate around $10^{13}$ Hz and potential aggregate rates up to $\sim 10^{16}$ Hz when using many parallel frequencies, while highlighting the trade-off between parallelism and bandwidth. These results suggest a path to fast, measurement-enabled optical coprocessors and extendable concepts to other bosonic platforms.

Abstract

Analog coprocessors are intensively developing nowadays with the aim to optimize energy computations of neural networks. In this work we focus on the possibility of using detection of collective oscillations in optical systems for computational purposes. We show that in a system of coupled resonators, collective oscillations can be used to implement matrix-vector multiplication. The matrix is formed by the coupling constants between the resonators, and the input vector is formed by the initial occupancies of the involved modes. The frequency of the collective oscillations is growing with the number of the involved modes, similarly to Rabi oscillations. The time needed for their detection, i.e., averaging, decreases with an increase in the input vector dimension. We discuss the limitations imposed on parallel computation in the system by restriction of the allowed optical frequency band.

Measurement-based acceleration of optical computations

TL;DR

This work proposes a measurement-based approach to accelerate optical linear computations by exploiting collective, Rabi-like oscillations in a central resonator coupled to side resonators. By averaging the central-mode occupancy over a time window, the output encodes a dot-product between a matrix of squared couplings and a vector of initial side-mode occupancies, enabling matrix-vector multiplication with a matrix formed by the couplings and an input vector from the initial occupancies. The key findings show that the collective oscillation frequency scales as , and for zero detuning, , leading to a reduction in computation time as . The paper also analyzes limits from non-resonant cross-talk in a restricted optical frequency band, providing estimates such as a per-frequency rate around Hz and potential aggregate rates up to Hz when using many parallel frequencies, while highlighting the trade-off between parallelism and bandwidth. These results suggest a path to fast, measurement-enabled optical coprocessors and extendable concepts to other bosonic platforms.

Abstract

Analog coprocessors are intensively developing nowadays with the aim to optimize energy computations of neural networks. In this work we focus on the possibility of using detection of collective oscillations in optical systems for computational purposes. We show that in a system of coupled resonators, collective oscillations can be used to implement matrix-vector multiplication. The matrix is formed by the coupling constants between the resonators, and the input vector is formed by the initial occupancies of the involved modes. The frequency of the collective oscillations is growing with the number of the involved modes, similarly to Rabi oscillations. The time needed for their detection, i.e., averaging, decreases with an increase in the input vector dimension. We discuss the limitations imposed on parallel computation in the system by restriction of the allowed optical frequency band.
Paper Structure (5 sections, 10 equations, 3 figures)

This paper contains 5 sections, 10 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The model
  3. Implementation of matrix-vector multiplication
  4. Limitation imposed by geometry and restricted frequency band
  5. Conclusion and discussion

Figures (3)

  • Figure 1: Schematic representation of the system with Hamiltonian Eq. (\ref{['Ham']}).
  • Figure 2: The dynamics of $\overline{\langle\hat{a}^\dag\hat{a}\rangle}_t$ (blue solid line) and $0.5\tilde{n}_b$ (orange dashed line). The parameters: $\omega=\omega_b=1$, $N=50$, $\Omega_k$ are set randomly between $5\cdot 10^{-3}$ and $5\cdot 10^{-2}$. Initial occupancies $\langle\hat{b}_k^\dag \hat{b}_k\rangle_0$ are set randomly between $0.1$ and $1$, $\langle\hat{a}^\dag\hat{a}\rangle_0=0$.
  • Figure 3: The average value of the computational time providing $3\%$ precision (blue circles) and $15\tau_R$ (red squares). The parameters are set similarly to Fig. \ref{['aa_sr']}.