Enhancing Optical Imaging via Quantum Computation

TL;DR

The paper addresses the challenge of imaging extremely weak optical signals where shot noise limits conventional schemes. It proposes a quantum processing pipeline that coherently maps photonic amplitudes into a qubit register, compresses the information, and uses quantum algorithms to sort into the PSF eigenbasis to directly estimate source observables without full state tomography. The authors show that for a star exoplanet system the approach yields orders of magnitude reductions in photon requirements and substantial SNR gains with modest quantum resources, achievable on near term hybrid hardware. The framework is general enough to apply to molecular imaging, satellite monitoring, and adaptive optics, and provides a practical path via spin-photon interfaces, quantum frequency conversion, and teleportation to processing qubits.

Abstract

Extracting information from weak optical signals is a critical challenge across a broad range of technologies. Conventional imaging techniques, constrained to integrating over detected signals and classical post-processing, are limited in signal-to-noise ratio (SNR) from shot noise accumulation in the post-processing algorithms. We show that these limitations can be circumvented by coherently encoding photonic amplitude information into qubit registers and applying quantum algorithms to process the stored information from asynchronously arriving optical signals. As a specific example, we develop a quantum algorithm for imaging unresolved point sources and apply it to exoplanet detection. We demonstrate that orders-of-magnitude improvements in performance can be achieved under realistic imaging conditions using relatively small scale quantum processors.

Figures (8)

• Figure 1: Sketch of a quantum processing enhanced imaging system. Step 1: The quantum state of the light collected through the optics is mapped to a pixel-qubit register in a heralded way by means of qubit-photon controlled gates followed by joint detection of the photonic modes. Step 2: For a weak optical signal where only a single photon is coherently distributed across the detection modes, the information can be compressed into a logarithmic number of memory qubits using a unary-to-binary encoding. Step 3: Quantum processing of the received light to extract the parameters of interest with higher SNR than possible from classical direct detection and post-detection processing.
• Figure 2: Quantum algorithm for sorting weak light signal into the PSF eigenbasis. Left to right: the quantum state of an incoming photon is first stored in a compressed form in a qubit memory register (red qubits). The state of a subsequent photon is then stored in a compressed form in a second memory register (green qubits). An auxiliary qubit (yellow) mediates a controlled $e^{\pm i \epsilon \mathcal{S}}$ gate between the two registers (with $\mathcal{S}$ being a swap operator), after which the register holding the later photon is measured, re-initialized and then used to store a subsequent photon state. To sort eigenstates to a given precision $\epsilon$, this procedure is repeated $O(1)$ times times to approximate the controlled application of $e^{\pm i\epsilon\rho}$ to the first register. A single-qubit rotation is then applied to the auxiliary qubit, and the approximate application $e^{\pm i\epsilon\rho}$ is repeated. The entire sequence is executed $O(1/\epsilon)$ times (up to logarithmic factors; see main text) to sort the initial photonic state into the PSF eigenbasis with error bounded by $\epsilon$: $\mathrm{QSP}_{\exp(ix\rho),f_s} (\rho \otimes \ket{0}\bra{0}) \approx r\ket{V_1}\bra{V_1} \otimes \ket{0}\bra{0} + (1-r)\ket{V_2}\bra{V_2} \otimes \ket{1}\bra{1}$. Here, $r$ is related to the relative star-to-exoplanet intensity. The single qubit rotations and phase ($\pm$) of $e^{\pm i\epsilon\rho}$ are chosen to approximate the application of a step function such that a final measurement of the auxiliary qubit reveals which eigenstate the register holds.
• Figure 3: (top) The QSP circuit requires two registers of the same dimension and one ancillary qubit. One register stores the first received state $\rho$, while the other stores subsequent states as they arrive at later times. (bottom) The approximation of the unitary $e^{-i x\rho}$ is implemented in $x\cdot k$ steps, to obtain a precision of $O(x/k^2)$. Each step applies a conditional $e^{-i\mathcal{S}/k}$ gate, followed by re-initializing the second register so that it is ready to receive another state. This operation implements a conditional $e^{-i \rho/k}$ gate to precision $O(1/k^2)$. The trigonometric approximation of the Heaviside function involves both positive and negative powers of $e^{i x\rho}$. Following the QSP procedure suggested in Ref. Motlagh2024, the first $K\sim L/2$ controlled gates in the QSP circuit applies anti-controlled $e^{i x\rho}$ and the remaining gates applies controlled $e^{-i x\rho}$. As shown in the main text, achieving an approximation of the Heaviside function to precision $\epsilon$ requires $x\sim\epsilon$. Accordingly, we can choose $k\sim 1/\epsilon$ in our algorithm, implying that only $O(1)$ steps are needed to approximate $e^{\pm i \epsilon \rho}$. However, since we need to implement $L\sim 1/\epsilon$ of these gates, the total number of such gates (and photons) required scales as $O(1/\epsilon)$.
• Figure 4: Absolute value of the polynomial $f_s$ which approximates $\Theta_s$ and the positions of the phases of $\exp(ix\rho)$ which are used to sort $\rho$ into its eigenvectors. The parameters $\Delta$ and $\delta$ determines the region where $\delta<f_s(\tau)<1-\delta$.
• Figure 5: Ratio of sample complexities between the tomography and the QSP-based scheme in the absence of noise