Gravitational-wave matched filtering on a quantum computer

TL;DR

This work demonstrates the first qubit-based matched filtering for gravitational-wave detection using a hybrid quantum-classical Monte Carlo algorithm that encodes data and templates via amplitude encoding and employs a divide-and-conquer encoding to enable a time-domain convolution with complexity around $O\big(L(\log N)^2\big)$. Implemented on noisy superconducting qubits through IBM Quantum hardware, the method achieves SNR results for GW190521 comparable to classical FFT-based approaches, validating the practicality of quantum-augmented signal processing with shallow circuits. While no asymptotic quantum advantage is yet observed over FFT, the study shows robust performance under current hardware and outlines pathways for energy-efficient scaling and application to higher-dimensional or multi-input problems as quantum hardware improves.

Abstract

State of the art quantum computers have very limited applicability for accurate calculations. Here we report the first experimental demonstration of qubit-based matched filtering for a detection of the gravitational-wave signal from a binary black hole merger. With our implementation on noisy superconducting qubits, we obtained a similar signal-to-noise ratio for the binary black hole merger as achievable with classical computation, providing evidence for the utility of qubits for practically relevant tasks. The algorithm we invented for this application is a Monte Carlo algorithm which uses quantum and classical computation together. It provides a quasi-quadartic speed-up for time-domain convolution, similar to achievable with fast Fourier transform.

Figures (7)

• Figure 1: The convolution gate describing the hybrid method and showing the asymptotic computation times of its parts, without optimizing by dividing the data into smaller segments. The shaded region points out the part with quantum operations. The total time complexity which is $\mathcal{O}(L(\log L)^2)$ in the figure reduces to $\mathcal{O}(L(\log N)^2)$ after that optimization (see Appendix \ref{['sec:appb']}).
• Figure 2: (a) Photo of the Falcon chip, the model of $ibmq\_guadalupe$ , next to a US penny (credit: IBM Research); (b) the qubit layout of the $ibmq\_guadalupe$. The qubits we used for encoding the data are encapsulated with orange lines and the qubit we used for encoding the signal template is encapsulated with red lines. These qubits were chosen due to the lowest CNOT and readout error rates at the time of execution.
• Figure 3: Scaled SNR time series around the gravitational-wave event from black hole merger GW190521. Blue circles show the classical result and orange crosses show the results obtained with the hybrid algorithm.
• Figure 4: Circuit to combine two $m$-qubit states. a and b do not depend on the input states $\ket{\psi}$ and $\ket{\phi}$. The depth of the subroutine is $\mathcal{O}(m)$ and $m$ qubits are discarded at each step.
• Figure 5: One of the circuits ran in the experiments for encoding