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Journal of Physics Conference Series

Applying Quantum State Preparation Algorithms to Gravitational Wave Data Analysis

Elizabeth Sarell, Ashwin Girish, Hector Spencer-Wood, M. Pürrer, Christopher Messenger, F. C. Speirits, Sarah Croke

Published Feb 1, 2026• 0 citations
Publisher

Abstract

Abstract Quantum state preparation is an important part of quantum computing, and ensuring gravitational wave template waveforms can be loaded efficiently is essential for preserving the advantages quantum algorithms could offer. Here, we look at improving the efficiency of amplitude encoding for gravitational waveforms by considering an approximation of the inspiral section. By inducing a small error into the Grover-Rudolph algorithm, we can reduce the number of quantum logic gates required as the number of qubits grows. This means that we can encode templates into a quantum processor in a form that requires modest numbers of both qubits and gates, opening the door to development of algorithms accessible to near-term quantum devices.

DOI
10.1088/1742-6596/3177/1/012076

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Abstract Quantum state preparation is an important part of quantum computing, and ensuring gravitational wave template waveforms can be loaded efficiently is essential for preserving the advantages quantum algorithms could offer. Here, we look at improving the efficiency of amplitude encoding for gravitational waveforms by considering an approximation of the inspiral section. By inducing a small error into the Grover-Rudolph algorithm, we can reduce the number of quantum logic gates required as the number of qubits grows. This means that we can encode templates into a quantum processor in a form that requires modest numbers of both qubits and gates, opening the door to development of algorithms accessible to near-term quantum devices.
We detail a quantum circuit capable of efficiently encoding analytical approximations to gravitational wave signal waveforms of compact binary coalescences into the amplitudes of quantum bits using both quantum arithmetic operations and hybrid classical-quantum generative modelling. The gate cost of the proposed method is considered and compared to a state preparation routine for arbitrary amplitudes, where we demonstrate up to a four orders of magnitude reduction in gate cost when considering the encoding of gravitational waveforms representative of binary neutron star inspirals detectable to the Einstein telescope. We demonstrate through a quantum simulation, that is limited to 28 qubits, the encoding of a second post-Newtonian inspiral waveform with a fidelity compared to the desired state of 0.995 when using the Grover-Rudolph algorithm, or 0.979 when using a trained quantum generative adversarial network with a significant reduction of required gates.
Sparse quantum state preparation is a common subroutine in quantum algorithms, where classical data with few nonzero entries must be loaded into a quantum state. In this work, we consider the Grover-Rudolph algorithm, which has recently been shown to efficiently prepare sparse states, and we propose two improvements. First, we extend an existing gate-merging procedure by allowing rotations to merge with virtual zero-angle gates on unreachable branches of the preparation tree, reducing the number of CNOTs and control qubits. Second, we introduce an approximate variant in which rotations with similar but not identical angles are merged at the cost of a small, controllable error in the prepared state. We derive a classically computable estimate of the resulting overlap with the target state, which is used to guide the merging decisions.
In this paper, we explore the application of variational quantum algorithms designed for classical optimization to the problem of matched filtering in the detection of gravitational waves. Matched filtering for detecting gravitational wave signals requires searching through a large number of template waveforms, to find one which is highly correlated with segments of detector data. This computationally intensive task needs to be done quickly for low latency searches in order to aid with follow-up multi-messenger observations. The variational quantum algorithms we study for this task consist of quantum walk-based generalizations of the Quantum Approximate Optimization Algorithm (QAOA). We present results of classical numerical simulations of these quantum algorithms using open science data from LIGO. These results show that the tested variational quantum algorithms are outperformed by an unstructured restricted-depth Grover search algorithm, suggesting that the latter is optimal for this computational task.
Quantum computational devices, currently under development, have the potential to accelerate data analysis techniques beyond the ability of any classical algorithm. We propose the application of a quantum algorithm for the detection of unknown signals in noisy data. We apply Grover's algorithm to matched-filtering, a signal processing technique that compares data to a number of candidate signal templates. In comparison to the classical method, this provides a speed-up proportional to the square-root of the number of templates, which would make possible otherwise intractable searches. We demonstrate both a proof-of-principle quantum circuit implementation, and a simulation of the algorithm's application to the detection of the first gravitational wave signal GW150914. We discuss the time complexity and space requirements of our algorithm as well as its implications for the currently computationally-limited searches for continuous gravitational waves.
Quantum computational devices currently under development have the potential to accelerate data analysis techniques beyond the ability of any classical algorithm. We propose the application of a quantum algorithm for the detection of unknown signals in noisy data. We apply Grover's algorithm to matched filtering, a signal processing technique that compares data to a number of candidate signal templates. In comparison to the classical method, this provides a speedup proportional to the square root of the number of templates, which would make possible otherwise intractable searches. We demonstrate both a proof-of-principle quantum circuit implementation and a simulation of the algorithm's application to the detection of the gravitational wave signal GW150914. We discuss the time complexity and space requirements of our algorithm as well as its implications for the currently computationally limited searches for continuous gravitational waves.
Loading classical data into quantum computers represents an essential stage in many relevant quantum algorithms, especially in the field of quantum machine learning. Therefore, the inefficiency of this loading process means a major bottleneck for the application of these algorithms. Here, we introduce two approximate quantum-state preparation methods for the noisy intermediate-scale quantum era inspired by the Grover-Rudolph algorithm, which partially solve the problem of loading real functions. Indeed, by allowing for an infidelity $\ensuremath{\epsilon}$ and under certain smoothness conditions, we prove that the complexity of the implementation of the Grover-Rudolph algorithm without ancillary qubits, first introduced by M\"ott\"onen et al., results into $\mathcal{O}({2}^{{k}_{0}(\ensuremath{\epsilon})})$, with nnn the number of qubits and ${k}_{0}(\ensuremath{\epsilon})$ asymptotically independent of nnn. This leads to a dramatic reduction in the number of required two-qubit gates. Aroused by this result, we also propose a variational algorithm capable of loading functions beyond the aforementioned smoothness conditions. Our variational Ansatz is explicitly tailored to the landscape of the function, leading to a quasioptimized number of hyperparameters. This allows us to achieve high fidelity in the loaded state with high speed convergence for the studied examples.