[Paper Review] Quantum Pattern Recognition of Classical Signal

Chao-Yang Pang, Cong-Bao Ding+1 more|ArXiv.org|Jul 6, 2007

Quantum Computing Algorithms and Architecture6 references3 citations

TL;DR

This paper proposes a quantum pattern recognition algorithm for classical radar signals that achieves $O(\sqrt{N})$ time complexity by integrating Grover's search with feature computation via the rotation-on-subspace method. It enables real-time detection of genuine space targets from saturated raids by matching signal features against known patterns using quantum amplitude amplification.

ABSTRACT

It's the key research topic of signal processing that recognizing genuine targets real time from the disturbed signal which has giant amount of data. A quantum algorithm for pattern recognition of classical signal which has time complexity O(sqrt(N)) is presented in this paper. Key Words: Pattern recognition, Grover's algorithm, Rotation on subspace

Motivation & Objective

• To address the challenge of real-time detection of genuine space targets from massive, noisy radar signals in saturated raid scenarios.
• To enable quantum speedup in classical signal pattern recognition by leveraging quantum amplitude amplification.
• To design a quantum algorithm that couples pattern matching with search, overcoming limitations of standard Grover’s algorithm.
• To demonstrate feasibility of quantum image and signal recognition for practical radar applications using quantum computing primitives.

Proposed method

• Utilizes a quantum loading scheme (QLS) to initialize all classical signal data into a superposition state with time complexity $O(\log N)$, effectively loading the entire signal database into quantum registers.
• Employs a generalized Grover iteration $G_{pr} = (2|\xi\rangle\langle\xi| - I)(O_d O_c U_L)^\dagger O_f O_d O_c U_L$ to couple pattern recognition computation with quantum search.
• Introduces an oracle $O_c$ to compute feature invariants (e.g., affine/projective invariants) from radar signals, ensuring robustness against noise.
• Uses an oracle $O_d$ to compute a similarity measure $d(c_i, c_{i_0})$ between candidate and reference pattern features.
• Applies a marking oracle $O_f$ that flips the phase of states where the similarity $d(c_i, c_{i_0})$ falls within a predefined threshold $\alpha$.
• Employs an iterative quantum multi-pattern recognition algorithm inspired by BBHT, dynamically adjusting the number of iterations to maximize success probability.

Experimental results

Research questions

• RQ1 Can quantum algorithms achieve sub-classical time complexity for real-time pattern recognition in classical radar signal processing?
• RQ2 How can quantum search be effectively coupled with complex pattern recognition computations such as feature extraction and similarity measurement?
• RQ3 What is the time complexity of a quantum pattern recognition algorithm that identifies multiple target patterns from a large, noisy signal set?
• RQ4 Can quantum amplitude amplification be adapted to detect genuine targets in saturated raid scenarios with high fidelity?
• RQ5 How does the algorithm perform when the total number of patterns $N$ is not a power of two?

Key findings

• The proposed quantum pattern recognition algorithm achieves a time complexity of $O(\sqrt{N})$, where $N$ is the total number of signal patterns including genuine, spurious, and virtual ones.
• The algorithm successfully identifies genuine targets when the similarity measure $d(c_i, c_{i_0})$ lies within a threshold $\alpha$, ensuring robustness against noise and false positives.
• The use of the rotation-on-subspace method allows the integration of complex feature computation (e.g., geometric invariants) into the Grover iteration, enabling practical pattern recognition.
• The algorithm is scalable to non-power-of-two $N$ by introducing virtual patterns, as supported by Long’s analysis.
• The iterative multi-pattern recognition strategy dynamically adjusts the number of Grover iterations to maximize measurement success probability, achieving high fidelity detection.
• The method demonstrates that quantum image and signal recognition for classical data is feasible, extending quantum advantage beyond pure database search.