[Paper Review] Quantum computing in neural networks

P. Gralewicz|ArXiv.org|Jan 21, 2004

Quantum Computing Algorithms and Architecture19 references3 citations

TL;DR

This paper proposes a neural network model that encodes quantum states using probabilistic spike trains, demonstrating that artificial neural circuits can implement universal quantum gates—specifically single-qubit rotations and a CNOT gate—via a spatial coding scheme. Simulations show feasible gate fidelity and coherence, suggesting neural networks could serve as macroscopic platforms for quantum computation.

ABSTRACT

According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a large-scale quantum computing using PMs, especially with neural networks which have the innate capability for probabilistic information processing. Restricting ourselves to a particular model, we construct and numerically examine the performance of neural circuits implementing universal quantum gates. A discussion on the physiological plausibility of proposed coding scheme is also provided.

Motivation & Objective

• To investigate whether neural networks can implement quantum computation by encoding quantum states in probabilistic spike trains.
• To demonstrate the feasibility of realizing universal quantum gates (e.g., single-qubit rotations and CNOT) using simplified neural circuit models.
• To assess the physiological plausibility of quantum state encoding in neural systems, focusing on coding schemes like dense and sparse spatial codes.
• To analyze resource requirements and performance limitations, particularly regarding noise, signal duration, and synaptic reliability.
• To explore alternative coding schemes—such as temporal probability waves—for more stable and efficient quantum information processing in neural networks.

Proposed method

• Uses the statistical interpretation of quantum mechanics to map n-qubit states to joint probability distributions of 2n binary random variables (pbits), enabling quantum state encoding in neural spike trains.
• Applies positive operator-valued measures (POVMs) to relate quantum density matrices to observable probability distributions, with the transformation expressed as $\hat{p} = A\hat{\varrho}$.
• Constructs neural circuits with deterministic neurons acting as counters to discretize linearly accumulated inputs, mimicking quantum gate operations.
• Employs a reduced neural model with simplified dynamics, assuming no synaptic noise and fixed time steps (~5 ms), to simulate gate performance over ~30 steps (~150 ms signal duration).
• Tests two coding schemes: 'dense' spatial code (2 neurons per qubit) and 'sparse' spatial code (no temporal correlations), evaluating their stability and performance.
• Uses numerical simulations to assess gate fidelity and coherence, focusing on signal-to-noise trade-offs and the impact of cellular noise on deterministic operation.

Experimental results

Research questions

• RQ1 Can neural circuits with probabilistic spike trains implement universal quantum gates such as single-qubit rotations and CNOT gates?
• RQ2 How do different neural coding schemes—dense spatial, sparse spatial, and temporal probability wave codes—affect the stability and performance of quantum gate implementations?
• RQ3 What are the key resource requirements (e.g., signal duration, neuron count, noise tolerance) for realizing quantum operations in neural networks?
• RQ4 How does the presence of noise and synaptic variability affect the fidelity and coherence of quantum gate operations in neural models?
• RQ5 To what extent can neural networks serve as macroscopic analogs for quantum computation, and what are the implications for understanding neural coding and quantum foundations?

Key findings

• Neural circuits can successfully implement universal quantum gates using a probabilistic encoding of quantum states in spike trains, with simulations achieving high fidelity for both 1-qubit and 2-qubit operations.
• The optimal signal duration for gate performance was found to be approximately 30 time steps (~150 ms), consistent with realistic neural processing timescales.
• The deterministic regime with sharp firing thresholds outperforms stochastic regimes in terms of fidelity, though noise may be harnessed via stochastic resonance in alternative coding schemes.
• The sparse spatial coding scheme, which lacks temporal correlations, is more stable than temporal coding, which is vulnerable to short-term synaptic plasticity effects.
• The dense spatial code requires two neurons per qubit but offers efficient encoding; however, processing costs are high due to the need for precise spike timing and correlation tracking.
• The study suggests that neural networks could serve as viable macroscopic platforms for quantum computation, with implications for both neuroscience and quantum information science.