[Paper Review] Quantum neural networks driven by information reservoir

Deniz Türkpençe, Tahir Çetin Akıncı+1 more|arXiv (Cornell University)|Sep 11, 2017

Quantum Information and Cryptography2 references3 citations

TL;DR

This paper proposes a quantum neural network (QNN) unit based on an interacting spin model coupled to a quantum information reservoir, using a collisional model to simulate both Markovian and non-Markovian dynamics. It finds that Markovian reservoirs enable stable, coherent steady-state outputs suitable for quantum neural computing, while non-Markovian dynamics induce memory effects that destabilize the output, making them detrimental for reliable computation.

ABSTRACT

This study concerns with the dynamics of a quantum neural network unit in order to examine the suitability of simple neural computing tasks. More specifically, we examine the dynamics of an interacting spin model chosen as a candidate of a quantum perceptron for closed and open quantum systems. We adopt a collisional model enables examining both Markovian and non-Markovian dynamics of the proposed quantum system. We show that our quantum neural network (QNN) unit has a stable output quantum state in contact with an environment carrying information content. By the performed numerical simulations one can compare the dynamics in the presence and absence of quantum memory effects. We find that our QNN unit is suitable for implementing general neural computing tasks in contact with a Markovian information environment and quantum memory effects cause complications on the stability of the output state.

Motivation & Objective

• To investigate the dynamics of a quantum neural network unit in closed and open quantum systems for neural computing applications.
• To assess the suitability of a spin-based quantum perceptron model for implementing neural computing tasks under different environmental conditions.
• To evaluate the impact of Markovian versus non-Markovian reservoirs on the stability and coherence of the QNN output state.
• To explore whether quantum reservoirs can serve as a platform for mixed-state quantum computing in neural network architectures.

Proposed method

• A collisional model is employed to simulate open quantum system dynamics, enabling the study of both Markovian and non-Markovian reservoir interactions.
• The QNN unit is modeled as an interacting spin system with dipole-dipole coupling, representing qubits as quantum nodes.
• The system Hamiltonian includes a flip-flop interaction between the QNN unit and input reservoirs, with coupling strengths tuned to control dynamics.
• Quantum mutual information and fidelity between the output state and target reservoir states are computed to assess information transfer and state stability.
• Coherence of the output node is quantified using the $l_1$-norm of coherence, enabling analysis of quantum effects in the steady state.
• Numerical simulations are performed for up to three input nodes with various reservoir states, including coherent superpositions.

Experimental results

Research questions

• RQ1 Can a quantum neural network unit achieve stable output states when coupled to a quantum information reservoir?
• RQ2 How do Markovian and non-Markovian reservoir dynamics affect the stability and coherence of the QNN output state?
• RQ3 To what extent can the output state retain quantum coherence, and can it support pure quantum effects in a mixed-state environment?
• RQ4 Can coupling strength and number of input nodes be used as control parameters to shape the steady-state output of the QNN?
• RQ5 Is non-Markovian dynamics beneficial or detrimental for quantum neural computing tasks?

Key findings

• In the Markovian regime, the QNN unit reaches a stable steady-state output that is a weighted statistical mixture of reservoir states, with residual coherence sufficient to reveal quantum effects.
• The fidelity between the output state and target reservoir states saturates at high values in the Markovian case, indicating effective information transfer.
• In the non-Markovian regime, quantum mutual information shows back-flow, and fidelity exhibits oscillatory behavior, indicating information leakage and instability.
• The output state in non-Markovian dynamics becomes fuzzy and unstable due to memory effects, with coherence also oscillating rather than stabilizing.
• Non-Markovian dynamics significantly reduce the reliability of the output state, making it unsuitable for consistent quantum neural computing tasks.
• The system demonstrates that weak coupling to a Markovian reservoir enables stable, controllable output states, supporting the feasibility of reservoir-driven quantum neural networks.