[Paper Review] Quantum Pattern Recognition With Liquid State NMR

Rodion Neigovzen, Jorge Luiz Neves+2 more|arXiv (Cornell University)|Feb 12, 2008

Quantum Computing Algorithms and Architecture5 citations

TL;DR

This paper proposes a quantum pattern recognition scheme that merges Hopfield neural networks with adiabatic quantum computation, using a problem Hamiltonian to encode both input and memorized patterns. It demonstrates, in a two-qubit liquid state NMR system, the ability to return a quantum superposition of multiple recognized patterns—showcasing a key quantum advantage over classical counterparts.

ABSTRACT

A novel quantum pattern recognition scheme is presented, which combines the idea of a classic Hopfield neural network with adiabatic quantum computation. Both the input and the memorized patterns are represented by means of the problem Hamiltonian. In contrast to classic neural networks, the algorithm can return a quantum superposition of multiple recognized patterns. A proof of principle for the algorithm for two qubits is provided using a liquid state NMR quantum computer.

Motivation & Objective

• To develop a quantum algorithm that extends classical Hopfield networks into the quantum domain for pattern recognition.
• To leverage adiabatic quantum computation to enable superposition-based recognition of multiple stored patterns simultaneously.
• To demonstrate feasibility of the scheme using a liquid state NMR quantum processor as a proof of principle.
• To explore the potential of quantum Hamiltonians in encoding both input and memorized patterns within a unified framework.

Proposed method

• The algorithm encodes input and memorized patterns as components of a single problem Hamiltonian.
• Adiabatic quantum computation is employed to evolve the system from a simple initial Hamiltonian to the final problem Hamiltonian, which encodes the recognition task.
• The ground state of the final Hamiltonian corresponds to a quantum superposition of recognized patterns.
• The system is initialized in the ground state of a transverse field Hamiltonian and evolved slowly to the problem Hamiltonian to preserve adiabaticity.
• The recognition outcome is extracted by measuring the final state, which collapses to a superposition of valid pattern matches.
• A two-qubit liquid state NMR quantum computer is used to implement and validate the protocol experimentally.

Experimental results

Research questions

• RQ1 Can adiabatic quantum computation be used to implement pattern recognition with quantum superposition of multiple recognized patterns?
• RQ2 How can both input and memorized patterns be encoded within a single quantum Hamiltonian for recognition?
• RQ3 What is the feasibility of implementing such a scheme in a scalable, physically realizable quantum system like liquid state NMR?
• RQ4 Does the quantum approach offer advantages over classical neural networks in terms of simultaneous pattern recognition?
• RQ5 How does the adiabatic evolution preserve the desired superposition state during computation?

Key findings

• The proposed scheme successfully generates a quantum superposition of multiple recognized patterns, demonstrating a core quantum advantage over classical Hopfield networks.
• The two-qubit implementation on a liquid state NMR platform confirms the feasibility of the algorithm in a physically realizable quantum system.
• The problem Hamiltonian effectively encodes both input and stored patterns, enabling unified recognition within a single quantum framework.
• Adiabatic evolution preserves the desired quantum state, ensuring the system reaches the ground state corresponding to recognized patterns.
• The experimental results validate the theoretical design, showing that the quantum system can identify multiple patterns simultaneously through superposition.