Quantum Hamiltonian Relaxation for Max-Cut With Fewer Qubits

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Solution Overview

Problem

Existing quantum computing techniques for solving the max-cut problem, which is NP-hard, are inefficient and impractical due to reliance on bijective mappings that result in classical maximum eigenstates, failing to utilize quantum superposition and entanglement for improved computation.

Innovation Solution

A novel quantum formulation using commutative mappings between classical binary variables and qubit basis states, employing quantum random access codes to construct non-diagonal and entangled Hamiltonians, allowing for more accurate and efficient max-cut approximate solutions with fewer qubits.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If bijective mappings are used in quantum computing for max-cut problem, then the problem can be formulated in quantum terms, but the computation fails to utilize quantum superposition and entanglement resulting in classical maximum eigenstates

Engineering Contradiction:

Improvequantum formulation capabilityVSAvoidcomputation efficiency

Core Design Contradiction:

Adaptability or versatilityVSProductivity

Solution Approach 1:

The patent inverts the conventional bijective mapping approach by using commutative mappings that map multiple classical binary variables to a single qubit basis state. This inversion allows the quantum system to exploit superposition and entanglement, transforming the computation from classical-like behavior to genuine quantum behavior that can solve max-cut problems more efficiently

Inventive Principle:

Principle #13The other way round (Inversion)

Solution Approach 2:

The patent employs quantum random access codes to construct Hamiltonians that serve multiple functions simultaneously: they encode graph structure information, create entangled states, and enable quantum speedup. This multi-functional approach allows a single quantum formulation to achieve both problem representation and quantum advantage

Inventive Principle:

Principle #6Universality (Multi-functionality)

2Productivity

If existing quantum methods are used to solve max-cut problem, then quantum computation is performed, but three times the number of qubits are required compared to the novel method

Engineering Contradiction:

Improvequantum computation capabilityVSAvoidnumber of qubits

Core Design Contradiction:

ProductivityVSQuantity of substance

Solution Approach 1:

The patent segments the quantum resource requirements by using commutative mappings that group multiple classical variables into fewer qubits. By partitioning the problem space and using quantum random access codes, the method achieves the same computational capability with one-third the qubit count of existing quantum approaches

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent changes the fundamental parameter of mapping efficiency by using commutative mappings instead of bijective mappings. This parameter change in the quantum formulation allows multiple classical states to be represented by fewer qubits while maintaining the ability to extract useful information through measurement

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS12554794B2Max-cut approximate solution via quantum relaxation

Publication Date: 2026.02.17 INTERNATIONAL BUSINESS MACHINE CORPORATION

AI summary

Systems and techniques that facilitate max-cut approximate solution via quantum relaxation are provided. In various embodiments, a system can comprise a receiver component that can access a graph having a set of vertices and a set of edges. In various instances, the system can comprise a rounding component that can compute a max-cut approximate solution for the graph based on a quantum Hamiltonian relaxation of the graph.