Quantum Graph Partitioning for Large Combinatorial Optimization
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Solution Overview
Problem
Current quantum computing methods for solving combinatorial optimization problems, such as Quantum Annealing and QAOA, are limited by the requirement for a number of qubits equal to the number of bits in the bit-string, which is impractical for problems with thousands of binary variables due to the scarcity and error susceptibility of quantum processors.
Innovation Solution
A quantum computing method that divides the graph structure of a cost function into disjunctive subgraph structures, maps each to a local cost Hamiltonian, determines eigenstates below a cut-off energy using a quantum processing device, and recombines these eigenstates to approximate the ground state, reducing the problem size and qubit requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If quantum annealing or QAOA is used to solve combinatorial optimization problems, then the problem can be formulated and solved using quantum mechanics, but the number of qubits required equals the number of bits in the bit-string, which becomes infeasible for moderate system sizes
Solution Approach 1:
The patent divides the original graph structure into multiple disjunctive subgraph structures, each handling a subset of discrete variables. This segmentation allows the problem to be solved using fewer qubits by processing smaller subproblems independently and combining their solutions, directly addressing the contradiction between solving capability and qubit requirement
Solution Approach 2:
The patent introduces an intermediary classical computer that receives the cost function, divides it into subproblems, maps them to local cost Hamiltonians, and combines the eigenstates from quantum processors. This intermediary coordinates the quantum subsystems and reduces the total qubit count needed while maintaining problem-solving capability
2Quantity of substance
If the number of qubits is increased to handle larger problems, then more discrete variables can be processed, but current quantum hardware comprises much less than thousands of properly working qubits
Solution Approach 1:
By segmenting the problem into subgraphs with fewer variables each, the patent enables solving of large-scale problems using current quantum hardware with limited qubit counts. Each subgraph can be processed on available quantum processors while the classical intermediary coordinates the overall solution
Solution Approach 2:
The patent transforms the problem from a single large quantum system requiring thousands of qubits to multiple smaller quantum systems that can be processed in parallel on current hardware, effectively adding a dimensional aspect to the computation strategy
3Reliability
If error corrected quantum computers are implemented, then reliable quantum computation is achieved, but the number of error corrected qubits is even lower due to the complexity of implementing a single error corrected qubit
Solution Approach 1:
The patent segments the quantum computation into multiple small subproblems that can be handled by a limited number of error-corrected qubits. This allows current error-corrected quantum hardware with fewer qubits to solve problems that would otherwise require thousands of qubits, working around the limitation rather than requiring more hardware
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This method effectively reduces the number of discrete variables to the number of eigenstates, enabling the solution of large-scale combinatorial optimization problems on current quantum hardware by leveraging existing quantum gates and measurements without additional modifications.
Implementation Method 1
a state is prepared in form of a quantum mechanical superposition of all possible bit-strings
Implementation Method 2
The measurement of the energy expectation value in the prepared state delivers information on the proximity of the prepared state to the sought ground state
Data Source
AI summary
Provided is a quantum computing method for obtaining an optimal solution of a problem with multiple discrete variables, wherein the problem is represented by a cost function, the method comprising:—generating a graph structure from the cost function,—dividing the graph structure into at least two disjunct subgraph structures, wherein each subgraph structure comprises a subset of the multiple variables,—mapping each subgraph structure to a local cost function represented as local cost Hamiltonian,—determining, for each local cost Hamiltonian, all eigenstates corresponding to an energy below a predetermined cut off energy using a quantum processing device, wherein each variable of the subset of multiple variables is represented by a qubit of the quantum processing device,—recombining the determined eigenstates, and-approximating a ground state from the recombined eigenstates, wherein the ground state represents the optimal solution.