Quantum Circuit Partitioning With Min-Cut for Limited Qubits
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Solution Overview
Problem
Current circuit-cutting methods for quantum circuits rely on manual selection of cut locations, which is not generalizable and inefficient for optimizing the number of cuts required to execute large quantum circuits on quantum computers with limited qubits, leading to high computational complexity.
Innovation Solution
An automated method using community detection and max-flow min-cut algorithms to iteratively convert an input quantum circuit into sub-circuits with a reduced number of qubits, by converting the circuit into a graph, identifying communities, and adjusting edge capacities to minimize cuts.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Extent of automation
If manual selection of cut locations is used, then the circuit can be divided into sub-circuits, but the number of cuts required is high and the method is not generalizable
Solution Approach 1:
The system performs self-service by automatically selecting cut locations through community detection and max-flow min-cut algorithms, eliminating the need for manual intervention while optimizing the circuit division process
Solution Approach 2:
The invention changes the approach from manual parameter selection to algorithmic parameter optimization by using community detection to identify densely connected regions and max-flow min-cut to determine optimal cut locations based on flow capacity
2Quantity of substance
If the number of cuts is increased to reduce qubit requirements, then the circuit can run on smaller quantum computers, but the computational complexity increases
Solution Approach 1:
The circuit is segmented into communities based on connectivity patterns, allowing systematic division into sub-circuits that can be executed on smaller quantum computers with fewer qubits
Solution Approach 2:
The invention optimizes the cutting strategy by adjusting edge capacities and using max-flow min-cut to minimize the number of cuts required, thereby reducing computational complexity while still achieving the goal of running on smaller quantum computers
3Adaptability or versatility
If existing circuit-cutting methods are used, then the circuit can be executed on limited hardware, but the processing time is high
Solution Approach 1:
The invention changes the optimization parameters by using community detection to identify natural divisions in the circuit and max-flow min-cut to optimize cut locations, reducing the number of sub-circuits needed and thereby reducing processing time
Solution Approach 2:
The system uses feedback from the community detection algorithm to inform the cutting strategy, where the identified community structures guide the selection of cut locations to minimize processing time while adapting to hardware constraints
Data Source
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AI summary
A method for converting an input quantum circuit with N qubits into output quantum sub-circuits with a number of qubits Nmax < N, comprises: a. converting the input quantum circuit into a graph; b. executing a community detection algorithm to divide the graph into communities; c. mapping the graph into a circuit flow network comprising a source node connected to nodes of a first community and a sink node connected to nodes of a second community; d. adjusting capacity of edges in the circuit flow network and identifying at least one cut location between the source node and the sink node using a max-flow min-cut algorithm; e. cutting the graph at said cut location(s) to obtain sub-circuits with at most Nc < N qubits; f. for each obtained sub-circuit, reiterating steps /a/ - /e/ using the obtained sub-circuit as input quantum circuit, until each sub-circuit obtained at step /e/ is an output sub-circuit with a number of qubits Nc ≤ Nmax.