Connectivity-Aware Quantum Circuit Generation Through Matrix Diagonalization
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Solution Overview
Problem
Conventional methods for generating quantum circuits from projection operators face challenges due to physical constraints on qubit connections, leading to inefficient circuits with a large number of gates and increased error probability.
Innovation Solution
An information processing apparatus that generates a quantum circuit by converting a matrix into a diagonal form through row operations based on qubit connection relationships, optimizing the circuit design to reduce the number of quantum gates and adhere to physical constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional methods are used to generate quantum circuits from projection operators, then the circuits can be generated without considering physical constraints, but the resulting circuits have a large number of gates and increased error probability
Solution Approach 1:
The patent changes the approach parameters by introducing matrix diagonalization as the core transformation method and incorporating qubit connection constraints as additional parameters in the circuit generation process. This transforms the conventional direct mapping method into a constrained optimization problem that produces more reliable circuits
Solution Approach 2:
The patent introduces an intermediate matrix representation that serves as a mediator between the projection operators and the final quantum circuit. The matrix diagonalization process acts as an intermediary transformation that systematically reduces gate count while respecting physical constraints
2Device complexity
If conventional methods generate quantum circuits without optimizing for connection relationships, then circuit generation is simpler, but the number of quantum gates increases and execution time extends beyond qubit coherence time
Solution Approach 1:
The patent performs preliminary matrix diagonalization and circuit optimization before actual quantum execution. By pre-processing the projection operators into optimized circuits that respect connection constraints, the system eliminates the need for time-consuming runtime optimizations and ensures execution completes within coherence time
Solution Approach 2:
The patent replaces the conventional trial-and-error or direct mapping circuit generation approach with a systematic matrix-based transformation method. This mathematical substitution provides a deterministic pathway to optimized circuits, replacing inefficient procedural generation
3Measurement precision
If quantum circuits are generated with more gates to handle projection operators, then measurement accuracy improves, but error probability increases due to more operations
Solution Approach 1:
The patent extracts the essential measurement information from projection operators through matrix diagonalization, separating the critical measurement components from redundant operations. This extraction process retains measurement precision while eliminating unnecessary gates that contribute to error accumulation
Data Source
AI summary
A storage unit stores operator information, which indicates a plurality of projection operators, each of which is indicated by a combination of a plurality of Pauli operators, and layout information, which indicates connection relationships between a plurality of qubits included in a quantum device. A processing unit generates a matrix including a plurality of rows corresponding to the plurality of qubits and a plurality of columns corresponding to the plurality of projection operators. The processing unit executes diagonalization that converts the matrix into a diagonal matrix through a row operation, the row operation selecting two rows based on connection relationships indicated by the layout information and using one of the two rows to update the other row. The processing unit generates a quantum circuit indicating gate operations for the quantum device based on the row operation performed during the diagonalization.