Quantum Circuit Synthesis Minimizing CNOT Gates
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Solution Overview
Problem
Existing technologies face challenges in efficiently synthesizing quantum circuits, particularly in reducing the number of CNOT gates and dealing with exponential growth of Clifford and CNOT-Dihedral groups with the number of qubits, leading to high computational costs and inefficiencies.
Innovation Solution
A system and method that iteratively generates quantum circuits from 1 to N two-qubit gates, adding single gates that represent distinct operations, and identifies a desired circuit with minimized CNOT gates, facilitating Clifford and CNOT-Dihedral quantum circuits, and performs randomized benchmarking to improve efficiency and reduce computational costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If existing technologies are used to reduce the number of CNOT gates in quantum circuits, then the number of CNOT gates can be reduced in general quantum circuits, but they fail to reduce CNOT gates in Clifford quantum circuits and CNOT-Dihedral quantum circuits
Solution Approach 1:
The patent segments the quantum circuit synthesis process into distinct phases: generating Clifford circuits with minimal CNOT gates, then separately optimizing CNOT-Dihedral circuits. This segmentation allows specialized optimization techniques to be applied to each circuit type, achieving CNOT gate reduction where previous general-purpose methods failed.
Solution Approach 2:
The patent changes the optimization parameters specifically for Clifford and CNOT-Dihedral circuits, using group-theoretic properties and algebraic structures unique to these circuit types. By adjusting the synthesis approach to account for the specific mathematical properties of these circuit families, the method achieves CNOT gate reduction that general methods cannot accomplish.
2Adaptability or versatility
If the size of Clifford and CNOT-Dihedral groups is considered with increasing number of qubits, then the group size grows exponentially providing more computational capability, but the synthesis complexity and computational costs increase significantly
Solution Approach 1:
The patent performs preliminary analysis of the Clifford and CNOT-Dihedral group structures before attempting circuit synthesis. By pre-characterizing the group properties, generating functions, and algebraic structures, the method prepares optimization strategies in advance, avoiding the need to handle the full exponential complexity during the synthesis process itself.
Solution Approach 2:
The patent replaces brute-force computational approaches with algebraic and group-theoretic methods. Instead of mechanically searching through the exponentially growing space of quantum circuits, the method uses mathematical structures of Clifford and CNOT-Dihedral groups to systematically construct optimal circuits, substituting computational brute force with mathematical elegance.
3Ease of manufacture
If iterative constructive approaches are used based on the number of qubits, then quantum circuits can be built step-by-step, but the process becomes increasingly time-consuming and computationally expensive
Solution Approach 1:
The patent maintains continuous optimization throughout the circuit construction process rather than performing discrete, time-consuming optimization steps after circuit generation. The method continuously refines CNOT gate placement and circuit structure as qubits are added, preventing the accumulation of suboptimal configurations that would require expensive re-optimization later.
Solution Approach 2:
The patent performs preliminary optimization setup by establishing optimization criteria and group-theoretic constraints before the iterative construction begins. This preliminary configuration allows the iterative process to proceed efficiently with pre-planned optimization strategies, rather than requiring complex optimization decisions at each iterative step.
Data Source
AI summary
Systems, computer-implemented methods, and computer program products to facilitate synthesis of a quantum circuit are provided. According to an embodiment, a system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can comprise a circuit generation component that generates, iteratively, quantum circuits from 1 to N two-qubit gates, wherein at least one or more iterations (1, 2, . . . , N) adds a single two-qubit gate to circuits from a previous iteration based on using added single 2-qubit gates that represent operations distinct from previous operations relative to previous iterations. The computer executable components can further comprise a circuit identification component that identifies, from the quantum circuits, a desired circuit that matches a quantum circuit representation.