Quantum Circuit Synthesis via Deterministic Walks
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Solution Overview
Problem
Current quantum circuit synthesis methods are inefficient and prone to errors, especially for multi-qubit systems, and require extensive resources due to the need for precise implementation of T gates, which are costly in terms of quantum resources.
Innovation Solution
A deterministic walk-based method using a parallel search algorithm for synthesizing quantum circuits, which reduces the search space and minimizes the use of expensive quantum resources by employing a meet-in-the-middle approach and parallel collision finding techniques to efficiently generate unitary matrices and reduce the T count.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional quantum circuit synthesis methods are used, then circuit synthesis can be performed, but the process is inefficient and requires extensive quantum resources including high T gate counts
Solution Approach 1:
The patent segments the quantum circuit synthesis problem into two independent sub-problems (forward propagation and backward propagation) that can be solved separately and then combined. This division allows each sub-problem to be optimized independently, reducing the overall computational complexity and resource requirements while maintaining synthesis accuracy.
Solution Approach 2:
The patent performs preliminary actions by pre-computing basis state transformations and storing them in lookup tables before the actual synthesis process. This pre-processing step eliminates the need for repeated computations during synthesis, significantly improving efficiency and reducing quantum resource consumption without compromising the accuracy of the final circuit.
2Reliability
If the search space for quantum circuit synthesis is exhaustive, then all possible circuits are considered, but the computational complexity becomes unmanageable
Solution Approach 1:
The patent divides the exhaustive search space into two manageable halves using forward and backward propagation through basis states. By segmenting the search process and using meet-in-the-middle techniques, the computational complexity is reduced from exponential to polynomial while maintaining the reliability of finding optimal circuits through systematic exploration of all possibilities.
Solution Approach 2:
The patent transforms the single-dimension exhaustive search problem into a multi-dimensional search by introducing basis state transformations and dual propagation directions. This dimensional change allows the search to proceed through intermediate basis states, effectively breaking down the complex search space into manageable layers that can be processed efficiently.
Data Source
AI summary
There is provided a method for implementing an algorithm for forming, or synthesizing, quantum circuits on a system capable of performing the quantum circuit synthesis by using a deterministic walk (i.e. a pseudo-random walk with a random or pseudo-random starting point). In one implementation, the deterministic walk is performed using a parallel search algorithm. In an implementation of the parallel search algorithm, a user utilizes a programming language to write instructions for a compiler. Then, a meet in the middle approach is utilized to separate the circuit into two halves. Next, the parallel search technique is used to find a claw, or a pair, which satisfies the circuit analysis. Subsequently there is the production of a result and/or a synthesis of the circuit if the pair is found.