Quantum Circuit Synthesis for Superposed States
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Solution Overview
Problem
Quantum computing faces challenges in minimizing error rates and reducing execution times due to noise susceptibility in quantum bits, particularly during gate operations.
Innovation Solution
The development of techniques for synthesizing quantum circuits with minimal depths and minimal numbers of unique layers of controlled two-qubit gates, such as the controlled-NOT gate, to prepare superposed states of quantum bit registers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If quantum circuits use more gates and layers to prepare superposed states, then the precision of state preparation improves, but the error rate increases and execution time increases
Solution Approach 1:
The patent applies parameter changes by transforming the quantum circuit synthesis problem into a graph theory problem with specific parameters: using edge-colored graphs where colors represent gate types, and finding optimal colorings that minimize the number of unique layers. This mathematical parameter transformation enables systematic optimization of circuit depth and gate count while maintaining state preparation precision.
Solution Approach 2:
The patent introduces a new dimensional framework by mapping quantum circuit layers to graph edge colorings. Instead of optimizing circuits layer-by-layer in sequential time dimension, the invention uses graph coloring theory to simultaneously optimize multiple layers across different dimensions (gate types, qubit pairs, connectivity constraints), reducing the overall circuit depth and unique layer count.
2Manufacturing precision
If quantum circuits use more gates and layers to prepare superposed states, then the precision of state preparation improves, but the execution time increases
Solution Approach 1:
The patent transforms the execution time optimization problem into a graph coloring parameter optimization problem. By representing circuit layers as edge colorings and using mathematical graph theory parameters (chromatic index, edge coloring constraints), the invention systematically minimizes the number of unique layers and overall circuit depth, directly reducing execution time while maintaining precision.
Solution Approach 2:
The patent applies preliminary action by pre-defining the graph structure and edge coloring scheme before actual circuit synthesis. The connectivity graph and its edge coloring are established in advance based on quantum processor constraints, allowing the synthesis algorithm to work within predetermined optimal parameters rather than iteratively adjusting circuit depth during synthesis, thus reducing total execution time.
3Reliability
If quantum circuits are optimized to minimize gates and layers, then error rates and execution times reduce, but the complexity of circuit synthesis increases
Solution Approach 1:
The patent replaces the mechanical/iterative trial-and-error approach of traditional quantum circuit synthesis with a mathematical graph theory framework. Instead of sequentially adjusting gates and layers through complex optimization routines, the invention substitutes this with deterministic graph coloring algorithms and mathematical optimization, simplifying the synthesis process while achieving minimal gate counts and circuit depths.
Solution Approach 2:
The patent creates a universal framework that handles multiple quantum processor connectivity topologies (linear, grid, all-to-all, custom) through a single graph theory approach. The edge-colored graph model and coloring algorithms universally apply to any connectivity constraint, eliminating the need for separate synthesis algorithms for each topology and reducing overall synthesis complexity.
Data Source
AI summary
A process is provided to generate a quantum circuit for preparing a target superposed state of a quantum bit register on a connectivity graph which comprises labeled edges and vertexes. The process comprises generating an initial layer of the quantum circuit which comprises a single-qubit gate to place the quantum bit register in an initial superposed state, and generating a sequence of layers following the initial layer, to generate the target superposed state. The sequence of layers comprises a plurality of layers of a same type of a controlled two-qubit gate which conditionally flips a state of a target quantum bit based on a state of a control quantum bit. A number of unique layers of the plurality of layers of the same type of a controlled two-qubit gate is no greater than a number of unique labels in a given set of labels for the connectivity graph.