Pauli Exponential Decomposition for Lower-Depth Quantum Circuits
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Solution Overview
Problem
Quantum computing systems face increased system noise and estimation errors due to high quantum circuit depth and width, leading to inefficiencies in qubit coherency time and resource utilization.
Innovation Solution
A system and method for decomposing exponential Pauli operators into Pauli and Clifford operators, followed by Clifford transformations, to reduce quantum circuit depth and width, thereby reducing the total quantum gate count and circuit complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If quantum circuit depth and width are increased to implement complex computations, then computational capability is improved, but system noise and estimation errors increase
Solution Approach 1:
The patent segments the exponential Pauli operator into multiple Pauli operators through decomposition. This breaks down a complex operation into simpler components that can be executed with fewer qubits and shallower circuit depth, thereby maintaining computational capability while reducing noise accumulation
Solution Approach 2:
The patent introduces Clifford transformations as intermediary operations that facilitate the decomposition and recombination of Pauli operators. These transformations enable the circuit to be rewritten in an equivalent form with reduced depth and width, achieving the same computational result with lower noise
2Productivity
If total quantum gate count is reduced to lower execution time, then productivity is improved, but circuit complexity reduction is needed
Solution Approach 1:
By decomposing the exponential Pauli operator into multiple Pauli operators, the patent enables parallel execution of independent operations and identifies redundant gates that can be removed, thereby reducing total gate count and execution time
Solution Approach 2:
The patent transforms the circuit representation by applying Clifford transformations that change the parameterization of the quantum gates. This reparameterization reveals optimization opportunities that reduce the number of gates required while preserving the computational function
3Reliability
If CNOT gate count is reduced to minimize noise, then reliability is improved, but circuit transformation complexity increases
Solution Approach 1:
The patent extracts CNOT gates from the circuit through systematic decomposition of Pauli operators. By identifying and removing redundant CNOT operations that do not contribute to the computational outcome, the circuit noise is reduced while the transformation process follows structured rules
Solution Approach 2:
Clifford transformations serve as intermediary operations that systematically rewrite the circuit in an equivalent form with fewer CNOT gates. These transformations provide a structured methodology that automates the reduction process, managing the transformation complexity
4Productivity
If qubit coherency time is optimized to execute more operations, then productivity is improved, but circuit depth must be reduced
Solution Approach 1:
The decomposition of the exponential Pauli operator segments the circuit into shallower layers with fewer sequential operations. This reduces the critical path length and overall circuit depth, allowing more operations to be completed within the qubit coherency time window
Solution Approach 2:
The patent performs preliminary decomposition and transformation of the circuit before execution, reorganizing operations to minimize depth. This preliminary optimization ensures that the circuit is prepared in its most efficient form, maximizing the utilization of available coherency time
Data Source
AI summary
Systems, computer-implemented methods, and/or computer program products to facilitate reduction of a quantum circuit are provided. A computer-implemented method can comprise performing, by a system operatively coupled to at least one processor, decomposition of an exponential of a first Pauli operator of 1 to n Pauli operators of the quantum circuit, and performing, by the system, a first Clifford transformation of a primary operator of the quantum circuit, where the primary operator can comprise a linear combination of primary Pauli operators, and where the first Clifford transformation can employ a result of the decomposition. Performing the decomposition can comprise decomposing the exponential of the first Pauli operator into a first non-Clifford operator and a first Clifford operator, with the first Clifford operator being employed for the first Clifford transformation. Additional decompositions and respective transformations can be performed iteratively until decomposition of all exponentials of the 1 to n Pauli operators.