Clifford Circuit Benchmarking With Hadamard Extraction
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Solution Overview
Problem
Current randomized benchmarking protocols in quantum computing are inefficient and prone to errors due to high computational complexity and reliance on accurate state preparation and measurement, especially as the number of qubits increases, making it challenging to detect low error probabilities effectively.
Innovation Solution
A method is introduced to generate a randomized benchmarking protocol using randomly generated Hadamard-free Clifford circuits, formed by combining uniformly distributed phase gates and conditional NOT gates, which are applied alternately with Hadamard gates to reduce the number of circuit elements and optimize the protocol length, allowing for more efficient noise measurement in quantum mechanical processors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard randomized benchmarking protocols are used with full Clifford circuits, then comprehensive noise characterization is achieved, but computational complexity increases and runtime becomes prohibitively long
Solution Approach 1:
The patent extracts and removes Hadamard gates from the Clifford circuit structure, creating Hadamard-free Clifford circuits. This extraction reduces the circuit complexity and runtime while maintaining the essential functionality for noise characterization through the alternating application of Hadamard layers with the reduced Clifford circuits.
Solution Approach 2:
The patent segments the Clifford circuit into distinct Hadamard layers and Hadamard-free Clifford circuit layers, creating an alternating structure. This segmentation allows for optimized generation and application of each layer type, reducing overall computational complexity while preserving the benchmarking protocol's effectiveness.
2Quantity of substance
If the number of qubits increases, then more comprehensive quantum system testing is enabled, but the number of random bits required and computational complexity increase exponentially
Solution Approach 1:
By removing Hadamard gates from the Clifford circuit structure, the patent reduces the number of random bits required for circuit generation. This extraction creates a more scalable protocol that can handle larger numbers of qubits without exponential increases in computational complexity.
Solution Approach 2:
The patent introduces dynamic alternating layers of Hadamard gates and Hadamard-free Clifford circuits, where the structure adapts to different numbers of qubits. This dynamic structure allows the protocol to scale efficiently by maintaining a consistent alternating pattern regardless of system size.
3Adaptability or versatility
If full Clifford circuits are used in randomized benchmarking, then complete gate set coverage is achieved, but the protocol length and number of circuit elements increase
Solution Approach 1:
The patent extracts Hadamard gates from the Clifford circuit while maintaining gate set coverage through the alternating layer structure. This extraction reduces protocol length by eliminating redundant Hadamard gates from the Clifford circuit itself while preserving their functionality in dedicated Hadamard layers.
Solution Approach 2:
The alternating Hadamard layers serve multiple functions: they provide the necessary Hadamard transformations for gate set coverage, act as separators between Clifford circuit applications, and enable efficient circuit generation. This multi-functionality reduces overall protocol length while maintaining versatility.
Data Source
AI summary
A method of generating a randomized benchmarking protocol includes providing a randomly generated plurality of Hadamard gates; applying the Hadamard gates to a plurality of qubits; and generating randomly a plurality of Hadamard-free Clifford circuits. Each of the plurality of Hadamard-free Clifford circuits is generated by at least randomly generating a uniformly distributed phase (P) gate, and randomly generating a uniformly distributed linear Boolean invertible matrix of conditional NOT (CNOT) gate, and combining the P and CNOT gates to form each of the plurality of Hadamard-free Clifford circuits. The method also includes combining each of the plurality of Hadamard-free Clifford circuits with corresponding each of the plurality of Hadamard gates to form a sequence of alternating Hadamard-free Clifford-Hadamard pairs circuit to form the randomized benchmarking protocol; and measuring noise in a quantum mechanical processor using the randomized benchmarking protocol.