Multi-Qubit Clifford Circuit Synthesis via Cost-Invariant Reduction
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Solution Overview
Problem
Conventional Clifford synthesizers and compilers struggle to efficiently compute and synthesize optimal multi-qubit Clifford circuits due to the intractable growth of Clifford group elements with the number of qubits, limiting their effectiveness to four qubits or less.
Innovation Solution
The system employs a cost-invariant reduction function to generate a library of n-qubit canonical representatives, each representing a cost-invariant equivalence class of Clifford group elements. This approach reduces the computational burden by synthesizing a single optimal circuit for each equivalence class, rather than computing every possible optimal circuit.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If conventional Clifford synthesizers compute a library of optimal Clifford circuits for all possible Clifford group elements with a given number of qubits, then the completeness of the circuit library is improved, but the computational time and resources required become intractable
Solution Approach 1:
The patent extracts only the essential information needed to represent Clifford circuits by focusing on cost-invariant equivalence classes rather than computing all possible circuits. The cost-invariant reduction function extracts canonical representatives that capture the unique structural properties of Clifford circuits up to local Clifford operations and qubit permutations, eliminating redundant computations.
Solution Approach 2:
The cost-invariant reduction function serves multiple purposes simultaneously: it classifies Clifford circuits by equivalence classes, identifies canonical representatives, and reduces the search space for optimal circuit synthesis. This multi-functional approach eliminates the need for separate computation steps and significantly reduces overall computational burden.
2Measurement precision
If conventional Clifford synthesizers compute optimal Clifford circuits for all possible Clifford group elements, then the accuracy of optimal circuit identification is improved, but the device complexity becomes intractable
Solution Approach 1:
The patent extracts only the essential structural information of Clifford circuits by representing them through cost-invariant equivalence classes. The canonical representatives capture all necessary properties for optimal identification while discarding redundant circuit representations that would increase computational complexity.
Solution Approach 2:
The patent changes the representation parameters from full circuit descriptions to cost-invariant equivalence classes characterized by canonical representatives. This parameter transformation reduces the complexity of the synthesizer while maintaining the ability to accurately identify optimal circuits through the reduced representation.
3Ease of manufacture
If conventional Clifford synthesizers use existing formulas for three or fewer qubits, then the ease of manufacture is improved, but the adaptability to larger qubit systems deteriorates
Solution Approach 1:
The cost-invariant reduction function provides a universal approach that works for any number of qubits by reducing all Clifford circuits to their canonical representatives within cost-invariant equivalence classes. This single framework replaces the need for separate formulas for different qubit counts and maintains ease of synthesis across all system sizes.
Solution Approach 2:
The patent introduces a dynamic reduction function that adapts its behavior based on the number of qubits while maintaining the same fundamental approach. The cost-invariant reduction algorithm naturally adjusts to handle different qubit counts without requiring separate implementations, providing both ease of manufacture and adaptability.
4Productivity
If conventional Clifford synthesizers use heuristic synthesis methods, then the productivity is improved, but the manufacturing precision deteriorates
Solution Approach 1:
The cost-invariant reduction function incorporates feedback mechanisms that systematically explore and evaluate circuit representations to identify true optimal solutions. By using canonical representatives and their associated costs, the method provides feedback that guides the synthesis process toward provably optimal circuits rather than relying on heuristic guesses.
Data Source
AI summary
Systems and techniques that facilitate efficient synthesis of optimal multi-qubit Clifford circuits are provided. In various embodiments, a system can receive as input a number n representing a quantity of qubits. In various instances, the system can generate, via a cost-invariant reduction function, as output a library of different n-qubit canonical representatives that respectively correspond to different cost-invariant equivalence classes of n-qubit Clifford group elements. In various embodiments, a system can receive as input a first Clifford group element. In various aspects, the system can search a database of canonical representatives, wherein different canonical representatives in the database respectively correspond to different cost-invariant equivalence classes of Clifford group elements. In various cases, the system can identify based on the search a second Clifford group element that implements the first Clifford group element and that has a lower entangling-gate cost than the first Clifford group element.