Probabilistic Quantum Circuits with Fallback Gate Reduction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for compiling high-level quantum algorithms into fault-tolerant circuits are inefficient, particularly in reducing the number of gates required and ensuring success within a predetermined number of cycles, especially for universal gate sets beyond Clifford+T.
Innovation Solution
The implementation of probabilistic quantum circuits with fallback (PQFs) that utilize a series of multi-qubit stages with a deterministic fallback circuit to achieve target rotations, reducing the number of gates and ensuring success with a finite number of trials, specifically in the Clifford+T, Clifford+π/12, and Clifford+V bases.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Repeat-Until-Success (RUS) circuits are used to reduce the expected number of elementary gates, then the gate count approaches the information-theoretic lower bound, but the circuit complexity increases and success is not guaranteed within a predetermined number of cycles
Solution Approach 1:
The circuit is divided into multiple stages, each attempting to implement the target rotation with decreasing complexity. Stage 1 uses the simplest approximation, and subsequent stages use progressively more complex circuits only if previous stages fail, segmenting the problem into hierarchical layers of increasing fidelity
Solution Approach 2:
The most complex fallback circuit is designed and prepared in advance to handle all possible failure cases from previous stages. This preliminary preparation ensures that success is guaranteed within a predetermined number of cycles, as the fallback circuit is specifically designed to correct any errors from earlier stages
2Productivity
If RUS circuits are used for general gate sets beyond Clifford+T, then synthesis efficiency improves, but the method is not readily applicable to more general gate sets
Solution Approach 1:
The multi-stage framework is designed to be universally applicable to any universal gate set by replacing the specific Clifford+T decomposition circuits with decompositions appropriate for the target gate set. The structural framework remains the same while the specific unitary operations adapt to different gate sets, making the method versatile across Clifford+T, Clifford+π/12, Clifford+V, and other universal gate sets
3Reliability
If deterministic fallback circuits are always used to guarantee success, then success is ensured within a predetermined number of cycles, but the number of gates increases and efficiency decreases
Solution Approach 1:
The circuit dynamically adapts its complexity based on measurement outcomes. Simple circuits are attempted first with the expectation of success, and only upon failure does the system transition to more complex circuits. This dynamic approach ensures reliability through the guaranteed fallback while maintaining efficiency by using simple circuits for the majority of successful cases
Data Source
AI summary
A Probabilistic Quantum Circuit with Fallback (PQFs) is composed as a series of circuit stages that are selected to implement a target unitary. A final stage is conditioned on unsuccessful results of all the preceding stages as indicated by measurement of one or more ancillary qubits. This final stage executes a fallback circuit that enforces deterministic execution of the target unitary at a relatively high cost (mitigated by very low probability of the fallback). Specific instances of general PQF synthesis method and are disclosed with reference to the specific Clifford+T, Clifford+V and Clifford+π/12 bases. The resulting circuits have expected cost in logb(1/ε)+O(log(log(1/ε)))+const wherein b is specific to each basis. The three specific instances of the synthesis have polynomial compilation time guarantees.