Trivalent Lattice Flag Qubit Mapping for Quantum Error Correction
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Solution Overview
Problem
Quantum circuits encoded on trivalent lattices face challenges in identifying flag qubit outcomes and correlating them to data qubit error configurations due to high weight errors from faults, leading to reduced effective distance and increased frequency collisions.
Innovation Solution
A system and method that encodes a quantum circuit to a trivalent lattice using a graph component to map ancilla qubits to data qubits via flag qubits based on a connectivity scheme, facilitating the identification of high weight errors and minimizing frequency collisions by implementing hexagonal and trapezoidal geometries, which reduce the degree of connectivity and correct errors through flag qubit measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If quantum circuits are encoded on trivalent lattices, then the code distance is maintained, but flag qubit outcomes cannot be accurately identified and correlated to data qubit error configurations
Solution Approach 1:
The patent segments the qubit system into distinct types (data qubits, flag qubits, and ancilla qubits) with specific roles. Flag qubits are introduced as intermediate elements that segment the error detection process, allowing independent analysis of flag outcomes and data qubit errors through the trivalent lattice structure.
Solution Approach 2:
Flag qubits serve as intermediaries between ancilla qubits and data qubits. The patent uses flag qubits as mediators to correlate fault outcomes with data qubit error configurations, enabling accurate identification of high weight errors without directly measuring all possible error states.
2Reliability
If faults occur in quantum circuits, then errors are introduced, but high weight errors reduce the effective distance
Solution Approach 1:
The patent performs preliminary action by pre-configuring flag qubits and their connectivity to data qubits before faults occur. The trivalent lattice structure is pre-established with flag qubits positioned to detect specific error patterns, enabling early identification of high weight errors before they propagate and reduce effective distance.
Solution Approach 2:
The patent implements feedback mechanisms where flag qubit measurement outcomes provide information about data qubit error configurations. This feedback loop allows the system to identify and correct high weight errors, maintaining effective distance despite fault occurrences.
3Ease of operation
If connectivity scheme is implemented, then qubit mappings are established, but frequency collisions increase
Solution Approach 1:
The patent applies local quality by assigning specific connectivity patterns to different regions of the trivalent lattice. Each flag qubit has localized connectivity to specific data qubits based on the quantum circuit's operational requirements, enabling optimized qubit mapping that minimizes frequency collisions in critical regions.
Data Source
AI summary
Techniques regarding encoding a quantum circuit to a trivalent lattice scheme to identify flag qubit outcomes are provided. For example, one or more embodiments described herein can comprise a system, which can comprise a memory that can store computer executable components. The system can also comprise a processor, operably coupled to the memory, and that can execute the computer executable components stored in the memory. The computer executable components can comprise a graph component that can encode a quantum circuit to a trivalent lattice that maps an ancilla qubit to a plurality of data qubits via a plurality of flag qubits based on a connectivity scheme of the quantum circuit.