Teleporting Magic States Between Color and Surface Codes
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Solution Overview
Problem
Current quantum computing methods face challenges in designing fault-tolerant Clifford circuits efficiently, particularly in reducing overhead costs and error rates, due to the need for extensive qubits and repetitive measurements, which increase runtime and resource consumption.
Innovation Solution
The use of Satisfiability Modulo Theories (SMT) solvers to encode Clifford circuit design problems, allowing for the construction of fault-tolerant circuits by formulating constraints as SMT decision problems, which can be solved to implement Clifford circuits on quantum hardware, including teleporting magic states from a quantum color code to a surface code for improved error correction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If quantum gates are encoded in error correcting code (e.g., surface code) to reduce error rates, then reliability improves, but device complexity and overhead number of qubits increase
Solution Approach 1:
The patent divides the quantum computational space into two distinct code spaces: a color code space for generating and storing magic states, and a surface code space for fault-tolerant computation. This segmentation allows each code to be optimized for its specific purpose, reducing the overall overhead compared to using a single code for all functions.
Solution Approach 2:
The patent introduces magic states as intermediary resources that are prepared in the color code space and then teleported to the surface code space. These magic states serve as a bridge between the two code spaces, enabling fault-tolerant implementation of non-Clifford gates without directly encoding them in the surface code, thus reducing the qubit overhead.
2Reliability
If measurements are repeated multiple times to reduce error rates, then reliability improves, but loss of time increases
Solution Approach 1:
The patent performs preliminary preparation of magic states in the color code space before the actual computation in the surface code space. By pre-preparing these resource states with the appropriate properties, the system avoids the need for repeated measurements during the computation itself, thereby reducing runtime while maintaining reliability.
3Reliability
If quantum gates are implemented with extensive qubits and repetitive measurements to ensure fault tolerance, then reliability improves, but productivity decreases
Solution Approach 1:
The patent segments the quantum computational tasks into magic state preparation (color code) and fault-tolerant computation (surface code). This allows the system to achieve fault tolerance through the surface code's error correction capabilities while maintaining productivity by using the color code's efficient magic state generation, avoiding the need for extensive repetitive measurements in the computation phase.
Data Source
AI summary
A technique for merging, via lattice surgery, a color code and a surface code, and subsequentially decoding one or more rounds of stabilizer measurements of the merged code is disclosed. Such a technique can be applied to bottom-up fault-tolerant magic state preparation protocol such that an encoded magic state can be teleported from a color code to a surface code. Decoding the stabilizer measurements of the merged code requires a decoding algorithm specific to the merged code in which error correction involving qubits at the border between the surface and color code portions of the merged code is performed. Error correction involving qubits within the surface code portion and within color code portion, respectively, may additionally be performed. In some cases, the magic state is prepared in a color code via a technique for encoding a Clifford circuit design problem as an SMT decision problem.