Surface Code Magic State Injection Using Controlled Hook Errors
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Solution Overview
Problem
Existing quantum computing systems face challenges in reliably encoding and retaining information for long periods due to high error rates, which are not addressed by conventional error correction methods, and magic state distillation is resource-intensive and costly.
Innovation Solution
The use of a hook error mechanism to intentionally introduce a controlled error during the surface code cycle, reducing the number of physical qubits and error mechanisms, and optimizing the circuit to minimize additional two-qubit interactions and connectivity, thereby improving the fidelity of magic state injection.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional error correction methods are used, then quantum information can be protected, but the number of physical qubits and error mechanisms increases
Solution Approach 1:
The patent intentionally introduces hook errors during the surface code cycle, converting a harmful error mechanism into a beneficial tool for magic state injection. By deliberately creating controlled errors that rotate logical observables, the system achieves magic state preparation without requiring additional physical qubits or complex error correction mechanisms.
Solution Approach 2:
The patent changes the parameter of error introduction from passive (correcting random errors) to active (intentional hook errors with specific rotation properties). This parameter change allows the system to use the same surface code infrastructure for both error correction and magic state injection, reducing overall device complexity.
2Reliability
If magic state distillation is used, then high-fidelity magic states can be obtained, but resource consumption and cost increase
Solution Approach 1:
The patent performs preliminary magic state injection during the surface code cycle itself, rather than requiring separate distillation processes. By injecting magic states as part of the regular error correction cycle using hook errors, the system eliminates the need for resource-intensive multi-round distillation protocols.
Solution Approach 2:
The surface code cycle is made multi-functional by simultaneously performing error correction and magic state injection. The same circuit operations that correct errors also introduce the necessary hook errors for magic state preparation, eliminating the need for dedicated distillation hardware and reducing resource consumption.
3Device complexity
If the surface code cycle is optimized to exclude no-operation entangling gates, then circuit complexity is reduced, but the number of additional two-qubit interactions must be minimized
Solution Approach 1:
The patent applies local quality by introducing hook errors at specific locations within the surface code lattice rather than uniformly across all qubits. This localized approach allows the circuit to maintain simple connectivity requirements while achieving the necessary error rotation effects only where needed for magic state injection.
Data Source
AI summary
Methods, systems, and apparatus for encoding a magic state in a surface code patch of physical qubits with a target distance. In one aspect, a method includes performing a first surface code cycle on a surface code patch of physical qubits with an initial distance to encode the magic state into the surface code patch. Performing the first surface code cycle introduces a hook error associated with a four-body stabilizer on a qubit included in the surface code patch, where the hook error rotates a logical observable of the surface code patch. Further, performing the first surface code cycle includes initializing the qubit in the magic state. One or more rounds of error detection are performed on the surface code patch that encodes the magic state. The surface code patch is expanded to the target distance based on results of the one or more rounds of error detection.