Asymmetric Cat Qubit Repetition Code for Fault-Tolerant Error Correction
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Solution Overview
Problem
Current implementations of cat-qubit repetition codes struggle to operate below the fault-tolerant error threshold, leading to a decrease in the lifetime of logical information as the number of physical data qubits increases.
Innovation Solution
The proposed solution involves a repetition code for cat-qubits that includes d data cat-qubits and at least d-1 ancillary cat-qubits, where the ancillary cat-qubits have a two-photon dissipation rate greater than that of the data cat-qubits. This configuration allows for error correction cycles that prepare ancillary cat-qubits in specific states, activate CNOT gates, and measure photon parity, thereby enhancing error tolerance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the number of physical data qubits is increased to improve error correction capability, then the protection against decoherence is improved, but the lifetime of logical information decreases when operating above the fault-tolerant error threshold
Solution Approach 1:
The patent changes the parameter of two-photon dissipation rate by introducing ancillary cat-qubits with a higher two-photon dissipation rate than the data cat-qubits. This parameter change enables the system to operate below the fault-tolerant error threshold while maintaining extended logical information lifetime, resolving the contradiction between error correction capability and information persistence
2Device complexity
If conventional repetition codes are used for cat-qubits, then the error correction complexity is reduced, but the system cannot operate below the fault-tolerant error threshold
Solution Approach 1:
The patent introduces ancillary cat-qubits as intermediary elements with specialized properties (higher two-photon dissipation rate) that mediate between the data cat-qubits and the error correction mechanism. These ancillary qubits enable the repetition code to operate below the fault-tolerant threshold without significantly increasing overall system complexity
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach allows for the implementation of a cat-qubit repetition code that is compatible with the fault-tolerant error threshold, significantly improving the error tolerance threshold and extending the lifetime of logical information.
Implementation Method 1
the two-photon dissipation rate of the ancillary cat-qubits is forced to be greater than the two-photon dissipation rate of the data cat-qubits
Implementation Method 2
respective ones of the ancillary cat-qubits are connected to two data cat-qubits by two respective CNOT gates
Implementation Method 3
measuring the parity of the number of photons of this ancillary cat-qubit
Data Source
AI summary
The disclosure relates to a repetition code for a cat qubit comprising a number d of data cat-qubits and at least ancillary cat-qubits, wherein the number d is greater than or equal to 3, each ancillary cat-qubit is connected to two data cat-qubits by two respective CNOT gates such that no data cat-qubit is connected to more than two ancillary cat-qubits, and the two-photon dissipation rate of the ancillary cat-qubits is greater than the two-photon dissipation factor of the data cat-qubits. Said repetition code is implemented by carrying out, for each ancillary cat-qubit, error correction cycles comprising at least the following steps: preparing the ancillary cat-qubit in a state suitable for the operator X: “I+>” or “I−>”; activating one of the two CNOT gates connected to said ancillary cat-qubit (6); activating the other CNOT gate connected to this ancillary cat-qubit; and measuring the photon-number parity of said ancillary cat-qubit.