Probabilistic Quantum Error Correction for Choi Rank Two Noise
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Solution Overview
Problem
Existing quantum error correction codes are either perfect, requiring more than two qubits to correct errors with certainty, or approximate, failing to achieve perfect recovery of the initial state. Additionally, known probabilistic codes do not effectively correct errors of Choi rank at most two when acting on two qubits only.
Innovation Solution
A probabilistic quantum error correction code that encodes one qubit of information using two data qubits, specifically designed to correct errors generated by a noise channel of Choi rank not greater than two. This code includes an error correction procedure with a positive probability of success, returning classical information indicating its status, and perfectly recovers the initial state if successful.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If perfect reconstruction codes are used to correct errors with certainty, then error correction reliability is improved, but the number of qubits required increases to more than two
Solution Approach 1:
The patent applies partial action by implementing error correction with a positive probability of success rather than requiring certainty. The code corrects errors of Choi rank at most two with probability p > 0, accepting that correction is not guaranteed but achieves the correction goal when successful, thereby resolving the contradiction between reliability and resource consumption.
2Device complexity
If approximate error correction codes are used to reduce qubit requirements, then device complexity is reduced, but perfect recovery of the initial state is not achieved
Solution Approach 1:
The patent applies local quality by designing the error correction code to perfectly recover the initial state when correction succeeds, while accepting that correction may fail with some probability. The code achieves perfect precision (pure state recovery) locally in the success case, rather than providing approximate recovery in all cases, thus resolving the contradiction between complexity and precision.
3Device complexity
If known probabilistic codes are used to operate on two qubits, then device complexity is reduced, but errors of Choi rank at most two are not effectively corrected
Solution Approach 1:
The patent applies parameter changes by specifically designing the encoding and decoding operations to target errors of Choi rank at most two. The code uses a two-qubit system with carefully chosen unitary transformations and measurement bases that are optimized for this specific error model, changing the parameters of the error correction approach to match the error characteristics, thereby resolving the contradiction between complexity and correction capability.
Data Source
AI summary
A quantum computer implemented probabilistic error correction method for use with quantum circuits with a noise channel N(X) that has a Choi rank not greater than two, such as N(X)=N0XN0†+N1XN1†. The method comprising steps of: encoding a first qubit into an encoded state |ψ, putting a second qubit into an arbitrary fixed state |d1, implementing two qubit unitary operation UE on the first qubit and the second qubit to obtain an encoded state UE(|ψ⊗|d1), and after the encoded state is affected by the noise N(X), implementing two qubit unitary operation UD, followed by measuring the second qubit in the {|d2, |d2⊥} basis measurement to obtain a classical label i∈{0,1}, next preparing a third qubit in the arbitrary fixed state |d3, and implementing two qubit unitary operation VD on the first qubit and the third qubit, followed by measuring the third qubit in the {|d4, |d4⊥} basis measurement to obtain a classical label j∈{0,1}, and when (i,j)=(0,0) accepting as an output δexp a decoded state of the first qubit, and when (i,j)≠(0,0) rejecting the output δexp of a decoded state of the first qubit.