CNOT Gate Using Asymmetrically Threaded SQUID for Cat Qubit Stabilization
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Solution Overview
Problem
Current experimental implementations of CNOT gates for cat qubits are impractical due to the requirement of numerous non-linear components and parametric drives, failing to effectively address engineering challenges and achieve the necessary error correction ratio of κ1 /κ2 below 5 * 10^-3.
Innovation Solution
A quantum system comprising a command circuit, an asymmetrically threaded superconducting quantum interference device, and linearly coupled target and control qubits, which minimizes hardware and control drives, stabilizes cat qubits using two-photon dissipation, and induces a CNOT Hamiltonian with compensation terms to reduce noise and error probabilities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If conventional quantum circuits use sequence of two-qubit gates (CNOT or CZ) between ancilla qubit and data qubits for syndrome measurement, then joint information of several data qubits can be extracted, but the device complexity and error probability increase due to multiple gate operations
Solution Approach 1:
The patent combines multiple two-qubit gate operations into a single collective interaction between the ancilla qubit and multiple data qubits. The Hamiltonian H = χ Σᵢ σ_zⁱ ⊗ σ_z^a merges what would traditionally require sequential CNOT gates into one simultaneous operation, reducing gate sequence complexity while maintaining the ability to extract joint syndrome information.
Solution Approach 2:
The ancilla qubit is designed to interact simultaneously with multiple data qubits through a universal coupling mechanism. The interaction Hamiltonian allows the same ancilla qubit to perform syndrome measurement for multiple data qubits in parallel, making the measurement process more efficient and reducing the number of required gate operations.
2Reliability
If the number of physical qubits increases to improve error correction code distance, then quantum error correction effectiveness improves, but the ratio κ1/κ2 becomes harder to maintain below the required threshold
Solution Approach 1:
The patent changes the interaction parameter from transverse coupling to longitudinal coupling, modifying the Hamiltonian from H ∝ σ_x^a ⊗ σ_xⁱ to H ∝ σ_z^a ⊗ σ_zⁱ. This parameter change in the coupling mechanism reduces the error rate per interaction, allowing the system to maintain κ1/κ2 < 5×10⁻³ even as the number of physical qubits increases for higher code distance.
Solution Approach 2:
The patent replaces the conventional transverse coupling mechanism with a longitudinal coupling mechanism. This substitution changes the fundamental interaction type between qubits, utilizing a different physical mechanism that inherently produces lower error rates during gate operations, thereby maintaining the required error threshold despite scaling up the system.
3Stability of the object's composition
If cat qubit stabilization uses two-photon drive and dissipation, then the qubit maintains its quantum state, but the execution time and error probability of quantum gates are affected by the ratio κ1/κ2
Solution Approach 1:
The patent exploits the asymmetric error profile of cat qubits, where bit-flip errors are suppressed exponentially while phase-flip errors dominate. By designing the longitudinal interaction to primarily induce phase-flip errors and using the repetition code to correct these specific errors, the system achieves high gate fidelity despite the inherent κ1/κ2 ratio constraints of stabilized cat qubits.
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 simplifies the implementation of CNOT gates, reduces error probabilities, and maintains bit-flip suppression, enabling high-fidelity quantum operations within the fault-tolerant error threshold, thus enhancing the performance of quantum error correction codes.
Implementation Method 1
connected to at least one resonant portion, said target cat qubit device having a first mode with a first resonant frequency and a second mode with a second resonant frequency, and said asymmetrically threaded superconducting quantum interference device being arranged such that when said command circuit delivers a radiation having said second resonant frequency to said a least one resonant portion to drive said second mode and delivers radiation in said flux lines to modulate a common flux and/or a differential flux
Implementation Method 2
stabilizes a target cat qubit having said first resonant frequency... stabilizing mechanism for stabilizing the target cat qubit, the stabilizing mechanism comprising a command circuit for delivering a radiation having a second resonant frequency to a resonant portion of the target cat qubit device to drive a second mode of the target cat qubit device
Implementation Method 3
a control superconducting qubit device having a third mode with a third resonant frequency for hosting a control qubit arranged such that a Rabi oscillation of the third mode is induced when it is subject to a radiation having said third resonant frequency
Implementation Method 4
said control superconducting qubit device being linearly coupled to said target cat qubit device such that said third mode is linearly coupled with said asymmetrically threaded superconducting quantum interference device
Data Source
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AI summary
A quantum system for performing a CNOT gate, comprising a command circuit for providing radiation, a target cat qubit device and a control qubit device, coupled linearly, the target cat qubit comprises a non-linear element that is ATS which serves two purposes : engineering the 2-photon conversion Hamiltonian for cat qubit stabilization and engineering the CNOT Hamiltonian for performing a CNOT gate with the control qubit device. At any point in time, the ATS serves either the role of cat qubit stabilization or the role of CNOT gate.