Cat Qubit Calibration via Non-Linear Superconducting Circuit
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Solution Overview
Problem
Current methods for calibrating cat qubits require the use of transmons, which introduce noise and are time-consuming, making them inefficient for stabilizing cat qubits in superconducting quantum processors.
Innovation Solution
A method for calibrating a quantum system that stabilizes cat qubits without using transmons, involving a non-linear superconducting quantum circuit with a first mode and a second mode for 2-to-1 photon exchange, using either parametric pumping or DC bias, and a command circuit to deliver microwave radiation or current bias, with operations including obtaining command circuit parameters, applying them, performing measurements, and repeating until calibration conditions are met.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If transmon is used for reading the memory mode to perform Wigner tomography, then the state of the cat qubit can be detected, but the calibration process becomes time-consuming and introduces noise that saturates the bit-flip time
Solution Approach 1:
The patent removes the transmon component from the calibration process entirely. Instead of using a transmon to perform Wigner tomography for reading the memory mode, the invention uses a dedicated measurement apparatus that directly measures the cat qubit state without requiring transmon-mediated tomography. This extraction of the harmful transmon element eliminates both the time-consuming nature of the calibration and the noise it introduces, while still enabling accurate state detection.
2Measurement precision
If transmon is used for reading the memory mode, then the cat qubit state can be measured, but the bit-flip time saturates to a few milliseconds due to dispersive frequency shifts from thermal excitations
Solution Approach 1:
The patent eliminates the transmon from the measurement chain. The new measurement apparatus directly couples to the memory mode and measures the cat qubit state without introducing the spurious cross-Kerr terms and dispersive frequency shifts that cause thermal excitations and bit-flip saturation. This extraction removes the source of unreliability while preserving measurement capability.
Solution Approach 2:
The patent introduces a dedicated measurement apparatus as an intermediary between the memory mode and the measurement system. This apparatus is specifically designed to measure the cat qubit state without introducing the harmful effects of transmons. It acts as a specialized mediator that enables accurate measurement while avoiding the noise and instability problems associated with using a transmon for the same purpose.
3Manufacturing precision
If conventional Wigner tomography calibration process is used, then the operating parameters can be determined, but the process is tedious and time-consuming
Solution Approach 1:
The patent removes the Wigner tomography step from the calibration process. Instead of performing full tomography to determine operating parameters, the invention uses a simplified measurement approach that directly provides the necessary calibration information. This extraction of the tomography step dramatically reduces calibration time while still achieving the required precision for determining operating parameters.
Solution Approach 2:
The patent applies partial action by performing only the necessary measurements for calibration without completing a full Wigner tomography. The measurement apparatus is designed to extract the essential calibration parameters through a reduced set of measurements, avoiding the excessive time requirement of full tomography while maintaining sufficient precision for operating parameter determination.
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 method allows for faster calibration without the need for transmons, reducing noise and significantly reducing the time required for calibration, enabling more efficient stabilization of cat qubits in quantum processors.
Implementation Method 1
a parametric pump or a DC bias
Implementation Method 2
4-wave mixing coupling said first mode and said second mode
Implementation Method 3
3-wave mixing coupling said first mode and said second mode
Implementation Method 4
a non-linear superconducting quantum circuit having a first mode with a first resonant frequency for hosting said cat qubit
Data Source
Figure 1~2
Figure 3~5
Figure 6~7
AI summary
A method for calibrating a quantum system for stabilizing a cat qubit, said quantum system (1) including a non-linear superconducting quantum circuit (3) having a first mode (a) with a first resonant frequency (ωa) for hosting said cat qubit and a second mode (b) with a second resonant frequency (ωb) and comprising a non-linear element (7) arranged to induce a 2-to-1 photon exchange between said first mode (a) and said second mode (b) either via a parametric pump and 4-wave mixing coupling said first mode (a) and said second mode (b) or via a DC bias and 3-wave mixing coupling said first mode (a) and said second mode (b), and a command circuit (5) for delivering microwave radiation or current bias to the non-linear superconducting quantum circuit (3) in order to provide said parametric pump or said DC bias and a first mode drive, comprising the following operations: a) obtaining a set of command circuit operating parameters, each set consisting of either a couple associating a parametric pump frequency (ωp) and a first mode drive frequency (ωz) if said non-linear element (7) performs a 4-wave mixing or a couple associating a DC bias value (IDC) and a first mode drive frequency (ωz) if said non-linear element (7) performs a 3-wave mixing, b) applying said set of command circuit operating parameters to said command circuit (5) during a period of more than 10 ns, c) performing at least one measurement in the group comprising a first mode photon number measurement and a second mode electromagnetic field measurement, d) repeating operations a) to c) until a calibration condition has been met, e) deriving a calibrated set of command circuit operating parameters based on the measurements obtained in operation c).