Josephson Parametric Modulation for Stable GKP Qubit Encoding
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Solution Overview
Problem
Current quantum error correction methods, such as surface codes, require a large number of high-quality two-level systems, leading to cost and control complexity issues in implementing fault-tolerant quantum calculations.
Innovation Solution
A superconducting microwave quantum circuit with a controllable-energy Josephson junction element connected to a linear passive circuit portion, exhibiting a target resonant mode with an impedance higher than 13 kohm, is used to implement modular operators for stabilizing GKP code qubits, thereby improving the coherence time to gate time ratio.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If surface codes are used for quantum error correction, then fault-tolerant quantum calculation can be achieved, but a large number of high-quality two-level systems are required, leading to increased cost and control complexity
Solution Approach 1:
The patent replaces the mechanical/electronic control of multiple two-level systems with a bosonic mode system that uses quantum optical effects. Instead of controlling many discrete qubits, the invention uses a continuous variable bosonic mode that can encode multiple logical qubits, thereby substituting a complex multi-component system with a simpler single-mode system that achieves the same fault-tolerance goal
Solution Approach 2:
The bosonic mode serves multiple functions simultaneously: it acts as both the quantum memory storing logical qubits and the medium for error correction operations. The same bosonic mode can encode multiple logical qubits and support various quantum gates, providing multi-functionality that reduces the overall system complexity compared to dedicated two-level systems for each function
2Reliability
If surface codes are implemented, then quantum error correction can be performed, but control complexity increases due to the need to control a large number of quantum systems
Solution Approach 1:
The patent merges the storage function and error correction function into a single bosonic mode system. Instead of separately controlling multiple qubits for storage and multiple ancillary qubits for error correction, the invention combines these functions into one unified bosonic mode that handles both tasks, thereby reducing control complexity
Solution Approach 2:
The bosonic mode system is designed to perform error correction autonomously through its inherent quantum optical properties. The system uses the bosonic mode's own quantum states and interactions to detect and correct errors without requiring complex external control mechanisms, enabling self-service error correction that simplifies operation
3Reliability
If cat codes are used, then one type of logic error can be eliminated, but concatenation with repetition code is required to correct both bit flip and phase flip errors, increasing system complexity
Solution Approach 1:
The patent changes the fundamental parameter of the quantum code from discrete variable (qubit-based cat codes) to continuous variable (bosonic mode). This parameter change allows the system to naturally correct both bit flip and phase flip errors through the continuous nature of the bosonic states, eliminating the need for code concatenation and reducing 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
The proposed solution allows for reliable stabilization of GKP code qubits, significantly improving the coherence time to gate time ratio compared to existing implementations, and enabling more efficient fault-tolerant quantum calculations.
Implementation Method 1
The energy of said Josephson junction element is controllable and modulated by at least two respective pulse trains
Implementation Method 2
a controllable-energy Josephson junction element connected to a linear passive circuit portion
Implementation Method 3
exhibiting a target resonant mode with an impedance higher than 13 kohm
Data Source
AI summary
A superconducting microwave quantum circuit includes a controllable-energy Josephson junction element connected to a linear passive circuit portion exhibiting a plurality of resonant modes, of which the Foster's first-form decomposition across the terminals of the Josephson junction element includes a target resonant mode exhibiting an impedance Z higher than 13 kohm and a pulsation w. The energy of the Josephson junction element is controllable and modulated by at least two respective pulse trains within which the pulses are separated by a duration 2π/w and have a width of less than one tenth of this duration, the amplitude of the pulses within each respective pulse train being modulated by a respective sinusoidal carrier and the pulse trains are respectively offset pairwise by a duration Δt such that |sin(w*At)| equals 13 kohm/Z, so that the resonant mode of pulsation w is stabilised in one of two GKP states encoding a qubit.