Josephson Four-Wave Mixing Circuit With Kerr Shift Cancellation

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Solution Overview

Problem

Existing quantum information processing technologies face challenges in precisely controlling qubits and implementing multi-qubit gates due to unwanted frequency shifts caused by self-Kerr and cross-Kerr interactions, which limit coherence times and operational fidelity.

Innovation Solution

A Josephson junction-based four-wave mixing circuit is designed with two capacitively coupled anharmonic oscillators, engineered to have equal resonant frequencies and opposite fourth-order nonlinearity, canceling out undesired diagonal interactions and preserving four-wave mixing capabilities.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Device complexity

If Josephson junction-based superconducting qubits are used to achieve strong coupling and simple two-qubit gates, then device complexity is reduced and scalability is improved, but unwanted frequency shifts from self-Kerr and cross-Kerr interactions increase, reducing coherence times and operational fidelity

Engineering Contradiction:
Improvequbit coupling structureVSAvoidquantum operation fidelity
Core Design Contradiction:
Device complexityVSReliability

Solution Approach 1:

The patent employs asymmetric coupling between the first and second nonlinear superconducting devices, where the coupling strength differs from the self-interaction strengths. This asymmetric configuration enables selective cancellation of unwanted frequency shifts while preserving the desired four-wave mixing interactions, thereby improving quantum operation fidelity without sacrificing the simplicity of the superconducting qubit architecture

Inventive Principle:
Principle #4Asymmetry

Solution Approach 2:

The patent adjusts the resonant frequencies and nonlinearity parameters of the two coupled nonlinear superconducting devices to specific relationships (equal resonant frequencies with opposite fourth-order nonlinearity). By carefully tuning these parameters, the system achieves cancellation of diagonal interactions (self-Kerr and cross-Kerr effects) while maintaining strong coupling for two-qubit gates, thus resolving the contradiction between device simplicity and operational fidelity

Inventive Principle:
Principle #35Parameter changes

2Ease of operation

If strong non-linearity from Josephson effect is utilized to enable simple multi-qubit gates, then gate implementation becomes easier, but frequency shifts from diagonal interactions increase, limiting coherence times

Engineering Contradiction:
Improvemulti-qubit gate implementationVSAvoidqubit coherence time
Core Design Contradiction:
Ease of operationVSDuration of action of moving object

Solution Approach 1:

The patent converts the harmful diagonal interactions (self-Kerr and cross-Kerr frequency shifts) into a beneficial configuration by coupling two devices with opposite fourth-order nonlinearity. The unwanted frequency shifts from each device cancel each other out, while the useful four-wave mixing interactions are preserved and enhanced. This transforms the harmful non-linearity into a benefit, allowing strong coupling for simple gates while maintaining long coherence times

Inventive Principle:
Principle #22Blessing in disguise (Convert harm into benefit)

Solution Approach 2:

The patent uses the second nonlinear superconducting device with negative anharmonicity as a counterweight to the first device with positive anharmonicity. The opposite signs of their fourth-order nonlinearities create equal and opposite frequency shifts that cancel each other, effectively neutralizing the harmful diagonal interactions while preserving the desired quantum interactions

Inventive Principle:
Principle #8Anti-weight (Counterweight)

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 eliminates frequency shifts, allowing for precise control of qubits and enhancing the fidelity of quantum operations by isolating the desired four-wave mixing interactions, thereby improving the scalability and coherence of quantum information processing.

Implementation Method 1

All superconducting qubit designs use at least one Josephson junction as a non-linear non-dissipative element. Superconducting qubits exhibit excellent quantum coherence and a strong non-linearity associated with the Josephson effect.

Methodology Applied
Scientific EffectJosephson effect: Josephson Effect

Implementation Method 2

engineered to have equal resonant frequencies and opposite fourth-order nonlinearity, canceling out undesired diagonal interactions

Methodology Applied
Scientific EffectDestructive interference: Interference

Implementation Method 3

Josephson junction-based four-wave mixing circuit is designed with two capacitively coupled anharmonic oscillators, engineered to have equal resonant frequencies and opposite fourth-order nonlinearity, preserving four-wave mixing capabilities

Methodology Applied
Scientific EffectFour-wave mixing:

Data Source

PatentEP3912200B1Josephson nonlinear circuit
Publication Date: 2024.05.15 YALE UNIVERSITY
  • EP3912200B1 patent drawingFigure 1
  • EP3912200B1 patent drawingFigure 2A~2B
  • EP3912200B1 patent drawingFigure 3A~3C

AI summary

Parametrically pumped four-wave mixing is a key building block for many developments in the field of superconducting quantum information processing. However, undesired frequency shifts such as Kerr, cross-Kerr and Stark shifts inherent with four-wave mixing, lead to difficulties in tuning up the desired parametric processes and, for certain applications, severely limit the fidelities of the resulting operations. Some embodiments include a Josephson four-wave mixing device consisting of a SQUID transmon coupled to a half-flux biased SNAIL transmon, a.k.a. capacitively shunted flux qubit. When the two transmons have matching frequencies, an interference effect cancels the negative Kerr of the SQUID transmon with the positive Kerr of the SNAIL transmon while preserving parametric four-wave mixing capabilities.