Fast Conditional Displacement of Quantum Oscillator
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Solution Overview
Problem
Current approaches to quantum computing in the circuit-QED regime face challenges in scaling due to degradation of coherence in individual components and introduction of new error channels as circuits grow, particularly in achieving fast and reliable universal control over bosonic cavity modes without increasing coupling strength, which is limited by the need for narrow bandwidth signals.
Innovation Solution
The implementation of an anti-symmetrical negatively-conditioning displacement signal with a bandwidth exceeding the frequency difference between ancilla qubit states, allowing for fast conditional displacement of electromagnetic modes without increasing coupling strength, utilizing a pair of Gaussian spectrum signals with opposite phases and central frequencies shifted apart to selectively displace modes based on the qubit state.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a narrow bandwidth signal is used for conditional displacement, then the coupling strength can be maintained at appropriate levels, but the gate operation time becomes excessively long
Solution Approach 1:
The patent applies asymmetry by using an anti-symmetrical displacement signal where the positive and negative lobes are positioned at different frequencies (ω+ and ω−) relative to the cavity mode. This asymmetric frequency positioning allows the signal to selectively interact with the cavity mode conditioned on the qubit state while maintaining appropriate coupling strength, thereby achieving fast gate operations without excessive coupling
Solution Approach 2:
The patent implements dynamics by making the displacement signal bandwidth adaptive to the frequency difference between qubit states. The signal bandwidth is dynamically adjusted to exceed the frequency separation (Δω), enabling the system to achieve fast conditional displacement while maintaining fidelity through optimized spectral matching between the control signal and the conditional frequency shifts
2Productivity
If the coupling strength is increased to speed up gate operations, then the gate time is reduced, but higher-order terms such as self-Kerr become significant and degrade fidelity
Solution Approach 1:
The anti-symmetrical signal structure with lobes at frequencies ω+ and ω− creates destructive interference for higher-order interaction terms. The asymmetric positioning ensures that the first-order conditional displacement is enhanced while the second-order self-Kerr effects and other unwanted interactions are suppressed, allowing fast operations without fidelity degradation
Solution Approach 2:
The patent changes the spectral parameters of the displacement signal by positioning its lobes at frequencies detuned from the cavity mode by ±Δω/2. This parameter adjustment allows the signal to resonate with the qubit-conditioned frequency shifts while avoiding direct resonant enhancement of higher-order cavity non-linearities, thereby maintaining fidelity at high speeds
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 enables substantial speedup in gate operations while maintaining high fidelity and avoiding undesired effects of higher-order terms, such as self-Kerr, even at substantial speedup factors, allowing for efficient universal control of bosonic cavity modes.
Implementation Method 1
SC qubit rotations (EM mode displacements) which are conditioned on number of photons (state of the SC qubit)
Data Source
AI summary
A method for displacement of an electromagnetic mode (EM) conditioned on the state of an ancilla qubit, the method may include displacing, by applying a displacement operation, an EM mode whose frequencies are conditioned on the state of the ancilla qubit and are spaced apart by a frequency difference, by providing a displacement signal having a bandwidth that exceeds the frequency difference and has a zero amplitude at one or more of the frequencies of the electromagnetic mode which are defined by the displacement operation not to be displaced and a non-zero amplitude at one or more frequencies of the mode which are defined by the displacement operation to be displaced.