Implementation of quantum gates by Floquet analysis of kicked quantum system
Implemented quantum gates via Floquet analysis; achieved high-fidelity iSWAP gate with t_gate ~170 ns.
Key Findings
Methodology
The study employs Floquet theory with Baker-Campbell-Hausdorff expansion and CMA-ES algorithm to analyze quasi-energy resonance conditions under periodic driving. Gaussian pulse trains were used to achieve double-excitation transfer in a seven-site chain, optimizing driving parameters for high-fidelity quantum gates.
Key Results
- In a three-qubit architecture, the iSWAP gate was achieved with fidelity close to 1, using driving parameters λ=4.62ℏ, T=10.95 ns.
- In a seven-site chain, double-excitation transfer was achieved with gate time t_gate ~170 ns, significantly below energy relaxation time T1.
- Under hardware imperfections, the protocol showed increased sensitivity to static parameter disorder, η ~ 10^-3.
Significance
This research provides a comprehensive framework for quantum gate engineering, bridging time-periodic control theory with practical quantum gate implementation, addressing bottlenecks in precise control of multi-qubit architectures in superconducting quantum processors.
Technical Contribution
The study introduces an innovative approach combining Floquet theory and CMA-ES algorithm, effectively navigating highly irregular fidelity landscapes, providing new theoretical guarantees and engineering possibilities, significantly enhancing quantum gate operation fidelity.
Novelty
This is the first application of Floquet analysis to quantum gate implementation, optimizing driving parameters through quasi-energy resonance conditions, achieving efficient quantum state transfer and gate operation with significant innovation compared to existing methods.
Limitations
- Increased sensitivity to static parameter disorder may affect stability in practical applications.
- Requires precise tuning of driving parameters, increasing experimental complexity.
Future Work
Future work could explore closed-loop topologies to reduce sensitivity to static disorder and investigate applicability across different quantum computing platforms.
AI Executive Summary
Quantum computing holds the potential to solve complex computational problems, but precise control of multi-qubit architectures remains a bottleneck. This study proposes a framework based on Floquet theory, analyzing quasi-energy resonance conditions under periodic driving to achieve high-fidelity quantum gate operations.
In a three-qubit architecture, the research team successfully synthesized the iSWAP gate with fidelity close to 1. By optimizing driving parameters, the study extended to a seven-site chain, achieving double-excitation transfer with gate time around 170 ns, significantly below energy relaxation time T1.
Although the method shows increased sensitivity to static parameter disorder, its comprehensive framework combining time-periodic control theory with practical quantum gate engineering offers a new solution for precise control in superconducting quantum processors, with broad application potential.
Deep Analysis
Background
Quantum computing has garnered interest due to its potential in cryptography, combinatorial optimization, and quantum chemistry. Unlike classical computing, quantum computing leverages superposition and entanglement to accelerate algorithms. Superconducting qubits are a key architecture for quantum computing, but high error rates in multi-qubit operations limit their application.
Core Problem
Precise control of multi-qubit architectures is a critical bottleneck in superconducting quantum processors. While single-qubit operations have achieved fidelities exceeding 99.99%, multi-qubit gates exhibit higher error rates, affecting the scalability of quantum computing.
Innovation
The study combines Floquet theory with CMA-ES algorithm to optimize quasi-energy resonance conditions under periodic driving, achieving high-fidelity quantum gates. Compared to existing methods, this approach effectively navigates highly irregular fidelity landscapes, significantly enhancing quantum gate operation fidelity.
Methodology
- �� Use Floquet theory to analyze quasi-energy resonance conditions under periodic driving.
- �� Combine Baker-Campbell-Hausdorff expansion to identify optimal driving parameters.
- �� Optimize driving parameters using CMA-ES algorithm to achieve high-fidelity quantum gates.
- �� Implement double-excitation transfer in a seven-site chain to validate scalability.
Experiments
The experimental design includes iSWAP gate synthesis in a three-qubit architecture and double-excitation transfer in a seven-site chain. Driving parameters are optimized using CMA-ES algorithm, assessing stability under different hardware imperfections.
Results
In a three-qubit architecture, the iSWAP gate was achieved with fidelity close to 1. In a seven-site chain, double-excitation transfer was achieved with gate time around 170 ns, significantly below energy relaxation time T1. Increased sensitivity to static parameter disorder, η ~ 10^-3.
Applications
The method can be used for high-fidelity quantum gate operations in superconducting quantum processors, applicable across different quantum computing platforms, with broad application potential.
Limitations & Outlook
Increased sensitivity to static parameter disorder may affect stability in practical applications. Requires precise tuning of driving parameters, increasing experimental complexity.
Plain Language Accessible to non-experts
Imagine a kitchen where a chef needs to prepare different dishes at different times. Floquet theory acts like a schedule, helping the chef use the right tools and ingredients at the right time. This way, the chef can efficiently complete all dishes without wasting time. Similarly, the study optimizes the timing and parameters of quantum gate operations using Floquet theory, achieving efficient quantum state transfer.
ELI14 Explained like you're 14
Imagine you're playing a complex game where you need to control multiple characters at once. Floquet theory is like a super helper in the game, guiding you to make the right decisions at the right time. This way, you can score higher in the game. The study optimizes quantum gate operations using Floquet theory, achieving efficient quantum state transfer, just like winning in the game.
Glossary
Floquet Theory
Floquet theory analyzes the quasi-energy spectrum of periodically driven systems, helping identify resonance conditions.
Used to optimize driving parameters for quantum gate operations.
iSWAP Gate
The iSWAP gate is a quantum gate used to exchange the states of two qubits.
Achieved high-fidelity iSWAP gate in a three-qubit architecture.
CMA-ES Algorithm
CMA-ES is an evolutionary strategy algorithm used to optimize complex non-convex functions.
Used to optimize driving parameters for quantum gate operations.
Quasi-Energy
Quasi-energy is the energy spectrum in periodically driven systems, determining the system's resonance dynamics.
Used to identify resonance conditions for quantum state transfer.
Gaussian Pulse
A Gaussian pulse is a periodic driving signal with finite width.
Used to achieve double-excitation transfer in a seven-site chain.
Open Questions Unanswered questions from this research
- 1 How to reduce sensitivity to static parameter disorder to improve stability in practical applications.
- 2 Explore applicability across different quantum computing platforms to verify the method's generality.
Applications
Immediate Applications
Superconducting Quantum Processors
Enhance fidelity of quantum gate operations in superconducting quantum processors, applicable across different quantum computing platforms.
Long-term Vision
Quantum Computing Platforms
Explore applicability across different quantum computing platforms to advance quantum computing technology.
Abstract
Precise control of multi-qubit architectures remains a critical bottleneck in superconducting quantum processors. In this work, we investigate the synthesis of high-fidelity quantum operations and state transfer protocols within an extended superconducting linear chain, scaling from three to seven sites. Using Floquet theory, we model the periodic drive as a train of delta-like pulses, mapping the quantum control problem onto quasi-energy resonance conditions. Combining the Baker-Campbell-Hausdorff expansion with Floquet spectral decomposition, we analytically identify optimal driving parameters, refined via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). In the three-qubit architecture, this enables high-fidelity synthesis of the iSWAP gate. Extending to a seven-site chain, we implement periodic trains of finite-width Gaussian pulses to activate distinct double-excitation transport channels with ultra-short gate durations t_gate (~170 ns). This achieves a clear scale separation from energy-relaxation times (T1) typical of fixed-frequency transmon devices with tunable couplers, such as IBM Quantum hardware. Finally, we benchmark stability under realistic imperfections, revealing a heightened sensitivity to static parameter disorder at the sub-percent level (eta ~ 10^-3) driven by spectral crowding, and discuss how closed-loop topologies could mitigate this constraint. This framework bridges time-periodic control theory and practical quantum gate engineering.