Evolution and Dynamical Decoupling-Based Protection of Multi-Order Quantum Coherence in a Three-Qubit NMR System

Core Concepts

This research investigates the dynamics and protection of different orders of quantum coherence in a three-qubit NMR system, demonstrating that modified robust dynamical decoupling (DD) sequences can effectively preserve various coherence orders and, consequently, two-qubit entanglement within a three-qubit star state.

Abstract

Bibliographic Information:

Gautam, A., Dorai, K., & Arvind. (2024). Evolution of different orders of coherence of a three-qubit system and their protection via dynamical decoupling on an NMR quantum processor. arXiv:2411.07187v1 [quant-ph].

Research Objective:

This study aims to experimentally investigate the dynamics of different orders of quantum coherence (zeroth, first, second, and third order) in a three-qubit NMR system and evaluate the effectiveness of robust dynamical decoupling (DD) sequences in protecting these coherence orders against environmental noise.

Methodology:

• A three-qubit NMR system was implemented using a 13C labeled diethylfluoromalonate sample.
• Different three-qubit quantum states exhibiting specific coherence orders were experimentally generated.
• The evolution of these coherence orders was monitored under free evolution and after applying standard and modified robust DD sequences (XY8, UR12, XY16, KDD20).
• The effectiveness of DD sequences in preserving coherence was evaluated by comparing the coherence decay rates under different conditions.
• A three-qubit star state was generated, and the entanglement in its two-qubit subsystems was protected using a modified XY8 DD sequence.
• Concurrence was used to quantify the entanglement of the two-qubit subsystems.

Key Findings:

• Standard robust DD sequences effectively protect third-order coherence but lead to rapid decay of other coherence orders.
• Applying robust DD sequences to the single qubit responsible for generating first-order coherence significantly improves its preservation.
• Modified robust DD sequences, designed to protect the spins involved in bipartite correlations, successfully preserve zeroth and second-order coherences.
• The modified XY8 DD sequence effectively protects the entanglement of two-qubit subsystems within a three-qubit star state.

Main Conclusions:

• Tailoring robust DD sequences to target specific coherence orders is crucial for their effective protection.
• Modified DD sequences can successfully preserve various coherence orders and, consequently, entanglement in multi-qubit systems.
• This study provides valuable insights into the dynamics and protection of quantum coherence, which is essential for developing practical quantum computers.

Significance:

This research contributes to the field of quantum information processing by demonstrating the effectiveness of modified robust DD sequences in preserving different orders of quantum coherence, a crucial step towards building fault-tolerant quantum computers.

Limitations and Future Research:

• The study focuses on a specific type of NMR system and a limited set of DD sequences.
• Future research could explore the effectiveness of other DD sequences and their optimization for different coherence orders and multi-qubit systems.
• Investigating the scalability of these techniques to larger quantum systems is crucial for practical quantum computing applications.

Stats

The reconstructed density matrices associated with the states |ψa0⟩ and |ψb0⟩ had high measured experimental fidelities of 0.984 and 0.978, respectively.
The reconstructed density matrices associated with the states |ψa1⟩ and |ψb1⟩ had high experimental fidelities of 0.99 and 0.985, respectively.
The reconstructed density matrices corresponding to the states |ψa2⟩ and |ψb2⟩ had measured experimental fidelities of 0.969 and 0.972, respectively.
The reconstructed density matrix for the state |ψ3⟩ had an experimental fidelity of 0.97.
State tomography was carried out to reconstruct the density matrix, with a computed fidelity of 0.92.

Quotes

"While quantum coherence is an essential component in QIP, significant advancements in its theory have been developed only recently [17]."
"Amongst all proposed coherence protection strategies, DD sequences have proven to be very successful in protecting single-qubit quantum states [42, 43] and several DD sequences have been successfully implemented to preserve entanglement in two NMR qubits and to freeze quantum discord in a dephasing noisy NMR environment [44, 45]."
"These quantifiers only reflect the total amount of coherence in a quantum state, which may not provide complete information, as discussed in [25]."
"Star states have all possible coherence orders and correlations present and have been shown to be useful for quantum error correction [46]."

Key Insights Distilled From

Evolution of different orders of coherence of a three-qubit system and their protection via dynamical decoupling on an NMR quantum processor

by Akanksha Gau... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2411.07187.pdf

Deeper Inquiries

How can these findings on dynamical decoupling be applied to other quantum computing platforms beyond NMR systems?

While this research was conducted using an NMR quantum processor, the findings on dynamical decoupling (DD) and coherence protection have significant implications for other quantum computing platforms. Here's how:

Universality of Decoherence: The fundamental challenge of decoherence, arising from the interaction of quantum systems with their environment, is universal across all quantum computing platforms. Whether it's superconducting qubits, trapped ions, or photonic systems, unwanted interactions lead to coherence loss.
Platform-Agnostic DD Principles: The core principles of DD, involving the application of carefully timed control pulses to mitigate the effects of noise, are platform-agnostic. The specific pulse sequences and their optimization might differ based on the platform's characteristics and the dominant noise sources, but the underlying concept remains applicable.
Adapting Pulse Sequences: The research highlights the importance of tailoring DD sequences to protect specific coherence orders. This principle can be extended to other platforms by identifying the dominant decoherence channels and designing DD sequences that effectively average out the corresponding noise contributions.
Beyond NMR-Specific Modifications: The modifications made to the standard DD sequences in this work, such as introducing additional pulses or adjusting interpulse delays, provide a framework for adapting DD to different platforms. While the exact modifications might not be directly transferable, the approach of fine-tuning DD sequences based on the specific coherence order to be protected is broadly relevant.
For instance, in superconducting transmon qubits, flux noise is a major source of decoherence. DD sequences specifically designed to mitigate the effects of flux noise, such as the "CPMG" (Carr-Purcell-Meiboom-Gill) sequence and its variants, have been successfully implemented. Similarly, in trapped ion systems, where magnetic field fluctuations can lead to coherence loss, DD sequences tailored to address these specific noise characteristics are employed.
Therefore, the insights gained from this NMR-based research, particularly the emphasis on understanding and controlling different coherence orders and the approach of modifying DD sequences accordingly, provide valuable guidance for developing effective decoherence mitigation strategies in various quantum computing platforms.

Could the focus on protecting specific coherence orders instead of overall state fidelity potentially lead to less effective quantum error correction techniques?

Focusing on protecting specific coherence orders, while offering advantages for understanding and controlling decoherence, might appear to potentially impact the effectiveness of quantum error correction (QEC) techniques. However, a nuanced perspective reveals a more complex relationship:

QEC and Coherence: QEC typically relies on encoding quantum information in a subspace of a larger Hilbert space, designed to be immune to specific types of errors. These errors often manifest as unwanted coherence terms arising from interactions with the environment.
Trade-offs and Optimization: Protecting specific coherence orders could, in principle, lead to a less uniform protection of the encoded quantum information, potentially making the QEC less effective against certain types of errors. However, it also opens up the possibility of optimizing DD sequences to target the most detrimental coherence terms for a given QEC code, potentially leading to improved performance.
Resource Considerations: Implementing full QEC often requires significant resource overhead, including additional qubits and quantum gates. Tailoring DD sequences to protect specific coherence orders relevant to the QEC code could potentially reduce this overhead by focusing on the most critical aspects of error suppression.
Beyond Fidelity: While overall state fidelity is a useful metric, it doesn't always capture the subtle ways in which errors can propagate and affect the outcome of a quantum computation. Focusing on specific coherence orders might provide a more detailed understanding of error channels and enable the development of more targeted and efficient QEC strategies.
Therefore, the relationship between protecting specific coherence orders and QEC effectiveness is not a simple trade-off. It presents both challenges and opportunities. By carefully considering the specific QEC code, the dominant error channels, and the available resources, it might be possible to leverage the insights from coherence-order-specific DD to enhance QEC performance. Further research is needed to explore this interplay in greater depth.

What are the potential implications of this research for understanding and controlling coherence in biological systems, such as those involved in photosynthesis or avian magnetoreception?

The findings of this research, particularly the ability to precisely control and protect specific coherence orders in a multi-qubit system, could have intriguing implications for understanding and potentially even controlling coherence in biological systems. Here's how:

Quantum Biology: There's growing evidence suggesting that quantum mechanical phenomena, including coherence, might play a role in certain biological processes. Photosynthesis and avian magnetoreception are prime examples where long-lived coherences have been observed, challenging classical explanations.
Probing Coherence Mechanisms: The techniques developed in this research, such as the modified DD sequences, could potentially be adapted to probe the nature and dynamics of coherence in biological systems. By applying tailored pulses and observing the response of the system, researchers could gain insights into the factors influencing coherence lifetimes and the role of the environment.
Environmental Noise: Biological systems are inherently noisy environments. The success of DD in mitigating noise in NMR systems suggests that similar principles might be applicable in biological contexts. Understanding how to decouple specific coherence terms from environmental noise could shed light on the mechanisms by which biological systems maintain coherence despite the noise.
Control and Manipulation: While still speculative, the ability to control coherence in biological systems could open up unprecedented possibilities. Imagine influencing the efficiency of photosynthesis by manipulating coherence lifetimes or even interfering with avian magnetoreception.
However, significant challenges remain in translating these findings to biological systems. The complexity of biological molecules and the difficulty in applying precise control pulses in vivo make it a daunting task. Nevertheless, the insights gained from this research provide a valuable starting point for exploring the fascinating interplay between coherence, noise, and function in the realm of quantum biology.