Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States (1603.05681v1)

Abstract: Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One example of such a hybrid quantum-classical approach is the variational quantum eigensolver (VQE) built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed among the candidates for first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even non-systematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we show how variational quantum-classical approaches fit in a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions with additional classical resources. We demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error correction codes.

• The paper introduces a hybrid quantum-classical hierarchy using Variational Quantum Eigensolvers (VQEs) to mitigate decoherence and determine excited states in quantum chemistry.
• A Quantum Subspace Expansion (QSE) method enhances variational approaches by expanding around a reference state to improve excited state determination and mitigate noise without requiring more quantum resources.
• Numerical evidence on the hydrogen molecule (H el{_2}) demonstrates that these methods effectively find excited electronic states and show robustness against decoherence channels like amplitude and phase damping.

Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States

The paper "Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States" presents a paper into hybrid quantum-classical computational strategies aimed at mitigating decoherence effects and improving the determination of excited states in quantum chemistry. The authors elaborate on the applicability of variational quantum eigensolvers (VQEs) in addressing these challenges. VQEs are particularly attractive for leveraging quantum resources to solve eigenvalue problems efficiently, coupling classical computational resources to address the inherently short coherence times of current quantum devices.

The authors introduce the concept of a Variational Channel State (VCS) as a model for the preparation of quantum states under the influence of decoherence. This model accounts for the effect of quantum channels on state preparation processes, offering a theoretical framework that helps in understanding how VQEs can be configured to counteract decoherence. The VCS model elucidates the transformation of the Hamiltonian under channel effects, demonstrating that the problem can still be treated as a Hermitian eigenvalue problem on a transformed quantum Hamiltonian, thus allowing for optimal state preparation even in non-ideal conditions.

Furthermore, a quantum subspace expansion (QSE) method is proposed. QSE allows one to enhance the variational approach by expanding around a reference quantum state to consider linear subspace variations. By capturing both ground and excited states more accurately, and by mitigating decoherence effects, QSE can significantly improve the computational output without additional quantum resource demands. The authors show that the method effectively compresses the dimensionality of the problem into a classic eigenvalue problem in a subspace spanned by the quantum reference state.

The authors provide numerical evidence indicating that QSE can determine excited electronic states of systems such as the hydrogen molecule (H$_2$), yielding results that align closely with exact states, even in the presence of decoherence channels such as amplitude and phase damping. These advances highlight the robustness of the hybrid quantum-classical paradigm in pushing the boundaries of computational chemistry on current quantum hardware.

In terms of practical and theoretical implications, the paper consolidates the role of VQEs as a viable approach in the near term for problems traditionally tackled by quantum chemistry, potentially paving the way for early demonstrations of quantum advantage in this domain. From a broader perspective, the authors suggest that by fostering robustness against noise and decoherence, these techniques could become integral to future quantum computing applications that demand precision beyond the reach of classical algorithms.

For future developments, the paper implies that continued exploration of quantum-classical hierarchies promises enhanced adaptability and efficiency when navigating between classically tractable and intractable problem spaces, particularly for pre-threshold quantum devices. The research therefore establishes important foundations for transitioning from theory to practice in hybrid quantum computing applications without reliance on advanced error correction.

In summary, the paper contributes significantly to the theoretical and methodological discourse surrounding hybrid quantum-classical computation, offering a refined understanding of how to effectively leverage quantum devices in tandem with classical computation to mitigate current quantum systems' key limitations.