Variational Hamiltonian Ansätze Efficiently Capture Critical States in the Rabi Model

Understanding the behaviour of matter at critical points is fundamental to modern physics, and recent advances allow researchers to simulate these complex states with increasing accuracy. Mei Peng, Xu-Dan Xie, and Dan-Bo Zhang, all from the Key Laboratory of Atomic and Subatomic Structure and Quantum Control, investigate these critical states using a novel approach applied to the quantum Rabi model. Their work demonstrates a method for preparing these states variationally, employing specifically designed quantum circuits that capture the interplay of different fluctuations within the system. The team’s findings reveal that the complexity of these circuits grows surprisingly slowly with system size, suggesting this technique offers a powerful and efficient way to explore critical states and potentially unlock new insights into the behaviour of matter at its most complex
Hong Kong Joint Laboratory of Quantum Matter, and Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China. Characterising quantum critical states is essential for understanding different phases of matter. The power of quantum simulators lies in their ability to prepare these critical states, which relies crucially on the structure of quantum circuits and, in turn, provides new insight into the states themselves. This work explores the critical states of the quantum Rabi model by preparing them variationally with Hamiltonian ansätze, a method that allows investigation of the intricate interplay among different quantum fluctuations.

Variational Quantum Simulation of Many-Body Systems

This research addresses the fundamental challenge of simulating the behavior of interacting quantum particles, a problem central to materials science, chemistry, and fundamental physics. Classical simulations become increasingly difficult as the number of particles grows, making quantum approaches essential. The team utilizes variational quantum algorithms (VQAs), which combine the strengths of quantum and classical computers. A quantum computer prepares and measures a parameterized quantum state, while a classical computer optimizes the parameters to approximate the ground state of the system. This work specifically focuses on simulating condensed matter systems, known for their strong electron correlations.

A crucial aspect of VQAs is the design of the quantum circuit, known as the ansatz. Researchers explore different ansatz types, including Unitary Coupled Cluster, known for its accuracy, and Hardware-Efficient Ansatz, designed for implementation on specific quantum hardware. The optimization of the ansatz parameters is also critical, with the team considering both gradient-based and gradient-free methods. Accurately estimating energy on the quantum computer is essential, and the team employs techniques to reduce statistical errors and noise. Leveraging symmetries within the system can significantly reduce computational cost and improve accuracy, and the team also explores error mitigation techniques to address the limitations of near-term quantum computers.

The research addresses a wide range of condensed matter problems, including the Fermi-Hubbard Model, the Heisenberg Model, and BCS Theory. It investigates quantum phase transitions, strongly correlated systems, quantum criticality, and exotic states of matter like spin liquids. The likely contributions include improved VQA techniques, such as novel ansatz designs, more efficient optimization algorithms, and better error mitigation strategies. The team demonstrates the ability to simulate challenging condensed matter problems beyond the reach of classical methods, benchmarking different techniques and analyzing their performance. The research also explores the hardware requirements for implementing VQAs on near-term quantum computers, with a strong emphasis on exploiting symmetries to improve efficiency and accuracy. This research has the potential to advance the field of quantum simulation, accelerate materials discovery, improve our understanding of condensed matter physics, and guide the development of quantum hardware.

Linear Scaling Variational State Preparation Demonstrated

Researchers have demonstrated a powerful new method for preparing and characterizing critical states in quantum systems, specifically focusing on the Rabi model. Critical states are particularly interesting because they represent points of dramatic change in a system’s behavior, and understanding them is crucial for advancing our knowledge of different phases of matter. This work introduces a variational approach using specifically designed quantum circuits, termed Hamiltonian ansätze, to efficiently prepare these complex states. The team’s method exhibits a remarkable scaling property; the complexity of the required quantum circuits grows linearly with the effective size of the system.

This is a significant achievement, as many other methods experience exponential growth in complexity, quickly becoming impractical for larger systems. This linear scaling suggests the approach can be extended to simulate critical states approaching the thermodynamic limit, a crucial step towards understanding macroscopic quantum phenomena. The circuits achieve this efficiency by progressively refining the quantum state, adding blocks in a way that increases only linearly with system size. Detailed analysis reveals how these circuits sculpt the initial quantum state into the target critical state. By examining the state’s evolution at each step, researchers observed a clear “squeezing” effect, where the initial, symmetrical distribution of quantum properties becomes increasingly focused.

This squeezing, visualized through the Wigner probability distribution, indicates the system is evolving towards a critically squeezed state. Furthermore, the population of the system shifts from the vacuum state to higher energy levels, but only even numbers of photons are populated, confirming the symmetry-preserving nature of the quantum circuit. This unexpected result demonstrates the circuit’s ability to generate a squeezed vacuum state without explicitly applying a squeezing operator. The optimization process within each layer of the circuit effectively acts as a squeezing mechanism, gradually transforming the initial state. By quantifying the squeezing behavior using canonical variable operators, the researchers confirmed the progressive focusing of quantum properties, providing a robust measure of the circuit’s performance. This innovative approach offers a promising new avenue for exploring and understanding complex quantum systems and their critical states.

Efficiently Simulating Quantum Critical States with HVA

This research investigates the critical states of the Quantum Rabi Model (QRM) using a variational approach with Hamiltonian ansätze (HVA). The team demonstrates that HVA efficiently captures the behavior of these critical states, even as the system size increases, with the required computational effort scaling linearly with system size. This suggests the method is well-suited for simulating complex quantum systems approaching a thermodynamic limit, despite the QRM lacking a traditional system size. The findings reveal that HVA progressively refines the initial quantum state towards the desired critical state, requiring only a linearly increasing number of computational blocks with system size.

This efficient squeezing of the initial state represents a new probe for understanding complicated critical states, and offers a practical approach for investigating these states on near-term quantum simulators. The authors acknowledge that simulating continuous variables on quantum computers typically demands substantial resources, but their hybrid quantum simulator, combining qubits with continuous variables, provides a more natural and efficient solution. The authors note the limitations of directly mapping continuous variables onto qubits due to the large number of qubits and complex circuits required. Future research could focus on further optimizing the hybrid quantum simulator and exploring its application to other complex quantum systems exhibiting critical behavior. The team’s work provides a valuable tool for investigating these systems and gaining deeper insights into their properties.