Rabi Oscillations Let D-Wave System Probe System Energy Levels

Researchers at Chuo University are applying a triangular-wave oscillating magnetic field to a D-Wave quantum annealer. This approach allows them to move beyond standard quantum annealing, which typically focuses on finding only the ground state of a quantum system. Instead, the team’s method directly accesses information about excited states within the well-studied transverse-field Ising Hamiltonian, a model central to understanding quantum phase transitions and non-equilibrium dynamics. The work proposes inducing Rabi oscillations to estimate energy gaps between states, potentially enabling simulations of larger systems than currently possible with classical computation. The researchers state this offers a new avenue for quantum-device-based simulation, addressing a key limitation of existing numerical methods hampered by exponentially growing computational costs.

Transverse-Field Ising Model & Quantum Phase Transitions

The ability to directly probe excited states within complex quantum systems represents a significant leap forward in simulating materials and understanding fundamental physics. Researchers are now leveraging the unusual capabilities of D-Wave quantum annealers to achieve this goal. The team’s innovation centers on applying a triangular-wave oscillating magnetic field to the D-Wave hardware, a technique moving beyond standard quantum annealing protocols. Conventional numerical methods, such as exact diagonalization and the density matrix renormalization group, struggle with the exponential growth of the Hilbert space as system size increases; for an Ising model with n spins, the Hilbert-space dimension is given by 2ⁿ. This limitation restricts analysis to relatively small systems, hindering investigations into larger, more complex materials. While tensor-network approaches and quantum Monte Carlo techniques offer partial solutions, they too encounter difficulties with higher-dimensional or strongly correlated systems.

The researchers propose a method that bypasses these classical limitations by directly accessing information about excited states, a feat previously difficult to achieve with D-Wave devices. The core of the method relies on inducing Rabi oscillations, the periodic switching between quantum states driven by an external field, to estimate the energy gaps between the ground and excited states. Although D-Wave devices cannot directly apply microwave fields, the team demonstrates that the triangular-wave magnetic-field modulation can be implemented using the existing hardware. By carefully controlling the frequency and waveform of this applied field, the system’s dynamical response can be investigated in detail, potentially revealing insights into quantum phase transitions.

The validity of the method is demonstrated through numerical simulations of relatively small systems, demonstrating the feasibility of the technique. They suggest it is potentially applicable to larger systems, providing a new avenue for quantum-device-based simulation, indicating the potential for scaling the method to tackle more complex problems. The ability to estimate energy gaps even for large-scale Hamiltonians, which are difficult to diagonalize using classical computers, promises to unlock new possibilities in quantum simulation and materials science.

Kota Yamada and Yuichiro Matsuzaki, both of the Department of Electrical, Electronic, and Communication Engineering at Chuo University, are developing a technique to extract more information from D-Wave quantum annealers than previously thought possible. This approach moves beyond simply finding the lowest energy state, a common goal in quantum annealing, and instead aims to map the system’s excited states. Analyzing excited states is challenging due to the exponential growth of computational demands as system size increases. This is achieved not through direct microwave manipulation, currently unavailable on D-Wave hardware, but by implementing the oscillating field modulation within the existing capabilities of the annealer. The core of their method relies on understanding how Rabi oscillations manifest in a two-level quantum system; as they explain, the frequency of these oscillations directly correlates with the energy gap between states.

Limitations of Classical Methods for Ising Model Analysis

The pursuit of understanding complex quantum systems, like those described by the transverse-field Ising model, increasingly relies on computational power. However, classical methods for analyzing these systems face inherent limitations when scaling to larger, more realistic configurations, hindering progress in fields from materials science to fundamental physics. These approaches become beyond a relatively small number of spins, typically several tens. This limitation is not merely a matter of processing speed; it’s a fundamental constraint imposed by the sheer volume of data required to represent the system’s quantum state. Researchers have long sought ways to circumvent these classical bottlenecks, and quantum annealing devices present a potential avenue. Previous attempts to measure energy gaps during quantum annealing required the preparation of a superposition of the ground and excited states, a feat unattainable with current D-Wave hardware.

This method requires oscillating the coupling strength between qubits, which makes experimental demonstration challenging. This context underscores the motivation behind the novel approach proposed in this work: a method capable of extracting energy gap information using presently available D-Wave devices. This technique allows for the direct assessment of excited states, a critical advancement.

Estimating Energy Gaps via Induced Rabi Oscillations

The pursuit of quantum system understanding often assumes classical computational power will remain the primary analytical tool; however, the inherent limitations of this approach are becoming increasingly apparent as systems grow in complexity. Researchers are now turning to quantum devices themselves to probe the very properties that elude classical simulation, and a team at Chuo University has proposed a novel method leveraging the unique capabilities of D-Wave quantum annealers. The researchers detail that, unlike conventional quantum annealing methods primarily designed for ground-state searches, their method enables the direct extraction of physical information related to excited states. Instead of attempting to circumvent these classical bottlenecks with increasingly sophisticated algorithms, the team proposes a direct measurement using the D-Wave architecture. This field acts as a pseudo drive, inducing Rabi oscillations and allowing the energy gap to be estimated.

The researchers acknowledge that current D-Wave hardware cannot directly apply microwave fields, but demonstrate that the proposed magnetic-field modulation is implementable within the existing system. The ability to directly access excited-state information, rather than relying on indirect inference, represents a significant step toward a more complete understanding of complex quantum phenomena and opens possibilities for simulating quantum systems in entirely new ways.