Abhishek Kumar of Virginia Tech and colleagues have developed Floquet-ADAPT-VQE, a quantum algorithm designed to simulate the complex behavior of quantum systems subjected to periodic forces. The work transforms a time-dependent Hamiltonian into a time-independent form using the Floquet-Hilbert space formalism, enabling the calculation of quasienergy, Floquet eigenstates and expectation values of observables.
This approach uses a fixed-depth quantum circuit applied to an initial Floquet eigenstate, a construction made possible by the formalism itself, and offers a path toward simulating these more challenging, non-equilibrium systems. The researchers demonstrate the algorithm through simulations of a periodically driven XYZ model with a magnetic field.
Floquet-Hilbert Space Transforms Periodic Hamiltonians for Quantum Simulation
The algorithm, dubbed Floquet-ADAPT-VQE, relies on encoding the time-dependent behavior of a quantum system within an auxiliary quantum register, effectively converting a time-evolving problem into a static one within an expanded computational space known as the Floquet-Hilbert space. This transformation allows for a systematic decomposition of the system’s Hamiltonian into Pauli operators, a format readily compatible with current qubit-based quantum computers. The resulting time-independent Hamiltonian facilitates the calculation of quasienergies, the equivalent of energies in systems subjected to periodic forces, and the preparation of associated Floquet states.
A key innovation lies in the identification of an auxiliary initial state whose squared Floquet energy remains consistent regardless of the number of auxiliary qubits or the frequency of the driving force, improving the convergence of the adaptive algorithm with fewer iterations. This optimization is important for reducing the computational resources required for accurate simulations, a persistent challenge in quantum computing.
This model, chosen for its complexity, allowed the team to validate the algorithm’s ability to accurately determine quasienergies and Floquet eigenstates. “Consequently, quantum simulation of these systems offers greater opportunity for achieving quantum advantage,” the paper states, highlighting the potential for surpassing the capabilities of classical computers in simulating these complex quantum phenomena. The work builds upon earlier approaches, including the detailed by Rudner and Lindner in 2020, and acknowledges related work on variational quantum computation of excited states published in Quantum in 2019.
Floquet-ADAPT-VQE Algorithm Calculates Driven System Quasienergies
This contrasts with many existing methods that focus on static systems, and positions the approach for potential quantum advantage in a more challenging domain. This optimization minimizes the number of ADAPT iterations, a process used to refine the quantum circuit, reducing the computational resources needed for accurate simulations. This fixed-depth approach is significant because it limits the complexity of the quantum circuit, a critical factor in minimizing errors and resource requirements on near-term quantum hardware. The development provides a pathway to explore non-equilibrium physics in periodically driven systems with greater computational efficiency and accuracy.
Fewer iterations translate to faster convergence and the ability to tackle larger, more realistic problems. “These contributions also pave the way for future algorithm development in this direction,” the researchers state.
XYZ Model Demonstrates Algorithm Performance
The researchers demonstrated the algorithm’s capabilities through numerical simulations using a periodically driven XYZ model featuring a magnetic field, a common test case for evaluating quantum simulation methods. This model allowed for a direct assessment of the algorithm’s ability to accurately capture the dynamics of a quantum system under periodic forcing. The work also highlights the benefits of employing the Floquet-Hilbert space formalism itself, providing a systematic way to decompose the extended Floquet Hamiltonian into Pauli components suitable for implementation on existing quantum computers.
Potential for Quantum Advantage in Non-Equilibrium Physics
Periodically driven quantum systems present unique challenges for simulation, demanding computational resources beyond those required for static systems. This increased complexity, however, also elevates the potential for demonstrating a quantum advantage, the ability to solve problems intractable for even the most powerful classical computers. The development of Floquet-ADAPT-VQE directly addresses this need, offering a pathway to explore phenomena like time crystals and unusual topological phases previously inaccessible to detailed simulation.
The approach builds on existing adaptive variational quantum algorithms, specifically those designed for ground state preparation and quantum dynamics simulations. The team’s work also draws on established theoretical frameworks for understanding periodically driven systems. References to prior research, including the work of Asbóth, Tarasinski and Delplace in 2014, demonstrate a grounding in the existing body of knowledge regarding chiral symmetry and bulk-boundary correspondence. We also explore potential applications of our algorithm for studying various non-equilibrium phenomena in periodically driven systems.
Beyond the specific implementation details, the algorithm’s design reflects a broader trend toward applying the strengths of quantum computing for tackling non-equilibrium physics. The ability to accurately simulate these systems could provide new insights into fundamental physical processes and potentially lead to the discovery of novel materials with tailored properties. The researchers explore potential applications for studying various non-equilibrium phenomena, suggesting a versatile tool for future investigations.
See today’s quantum computing news on Quantum Zeitgeist for the latest breakthroughs in qubits, hardware, algorithms, and industry deals.
