Mechanical analogues of spin Hamiltonians and dynamics

Sean Greenaway, Adam Smith, Florian Mintert +1 more

We experimentally assess the suitability of transmon qubits with fixed frequencies and fixed interactions for the realization of analogue quantum simulations of spin systems. We test a set of necessary criteria for this goal on a commercial quantum processor using full quantum process tomography and more efficient Hamiltonian tomography. Significant single qubit errors at low amplitudes are identified as a limiting factor preventing the realization of analogue simulations on currently available devices. We additionally find spurious dynamics in the absence of drive pulses, which we identify with coherent coupling between the qubit and a low dimensional environment. With moderate improvements, analogue simulation of a rich family of time-dependent many-body spin Hamiltonians may be possible.

Kristel F. L. Michielsen

Jens Bolte, Rainer Glaser

In a semiclassical context we investigate the Zitterbewegung of relativistic particles with spin 1/2 moving in external fields. It is shown that the analogue of Zitterbewegung for general observables can be removed to arbitrary order in ℏ by projecting to dynamically almost invariant subspaces of the quantum mechanical Hilbert space which are associated with particles and anti-particles. This not only allows us to identify observables with a semiclassical meaning, but also to recover combined classical dynamics for the translational and spin degrees of freedom. Finally, we discuss properties of eigenspinors of a Dirac–Hamiltonian when these are projected to the almost invariant subspaces, including the phenomenon of quantum ergodicity.

David S. Park

Nishad Maskara, Stefan Ostermann, James Shee +9 more

Simulations of quantum chemistry and quantum materials are believed to be among the most important applications of quantum information processors. However, realizing practical quantum advantage for such problems is challenging because of the prohibitive computational cost of programming typical problems into quantum hardware. Here we introduce a simulation framework for strongly correlated quantum systems represented by model spin Hamiltonians that uses reconfigurable qubit architectures to simulate real-time dynamics in a programmable way. Our approach also introduces an algorithm for extracting chemically relevant spectral properties via classical co-processing of quantum measurement results. We develop a digital–analogue simulation toolbox for efficient Hamiltonian time evolution using digital Floquet engineering and hardware-optimized multi-qubit operations to accurately realize complex spin–spin interactions. As an example, we propose an implementation based on Rydberg atom arrays. In addition, we show how detailed spectral information can be extracted from the dynamics through snapshot measurements and single-ancilla control, enabling the evaluation of excitation energies and finite-temperature susceptibilities from a single dataset. To illustrate the approach, we show how to use the method to compute key properties of a polynuclear transition-metal catalyst and two-dimensional magnetic materials. Quantum simulations of chemistry and materials are challenging due to the complexity of correlated systems. A framework based on reconfigurable qubit architectures and digital–analogue simulations provides a hardware-efficient path forwards.

David S. Park