Discretization of Bosonic System

Carlos R. Handy, Jian Qun Pei

The eigenvalue moment method for bosonic systems, recently developed by C. R. Handy and D. Bessis [Phys. Rev. Lett 55, 931 (1985)], is extended to discrete quantum mechanics. The relevant formalism is described and applied in the context of the discretized harmonic and sextic anharmonic potentials. Rapidly converging bounds to the associated ground-state energies are obtained for fixed lattice spacing a satisfying a<O(1).

Robert W. Carroll

Tianren Gu, Xiao Yuan, Bujiao Wu

Abstract Boson is one of the most basic types of particles and preserves the commutation relation. An efficient way to measure a bosonic system is important not only for simulating complex physics phenomena of bosons (such as nuclei) on a qubit based quantum computer, but for extracting classical information from a quantum simulator/computer that itself is built with bosons (such as a continuous variable quantum computer). Extending the recently proposed measurement schemes for qubits, such as shadow tomography and other local measurement schemes, here we study efficient measurement approaches for bosonic systems. We consider truncated qudit and continuous variable systems, corresponding to simulated bosons on a discrete quantum computer and an inherent boson system, respectively, and propose different measurement schemes with theoretical analyses of the variances for these two cases. We numerically test the schemes for measuring nuclei vibrations simulated using a discrete quantum computer and a continuous variable Gaussian state, and the simulation results show great improvement of the performance of the proposed method compared to conventional ones.

J. Oitmaa

J. Oitmaa

Krzysztof Giergiel, Jia Wang, Bryan J. Dalton +2 more

We show that interacting bosons on a ring which are driven periodically by a rotating potential can support discrete time crystals whose absolute stability can be proven. The absolute stability is demonstrated by an exact mapping of discrete-time-crystal states to low-lying eigenstates of a time-independent model that reveals spontaneous breaking of space translation symmetry. The mapping ensures that there are no residual time-dependent terms that could lead to heating of the system and destruction of discrete time crystals. We also analyze periodically kicked bosons where the mapping is approximate only and cannot guarantee the absolute stability of discrete time crystals. Besides illustrating potential sources of instability, the kicked bosons model demonstrates a rich field for investigating the interplay between different time and space symmetry breaking, as well as the stability of time crystal behavior in contact with a thermal reservoir.