Geometric Quantum Computing and Dissipation Models

Changyong Chen, Xiaolong Zhang, Zhi Jiao Deng +2 more

We introduce a general displacement operator to investigate the unconventional geometric quantum computation with dissipation under the model of many identical three-level atoms in a cavity, driven by a classical field. Our concrete calculation is made for the case of two atoms, based on a previous scheme [S.-B. Zheng, Phys. Rev. A 70, 052320 (2004)] for the large-detuning interaction of the atoms with the cavity mode. The analytical results we present will be helpful for experimental realization of geometric quantum computation in real cavities.

Eduardo Jose Bayro-Corrochano

Eduardo Jose Bayro-Corrochano

Ludmila Viotti, Fernando C. Lombardo, Paula I. Villar

We follow a generalized kinematic approach to compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models, which provide a fully quantum description for a two-level system interacting with a single mode of the (cavity) electromagnetic field, in a perfect or dissipative cavity, respectively. In the dissipative model, the nonunitary effects arise from the outflow of photons through the cavity walls and the incoherent pumping of the two-level system. Our approach allows to compare the geometric phases acquired in these models, leading to an exhaustive characterization of the corrections introduced by the presence of the environment. We also provide geometric interpretations for the observed behaviors. When the resonance condition is satisfied, we show the geometric phase is robust, exhibiting a vanishing correction under a nonunitary evolution. This fact is supported with a geometrical explanation as well.

James Purcell, Abhishek Rajput, Toby S. Cubitt

Dissipative processes have long been proposed as a means of performing computational tasks on quantum computers that may be intrinsically more robust to noise. In this work, we prove two main results concerning the error-resilience capabilities of two types of dissipative algorithms: dissipative ground state preparation in the form of the dissipative quantum eigensolver (DQE), and dissipative quantum computation (DQC). The first result is that under circuit-level depolarizing noise, a version of the DQE algorithm applied to the geometrically local, stabilizer-encoded Hamiltonians that arise naturally when fermionic Hamiltonians are represented in qubits, can suppress the additive error in the ground space overlap of the final output state exponentially in the code distance. This enables us to get closer to fault-tolerance for this task without the associated overhead. In contrast, for computation as opposed to ground state preparation, the second result proves that DQC is no more robust to noise than the standard quantum circuit model.

Yuncheng Xie, Haozhe Shi, Zhuocheng Ma +2 more

In periodically driven open quantum systems, nonnormality renders the Floquet spectrum insufficient as the system approaches the thermodynamic limit, so that pseudospectra are needed to characterize the dynamics accurately. While conventional approaches mainly focus on the local dynamics of isolated pseudospectra, their global connections and the resulting physical consequences for observables have remained largely unexplored. Here, we uncover this collective behavior by classifying the unit disk into distinct domains of exponential, algebraic, and bounded accuracy according to the asymptotic size-scaling laws of pseudospectral residuals, yielding an underlying geometric structure. We demonstrate the physical implications of this structure through two exactly solvable models. First, in a dissipative shift chain, parameter tuning drives geometric transitions that are detectable via spin-wave observables. Second, in a chiral XY model, we use this geometric structure to explain the origin of a measurable phenomenon: two correlation signals exchange their retention order under continuous parameter tuning. Our findings not only establish a new theoretical paradigm for understanding dissipative Floquet quantum systems, but also predict geometry-driven observables for quantum computing experiments.