Polariton condensates for classical and quantum computing

A.K. Fedorov, 2, 3 N. Gisin, 5 S.M. Beloussov, and A.I. Lvovsky 6 Schaffhausen Institute of Technology, Schaffhausen 8200, Switzerland Russian Quantum Center, Skolkovo, Moscow 143025, Russia National University of Science and Technology “MISIS”, Moscow 119049, Russia Schaffhausen Institute of Technology, Geneva, Switzerland Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland Department of Physics, University of Oxford, Oxford OX1 3PG, UK (Dated: April 1, 2022)

Quantum computing at the quantum advantage threshold: a down-to-business review

Bound pairs consisting of a vortex and an antivortex are expected to dominate the low-temperature physics in a variety of two-dimensional systems. The observation of such bound pairs, however, remains elusive. A study now establishes non-equilibrium condensates of exciton-polaritons as a platform for exploring the physics of vortex–antivortex pairs.

https://absimage.aps.org/image/MAR09/MWS_MAR09-2008-002638.pdf

Single vortex-antivortex pair in an exciton polariton condensate

The aperiodic Fourier modal method in contrast-field formulation is a numerical discretization and solution technique for solving scattering problems in electromagnetics. Typically, spectral discretization is used in the finite periodic direction and spatial discretization in the orthogonal direction. In the light of the fact that the structures of interest often have a large width-to-height ratio and that the two discretization approaches have different computational complexities, we propose exchanging the directions for spatial and spectral discretization. Moreover, if the scatterer has repeating patterns, swapping the discretization directions facilitates the reuse of previous computations. Therefore, the new method is suited for scattering from objects with a finite number of periods, such as gratings, memory arrays, metamaterials, etc. Numerical experiments demonstrate a considerable reduction of the computational costs in terms of time and memory. For a specific test case considered in this paper, the new method (based on alternative discretization) is 40 times faster and requires 100 times less memory than the method based on classical discretization.

Efficient solution of Maxwell's equations for geometries with repeating patterns by an exchange of discretization directions in the aperiodic Fourier modal method

The appearance of quantized vortices in the classical “rotating bucket” experiments of liquid helium and ultracold dilute gases provides the means for fundamental and comparative studies of different superfluids. Here, we realize the rotating bucket experiment for optically trapped quantum fluid of light based on exciton-polariton Bose-Einstein condensate in semiconductor microcavity. We use the beating note of two frequency-stabilized single-mode lasers to generate an asymmetric time-periodic rotating, nonresonant excitation profile that both injects and stirs the condensate through its interaction with a background exciton reservoir. The pump-induced external rotation of the condensate results in the appearance of a corotating quantized vortex. We investigate the rotation frequency dependence and reveal the range of stirring frequencies (from 1 to 4 GHz) that favors quantized vortex formation. We describe the phenomenology using the generalized Gross-Pitaevskii equation. Our results enable the study of polariton superfluidity on a par with other superfluids, as well as deterministic, all-optical control over structured nonlinear light.

https://www.science.org/doi/pdf/10.1126/sciadv.add1299?download=true

Quantum vortex formation in the “rotating bucket” experiment with polariton condensates

The authors propose a platform for quantum computation based on Bose-Einstein condensates of exciton polaritons

https://link.aps.org/pdf/10.1103/PhysRevResearch.3.013099

Split-ring polariton condensates as macroscopic two-level quantum systems

Superposition states of circular currents of exciton-polaritons mimic the superconducting flux qubits. The phase of a polariton fluid must change by an integer number of $2\pi$, when going around the ring. If one introduces a ${\pi}$-phase delay line in the ring, the fluid is obliged to propagate a clockwise or anticlockwise circular current to reduce the total phase gained over one round-trip to zero or to build it up to $2\pi$. We show that such a $\pi$-delay line can be provided by a dark soliton pinned to a potential well created by a C-shape non-resonant pump-spot. The resulting split-ring polariton condensates exhibit pronounced coherent oscillations passing periodically through clockwise and anticlockwise current states. These oscillations may persist far beyond the coherence time of polariton condensates. The qubits based on split-ring polariton condensates are expected to possess very high figures of merit that makes them a valuable alternative to superconducting qubits. The use of the dipole-polarized polaritons allows to control coherently the state of the qubit with the external electric field. This is shown to be one of the tools for realization of single-qubit logic operations. We propose the design of an $i$SWAP gate based on a pair of coupled polariton qubits. To demonstrate the capacity of the polariton platform for quantum computations, we propose a protocol for the realization of the Deutsch's algorithm with polariton qubit networks.

Split-ring polariton condensates as macroscopic two-level quantum systems.

Superposition states of circular currents of exciton-polaritons mimic the superconducting flux qubits. The current states are formed by a macroscopic number of bosonic quasiparticles that compose a single quantum state of a many-body condensate. The essential difference between a polariton fluid and a supercurrent comes from the fact that polaritons are electrically neutral, and the magnetic field would not have a significant effect on a polariton current. Nevertheless, the phase of a polariton condensate must change by an integer number of $2\pi$, when going around the ring. If one introduces a $\pi$-phase delay line in the ring, the system is obliged to propagate a clockwise or anticlockwise circular current to reduce the total phase gained over one round-trip to zero or to build it up to $2\pi$. We show that such a $\pi$-delay line can be provided by a dark soliton embedded into a ring condensate and pinned to a potential well created by the C-shape non-resonant pump-spot. The physics of resulting split-ring polariton condensates is essentially similar to the physics of flux qubits. In particular, they exhibit pronounced coherent oscillations passing periodically through clockwise and anticlockwise current states. We predict that these oscillations should persist far beyond the coherence time of the polariton condensates. As a consequence the qubits based on split-ring polariton condensates are expected to be characterized by a very high figure of merit that makes them a valuable alternative to superconducting qubits.

Yan Xue

Papers

Split-ring polariton condensates as macroscopic two-level quantum systems

Split-ring polariton condensates as macroscopic two-level quantum systems.

Split-ring polariton condensate as a macroscopic two-level quantum system