Session D53: Continuous Variable Quantum Computation and Spin Qubits

A Proximitized Quantum Dot in Germanium

Hole spin qubits in strained planar germanium quantum wells (Ge/SiGe) [1] have emerged as a promising qubit candidate for quantum information processing and simulation evidenced by the demonstration of single qubit fidelities above 99.99% [2], tune-up of a 4x4 quantum dot array [3] and the execution of multi-qubit quantum logic [4]. Recently, hard-gapped superconductivity has been engineered for the first time in Ge/SiGe, in a wide range of mesoscopic devices [5]. The demonstration of an isotopically purifiable semiconductor platform that can host clean superconductivity places Ge/SiGe in a uniquely advantageous position, facilitating many opportunities for hybrid superconducting-semiconducting quantum dots, including high fidelity two-qubit gates [6], extended range qubit-qubit coupling without the need for resonators [7], and integration with circuit QED [8]. In this work we make initial steps toward these goals, by presenting a proximiti zed germanium quantum dot (QD) coupled to a superconducting lead (S). We show the emergence of a superconducting gap within the charging energy of a quantum dot via bias spectroscopy, with tunable S-QD coupling. We use this to demonstrate switching between singlet and doublet ground states. We further characterize critical magnetic field strength, finding remarkably robust critical field strength of 0.911 T along the out-of-plane axis. Finally, we study spin splitting of sub-gab states, finding an out-of-plane g-factor of 6.11, and a large anisotropy of the g-factor for in- and out-of-plane field orientations. These results constitute a promising first step towards hybrid superconducting-semiconducting quantum information processing with hole spin qubit in Ge/SiGe.   

Optical and microstructural characterization of epitaxial Er-doped CeO2 on silicon

Erbium-doped cerium oxide (Er:CeO₂) is a promising defect-host combination for applications in quantum memories for wide-area fiber optic-based quantum networks, due to the telecom-compatible (~1.5 μm) 4f-4f optical transition of Er, predicted long electron spin coherence time for defects in CeO₂,¹ and small lattice mismatch between silicon and CeO₂. Here we report on epitaxial Er:CeO₂ thin films grown on silicon by molecular beam epitaxy, with Er doping in the 1-100 ppm regime.² We verify the CeO₂ host structure via thorough microstructural study, and then characterize the spin and optical properties of the embedded Er³⁺ ions as a function of doping density. Studying the Z₁-Y₁ optical transition near 1530 nm at 3.5 K with 2-3 ppm Er, we find spectral diffusion-limited homogeneous linewidths as narrow as 5 MHz, along with inhomogeneous linewidths of 10 GHz and optical excited state lifetimes of 3.5 ms; further measurements at 4 K yield EPR linewidths of 250 MHz. We then discuss routes for optical and spin linewidth improvement via growth optimization and post-growth treatment.

(1) S. Kanai, et al. PNAS. 119, e2121808119 (2022).

(2) G. Grant, et al. arXiv:2309.16644 (2023).   

Optical and spin coherence of Er3+ in epitaxial CeO2 on silicon

Trivalent erbium ions (Er³⁺) are promising spin defects for developing quantum memories in quantum communication networks due to their unique spin-photon interface at telecommunication band. To this end, controlling the local host environment to enable long-lived Er³⁺ electron spins in a technology compatible platform is key. Here, we report on a new qubit system Er³⁺: CeO₂ (cerium dioxide) epitaxially grown on silicon with near-zero nuclear spin environment critical for supporting long-lived spins¹ and in a silicon compatible platform² for device integration.  We study the optical and spin coherence properties of Er³⁺ in this system and demonstrate narrow homogeneous linewidth of 440 kHz with an optical coherence time of 0.72 μs at 3.6 K³. The slow spin-lattice relaxation enables direct observation of spin dynamics at 3.6 K. The Er³⁺ electron spins have a reasonable long spin relaxation of 2.5 ms and a spin coherence of 0.66 μs (in the isolated ion limit)³. These findings indicate the potential of Er³⁺:CeO₂ qubit systems as a scalable platform for quantum networks and communication applications.

(1) S. Kanai, et al. PNAS. 119, e2121808119 (2022).

(2) G. Grant, et al. arXiv:2309.16644 (2023).

(3)  J. Zhang, et al. arXiv:2309.16785 (2023).   

Spin polarization and temperature dependent lifetime of Vanadium qubits in SiC

Optically active solid-state spin defects have drawn great interest for their potential applications in quantum information science. In particular, vanadium (V⁴⁺) dopants in silicon carbide (SiC) have recently emerged as a promising platform for quantum communication due to its favorable characteristics including bright emission in the telecom O-band (1278 – 1388 nm) and an optically addressable electron-nuclear spin system within a commercially mature electronic platform. As a novel defect system, there remain important open questions regarding the fundamental properties of these qubit systems for quantum applications. Here, we further characterize the optical and spin properties of V⁴⁺ defects at different sites in 4H- and 6H-SiC at temperatures below 4K. We demonstrate all-optical spin polarization and readout, which we use to probe the spin lifetimes and its temperature dependence. Our results suggest that V⁴⁺ in SiC is a promising candidate for applications in quantum communication and networks.   

Towards Non-Abelian Quantum Signal Processing: Error-Corrected Universal Gate Teleportation for GKP Codes

Quantum signal processing (QSP) is a technique for preparing arbitrary unitary operations using multiple single-qubit rotations where the control paramters are classical variables. We extend the concept of quantum signal processing to the case of multiple control parameters which are themselves non-commuting quantum operators--namely the positions and momenta of quantum harmonic oscillators. The non-commutativity of the control parameters implies that they unavoidably suffer intrinsic quantum fluctuations, but the richer commutator algebra also significantly enhances the power of quantum signal processing and reduces circuit depths. Non-abelian QSP provides a strong framework with which to analyze quantum control of hybrid continuous-variable (CV) -- discrete-variable (DV) systems comprising oscillators and qubits such as those found in trapped-ion and superconducting circuit QED systems. We illustrate the power of this framework with applications to the Gottesman-Kitaev-Preskill codes. The framework's versatility bridges the gap between theoretically ideal infinitely-squeezed GKP states and experimentally realistic finitely-squeezed GKP states, significantly enhancing the fidelity of practical GKP gate operations. In particular, for this talk, we introduce an error-corrected universal single and multi-qubit logical gate teleportation scheme which corrects errors on the oscillator (GKP qubit) while teleporting the gates using a single ancilla qubit. We develop a novel piece-wise gate teleportation approach that mitigates the effects of ancilla dephasing, making ancilla bit flips the leading source of noise. Our scheme can be realized in a fault-tolerant manner using a biased-noise ancilla at no additional cost in comparison to the stabilization circuit of the GKP codes. Such construction was only possible due to the understanding of hybrid oscillator-qubit systems that we achieved from the non-abelian QSP framework.   

Continuous variable quantum computation of the $O(3)$ model in 1+1 dimensions

We formulate the $O(3)$ non-linear sigma model in 1+1 dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous variable (CV) approach to quantum computing. We construct the ground state and excited states using the coupled-cluster Ansatz and find excellent agreement with the exact diagonalization results for a small number of lattice sites. We then present the simulation protocol for the time evolution of the model using CV gates and obtain numerical results using a photonic quantum simulator. We expect that the methods developed in this work will be useful for exploring interesting dynamics for a wide class of sigma models and gauge theories, as well as for simulating scattering events on quantum hardware in the coming decades.   

Exotic Quantum State Generation

This work introduces a novel approach to generating exotic quantum states. We initiate the process with a vacuum state, proceeding to generate exotic states through a sequence of squeezing and entangling operations. These operations are followed by photon number measurements on an ancillary mode and are repeated as necessary. The optimal parameters are determined through iterative optimization techniques, adjusting the parameters of quantum operations applied to the initial state with the aim of maximizing fidelity with the target quantum state. This iterative refinement process continues until the desired level of fidelity is achieved, ensuring that the generated quantum state closely approximates the target state. Considering the simplicity and straightforward nature of the steps needed to generate the exotic state once optimal parameters are established, we are confident in the significant potential of this approach. To illustrate the effectiveness of this approach in reproducing complex quantum states, we have achieved high fidelity in generating various exotic states, including a 99.33% fidelity for a cat state, 95.60% fidelity for a 4-component cat state, and 99.01% fidelity for a GKP state. Given our success in achieving high fidelities, we will explore the production of Continuous Variable Cluster States in future work.   

Classical-Nonclassical Polarity of Gaussian States

Gaussian states with nonclassical properties such as squeezing and entanglement serve as crucial resources for quantum information processing. Accurately quantifying these properties within multi-mode Gaussian states has posed some challenges. To address this, we introduce a unified quantification: the 'classical-nonclassical polarity', represented by $mathcal{P}$.

For a single mode, a positive value of $mathcal{P}$ captures the reduced minimum quadrature uncertainty below the vacuum noise, while a negative value represents an enlarged uncertainty due to classical mixtures. For multi-mode systems, a positive $mathcal{P}$ indicates bipartite quantum entanglement.

We show that the sum of the total classical-nonclassical polarity is conserved under arbitrary linear optical transformations for any two-mode and three-mode Gaussian states. For any pure multi-mode Gaussian state, the total classical-nonclassical polarity equals the sum of the mean photon number from single-mode squeezing and two-mode squeezing.

Our results provide a new perspective on the quantitative relation between single-mode nonclassicality and entanglement, which may find applications in a unified resource theory of nonclassical features such as the consersion between varied kinds of nonclassical properties. Moreover, the conservation relation could give rise to a solution of high-mode entanglement quantification in terms of Gaussian states.   

Analysis of Optical GKP State Generation Using Shaped Free Electrons

The Gottesman-Kitaev-Preskill (GKP) bosonic error-correcting codes are the major candidates to realize fault-tolerant quantum computing and communication with bosonic systems. Especially, the correction capabilities of the optical GKP states may combat fiber attenuation to efficiently produce high-fidelity entanglement over long distances. However, due to weak optical nonlinearities and the absence of efficient and high-fidelity microwave-to-optical transduction,  it remains highly challenging to produce the necessary GKP states in the optical domain scalably.

A recent proposal [Dahan et al., PRX 13, 031001 (2023)] considers the use of a shaped free electron to rapidly impart nonlinearities onto the photonic mode, generating a GKP state upon post-selection. We seek to understand and improve this approach in a few ways. To better represent the noise on the electron state, we rigorously describe the electronic wavefunction as a continuous-variable system in time-frequency space. Furthermore, we use the electron-photon interaction to produce more general states, such as the GKP qu-naught state, which can be used to produce a GKP Bell pair with a balanced beamsplitter. Finally, we remove the electron measurement by considering alternate state preparation procedures, reducing the experimental overhead and improving the post-selection.   

Q-Flow: Generative Modeling for Open Quantum Dynamics with Normalizing Flows

Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix ρ is high-dimensional, customized deep generative neural networks have been instrumental in modeling ρ. However, the complex-valued nature and normalization constraints of ρ, as well as its complicated dynamics, prohibit a seamless connection between open quantum systems and the recent advances in deep generative modeling. Here, we lift that limitation by utilizing a reformulation of open quantum system dynamics to a partial differential equation (PDE) for a corresponding quasiprobability distribution Q, the Husimi Q function. Thus, we model the Q function seamlessly with off-the-shelf deep generative models such as normalizing flows. Additionally, we develop novel methods for learning normalizing flow evolution governed by high-dimensional PDEs based on the Euler method and the application of the time-dependent variational principle. We name the resulting approach Q-Flow and demonstrate the scalability and efficiency of Q-Flow on open quantum system simulations, including Fokker-Plank and dissipative Bose-Hubbard models. Q-Flow is superior to conventional PDE solvers and state-of-the-art physics-informed neural network solvers, especially in high-dimensional systems.   

Piquasso: A Photonic Quantum Computer Simulation Software Platform

We introduce the Piquasso quantum programming framework, a full-stack open-source software platform for the simulation and programming of photonic quantum computers. Piquasso can be programmed via a high-level Python programming interface enabling users to perform efficient quantum computing with discrete and continuous variables. Via optional high-performance C++ backends, Piquasso provides state-of-the-art performance in the simulation of photonic quantum computers. The Piquasso framework is supported by an intuitive web-based graphical user interface where the users can design quantum circuits, run computations and visualize the results.   

Linear optical fusion gate onto qubits boosted by high-dimensional entanglement

Photonic modes are suitable to carry high-dimensional quantum information as qudits, and the use of high-dimensional entanglement between qudits is expected to increase the information capacity. However, compared with the use of photonic modes as qubits, it is much more difficult to process qudits with keeping their dimensions, e.g., to generate multi-partite entangled qudits with linear optics, which considerably narrows the range of applications as qudits. We propose linear optical fusion gates which project a pair of qudit systems onto a Bell state in two-dimensional subspaces. These enable us to generate a two-dimensional Bell state by applying it to halves of two pairs of d-dimensional maximally entangled states with success probability 1-1/d without ancilla photons (1-1/d^l+1 with 2(2^l-1) ancilla photons (l=1, 2, ...)). These success probabilities are higher than the conventional type-II fusion gates, corresponding to d=2. Thus, this work increases usability of photonic qudits, especially in efficient generation of large-scale multipartite two-dimensional entangled states for quantum computation and communication.