Session Z69: Recent advances in bosonic quantum error correction

Introducing the Kapitzonium - Quantum control and noise protection of a Floquet $0-pi$ qubit

Time-periodic systems allow engineering new effective Hamiltonians from limited physical interactions. For example, the inverted position of the Kapitza pendulum emerges as a stable equilibrium with rapid drive of its pivot point.

In this work, we propose the emph{Kapitzonium}: a Floquet qubit that is the superconducting circuit analog of a mechanical Kapitza pendulum.

Under periodic driving, the emerging qubit states are exponentially protected against bit and phase flips caused by dissipation, which is the primary source of decoherence of current qubits. However, we find that dissipation causes leakage out of the Floquet qubit subspace.

We engineer a passive cooling scheme to stabilize the qubit subspace, which is crucial for high fidelity quantum control under dissipation.

Furthermore, we introduce a hardware-efficient fluorescence-based method for qubit measurement and discuss the experimental implementation of the Floquet qubit. The proposed {Kapitzonium} is one of the simplest Floquet qubits that can be realized with current technology -- and it already has many intriguing features and capabilities. Our work provides the first steps to develop more complex Floquet quantum systems that can be engineered from the ground up to realize large-scale protected engineered dynamics.   

Encoding qubits in multiple oscillators

Codes based on harmonic oscillators are a promising approach to quantum error correction. Due to their long lifetimes and their large intrinsic Hilbert space, harmonic oscillators such as microwave cavities provide a hardware-efficient approach to error correction compared to qubit register-based codes. In particular, the grid codes introduced by Gottesman, Kitaev and Preskill (GKP) have been numerically and experimentally shown to exhibit long logical lifetimes. However, a recurring challenge with bosonic codes is that they are limited by the lifetime of the ancilla used for quantum control of bosonic modes.

In this talk, I will show that we can tackle this challenge by encoding a logical qubit in multiple modes instead of a single one. Interestingly, these multimode codes have several properties that make them an attractive option as the basis for a quantum computer. More precisely, we introduce a method to autonomously stabilize the code space of multimode GKP codes, and introduce a two-mode grid code which has improved properties with respect to traditional single mode GKP codes. When stabilized with a qubit ancilla, we numerically show that this code has improved robustness against ancilla decay.   

Exploring connections between continuous and discrete variable theorems via the Gottesman-Kitaev-Preskill code

Bosonic codes protect quantum information by embedding discrete-variable (DV) logical Hilbert subspaces into the larger continuous-variable (CV) physical Hilbert space of bosonic modes. Besides the practical use of these codes in the lab, the mathematical connection between DV and CV systems allows applying theorems from one area to the other, leading us to two main results. First, we discriminate circuits—defined with input, operations, and measurements—that cannot provide a quantum computational advantage in CV [1]. With rotation-symmetric bosonic (RSB) codes and the Gottesman-Kitaev-Preskill (GKP) code, families of CV circuits with large Wigner negativity—a necessary resource for computational advantage—correspond to Clifford circuits in DV. Thus, by applying known DV results, we conclude that we can efficiently simulate them with classical computers. Second, we define a measure for magic resource in multiqubit pure states [2], a desired property in fault-tolerant quantum computation. With the GKP code and the resource theory of Wigner logarithmic negativity in CV, we construct the measure and prove its properties for the DV system. The analytical expression of the magic measure allows easy computations with large systems and connects to the st-norm, a previously regarded one-way magic witness.

[1] L. García-Álvarez, C. Calcluth, A. Ferraro, G. Ferrini, Efficient simulatability of continuous-variable circuits with large Wigner negativity, Phys. Rev. Research 2, 043322 (2020).

[2] O. Hahn, A. Ferraro, L. Hultquist, G. Ferrini, and L. García-Álvarez, Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding, Phys. Rev. Lett. 128, 210502 (2022).   

Hybrid quantum information processing with spin and motional states of trapped ions

Hybrid approach to quantum information processing that involves both motional and spin states of trapped ions offers access to a larger Hilbert space and hardware efficient encoding of quantum information compared to the qubit only schemes. Here I present an experimental implementation of controlled-beamsplitter and controlled-SWAP gates that involves quantum states of two bosonic modes and a control qubit in a system of trapped Yb-171 ions. I discuss how to apply the controlled-SWAP gate to measure overlap between infinite dimensional quantum states of harmonic oscillators and show how this overlap test can be used for quantum enhanced machine learning algorithms.   

Real-time quantum error correction beyond break-even

The ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract the natural tendency of a complex system to decohere. This cooperative process, which requires participation of multiple quantum and classical components, creates a special type of dissipation that removes the entropy caused by the errors faster than the rate at which these errors corrupt the stored quantum information. Previous experimental attempts to engineer such a process faced an excessive generation of errors that overwhelmed the error-correcting capability of the process itself. Whether it is practically possible to utilize QEC for extending quantum coherence thus remains an open question. We answer it by demonstrating a fully stabilized and error-corrected logical qubit whose quantum coherence is significantly longer than that of all the imperfect quantum components involved in the QEC process, beating the best of them with a coherence gain of $G = 2.27 pm 0.07$. We achieve this performance by combining innovations in several domains including the fabrication of superconducting quantum circuits and model-free reinforcement learning.