Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session L07: Autonomous QEC and Bosonic CodesFocus

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Sponsoring Units: DQI Chair: Theodore Yoder, IBM TJ Watson Research Center Room: 102 
Wednesday, March 4, 2020 8:00AM  8:12AM 
L07.00001: Protecting a bosonic qubit with autonomous quantum error correction I – Theory Chen Wang, Jeffrey Gertler Existing demonstrations of quantum error correction are based on an active schedule of measurement and recovery operations which is hardware intensive and incurs additional error overhead. It is theoretically possible to correct quantum errors with dissipation in a continuous and autonomous fashion, without a classical controller. While dissipative confinement of a quantum system to a twostate manifold had been demonstrated, so far it has remained challenging to achieve a dissipation operator that counters the dominant natural errors in order to extend the lifetime of an encoded qubit. Here we present an autonomous error correction scheme for a bosonic qubit in a superconducting cavity, which directly corrects the dominant error channel of the system: single photon loss. In this Part I of the talk, we discuss this dissipative error correction protocol, its design considerations, as well as its expected performance and limitations. 
Wednesday, March 4, 2020 8:12AM  8:24AM 
L07.00002: Protecting a bosonic qubit with autonomous quantum error correction II – Experiment Jeffrey Gertler, Brian Baker, Juliang Li, Jens Koch, Chen Wang Existing demonstrations of quantum error correction are based on an active schedule of measurement and recovery operations which is hardware intensive and incurs additional error overhead. It is theoretically possible to correct quantum errors using dissipation in a continuous and autonomous fashion, without a classical controller. While dissipative confinement of a quantum system to a twostate manifold had been demonstrated, so far it has remained challenging to achieve a dissipation operator that counters the dominant natural errors in order to extend the lifetime of an encoded qubit. Here we present an autonomous error correction scheme for a bosonic qubit in a superconducting cavity, which directly corrects the dominant error channel of the system: single photon loss. In this Part II of the talk, we present our circuit QED setup and experimental results. 
Wednesday, March 4, 2020 8:24AM  8:36AM 
L07.00003: AllGaussian universality and fault tolerance with the GottesmanKitaevPreskill code Ben Q Baragiola, Giacomo Pantaleoni, Rafael Alexander, Angela Karanjai, Nicolas C Menicucci The GottesmanKitaevPreskill (GKP) encoding of a qubit within an oscillator is particularly appealing for faulttolerant quantum computing with bosons because Gaussian operations on encoded Pauli eigenstates enable Clifford quantum computing with error correction. We show that applying GKP error correction to Gaussian input states, such as vacuum, produces distillable magic states, achieving universality without additional nonGaussian elements. Fault tolerance is possible with sufficient squeezing and low enough external noise. Thus, Gaussian operations are sufficient for faulttolerant, universal quantum computing given a supply of GKPencoded Pauli eigenstates. 
Wednesday, March 4, 2020 8:36AM  8:48AM 
L07.00004: Stabilization of finiteenergy GottesmanKitaevPreskill bosonic codes Baptiste Royer, Shraddha Singh, Steven Girvin Due to their large Hilbert space and their high quality factors, microwave cavities are an attractive candidate for the encoding of logical quantum information. One promising choice of encoding in these cavities is the GottesmanKitaevPreskill (GKP) code which allows to protect against small displacements in phase space. However, in their ideal form, GKP codewords contain an infinite amount of energy and, consequently, their experimental implementation cannot be exact. Nevertheless, recent experiments [Flühmann et al., Nature (2019), CampagneIbarcq et al., arXiv:1907.12487] have demonstrated that it is possible to obtain long coherence times for GKP logical qubits. In this talk, we investigate improved stabilization strategies tailored specifically for finiteenergy GKP codes and study how these protocols perform in a superconducting implementation with realistic parameters. 
Wednesday, March 4, 2020 8:48AM  9:00AM 
L07.00005: Pathindependent gates for errorcorrected quantum computing: Theory WenLong Ma, Philip Reinhold, Serge Rosenblum, Robert Schoelkopf, Liang Jiang Universal control of a quantum system can usually not be achieved by direct control of the system. To realize the missing unitary gates for universal control, we can couple an ancilla system with more complete functionality to the logical system and jointly control both systems. However, the ancilla often suffers much stronger noise than the logical system. Here, we propose a general class of quantum gates on the logical system that is path independent (PI) of Markovian ancilla error trajectories, including both ancilla relaxation and dephasing errors. By fixing the initial and final ancilla states, the designed gates can be PI of infiniteorder ancilla dephasing errors, finiteorder ancilla relaxation errors, and the combination of both. The PI gates can also be made errortransparent to the firstorder logical system errors. As an example, we show that the photonnumber selective arbitrary phase (SNAP) gates in circuit QED belong to such a class of PI gates. This proposal provides a hardwareefficient approach toward faulttolerant quantum computation with systemspecific error models. 
Wednesday, March 4, 2020 9:00AM  9:12AM 
L07.00006: PathIndependent Gates for ErrorCorrected Quantum Computing: Experiment Serge Rosenblum, Philip Reinhold, WenLong Ma, Luigi Frunzio, Liang Jiang, Robert Schoelkopf In future faulttolerant quantum computers, errors resulting from noise and decoherence must be detected and corrected in realtime. This is particularly important while applying logical gates, which can cause errors to quickly spread throughout the system. 
Wednesday, March 4, 2020 9:12AM  9:24AM 
L07.00007: Errortransparent operations on a logical qubit protected by quantum error correction Yuwei Ma, Yuan Xu, Xianghao Mu, Weizhou Cai, Ling Hu, Weiting Wang, Xiaoxuan Pan, Haiyan Wang, Yipu Song, Changling Zou, Luyan Sun Universal quantum computation is striking for its unprecedented capability in processing information, but its scalability is challenging in practice because of the inevitable environment noise. Although quantum error correction (QEC) techniques have been developed to protect stored quantum information from leading orders of errors, the noiseresilient processing of the QECprotected quantum information is highly demanded but remains elusive. Here, we demonstrate phase gate operations on a logical qubit encoded in a bosonic oscillator in an errortransparent (ET) manner. The ET gates are extended to the bosonic code and are able to tolerate errors during the gate operations, regardless of the random occurrence time of the error. With precisely designed gate Hamiltonians through photonnumberresolved ACStark shifts, the ET condition is fulfilled experimentally. We verify that the ET gates outperform the nonET gates with a substantial improvement of the gate fidelity after an occurrence of the singlephotonloss error. Our ET gates in the superconducting quantum circuits are readily for extending to multiple encoded qubits and a universal gate set is within reach, paving the way towards faulttolerant quantum computation. 
Wednesday, March 4, 2020 9:24AM  9:36AM 
L07.00008: Highimpedance circuits for parity measurements of cat qubits Clarke Smith, Marius Villiers, Raphaël Lescanne, Antoine Marquet, Camille Berdou, Takis Kontos, Mazyar Mirrahimi, Zaki Leghtas Encoding a qubit in the two degenerate steady states of an oscillator—which only exchanges pairs of photons with its environment—can exponentially suppress the bitflip rate for large phasespace separations. The unsuppressed phase flips of these socalled "cat qubits" correspond to a change in the photon number parity of the oscillator, and they could be corrected using redundant encoding. In such a scheme, errors are detected via measurements of the joint parity between cat qubits, which could be implemented at the Hamiltonian level using effective paritytype couplings. We show that a paritytype Hamiltonian emerges from the conventional Josephson potential in the limit of high oscillator impedance. Here, the high impedance guarantees large fluctuations of the superconducting phase, which translates into large displacements in oscillator phase space. We present the design of a superconducting circuit that effectively realizes the paritytype Hamiltonian, as well as the status of its experimental implementation. 
Wednesday, March 4, 2020 9:36AM  9:48AM 
L07.00009: Experimental implementation of faulttolerant error syndrome measurement for paircat code (1/2) Akshay Koottandavida, Ioannis Tsioutsios, Shantanu O Mundhada, Luigi Frunzio, Michel H. Devoret Stabilized quantum manifolds of a bosonic system can encode errorprotected qubits. In particular, a singlemode manifold spanned by cat states can exponentially suppress against phaseflip errors. However, errors due to photon loss cannot be corrected without stopping the stabilization process, using existing microwave superconducting circuit technology. Phaseflip suppression can also be achieved by stabilizing a manifold spanned by paircat states, which are superpositions of the twomode states called BarutGirardello/paircoherent states. Moreover, it is now possible to detect, in a faulttolerant manner, photonloss errors in either mode, simultaneously with the manifold stabilization, by monitoring the photonnumber difference between them. In this talk, we will present an experimental implementation of cavities and superconducting devices that is compatible with such encoding. We will also report on techniques of continuous monitoring of the photon number difference between the modes. Partone of this twopart presentation will introduce the basic theoretical concepts of paircat codes and the design parameters of our experimental implementation. 
Wednesday, March 4, 2020 9:48AM  10:00AM 
L07.00010: Experimental implementation of faulttolerant error syndrome measurement for paircat code (2/2) Ioannis Tsioutsios, Akshay Koottandavida, Shantanu O Mundhada, Luigi Frunzio, Michel H. Devoret Stabilized quantum manifolds of a bosonic system can encode errorprotected qubits. In particular, a singlemode manifold spanned by cat states can exponentially suppress against phaseflip errors. However, errors due to photon loss cannot be corrected without stopping the stabilization process, using existing microwave superconducting circuit technology. Phaseflip suppression can also be achieved by stabilizing a manifold spanned by paircat states, which are superpositions of the twomode states called BarutGirardello/paircoherent states. Moreover, it is now possible to detect, in a faulttolerant manner, photonloss errors in either mode, simultaneously with the manifold stabilization, by monitoring the photonnumber difference between them. In this talk, we will present an experimental implementation of cavities and superconducting devices that is compatible with such encoding. We will also report on techniques of continuous monitoring of the photon number difference between the modes. Parttwo of this twopart presentation will present our most recent experimental progress. 
Wednesday, March 4, 2020 10:00AM  10:12AM 
L07.00011: Progress on faulttolerant quantum computing with concatenated bosonicqubit codes Arne Grimsmo, Stefanus Edgar Tanuarta, Juliette Soule, Ben Q Baragiola, Joshua L. A. Combes In this talk I will discuss ongoing work to quantify the performance of bosonic error correcting codes concatenated with conventional qubit codes. There are two questions we are trying to answer: 1. When does using a bosonic code at the ground level of a concatenated scheme outperform using twolevel systems? 2. How do different bosonic codes compare to each other. We would like to answer both of these questions in a faulttolerant setting that includes state preparation and measurement noise, as well as noise during the error correction circuit. 
Wednesday, March 4, 2020 10:12AM  10:24AM 
L07.00012: FaultTolerant Bosonic Quantum Error Correction with the SurfaceGKP Code Kyungjoo Noh, Christopher Chamberland Bosonic quantum error correction is a viable option for realizing errorcorrected quantum information processing in continuousvariable bosonic systems. Here, we consider the concatenation of the bosonic GottesmanKitaevPreskill (GKP) code with the surface code, namely, the surfaceGKP code. In particular, we thoroughly investigate the performance of the surfaceGKP code by assuming realistic GKP states with a finite squeezing and noisy circuit elements due to photon losses. By using a minimumweight perfect matching decoding algorithm on a 3D spacetime graph, we show that faulttolerant bosonic quantum error correction is possible with the surfaceGKP code if the squeezing of the GKP states is higher than 11.2dB in the case where the GKP states are the only noisy elements. We also show that the squeezing threshold changes to 18.6dB when both the GKP states and circuit elements are comparably noisy. At this threshold, each circuit component fails with probability 0.69%. Finally, if the GKP states are noiseless, faulttolerant quantum error correction with the surfaceGKP code is possible if each circuit element fails with probability less than 0.81%. 
Wednesday, March 4, 2020 10:24AM  11:00AM 
L07.00013: Majorana dimer models of holographic quantum error correction Invited Speaker: Alexander Jahn Holographic quantum errorcorrecting codes have been proposed as toy models describing key aspects of the AdS/CFT correspondence. In this talk, we introduce a versatile framework of Majorana dimers capturing the intersection of stabilizer and Gaussian Majorana states. This picture allows for an efficient contraction with a simple diagrammatic interpretation and is amenable to analytical study of holographic quantum errorcorrecting codes. Equipped with this framework, we revisit the recently proposed hyperbolic pentagon code (HyPeC) and demonstrate efficient computation of boundary state properties for generic logical bulk input. We show that the dimers characterizing boundary states of the HyPeC follow discrete bulk geodesics. From this geometric picture, properties of entanglement, quantum error correction, and bulk/boundary operator mapping immediately follow, offering a fresh perspective on holography. We also elaborate upon the emergence of the RyuTakayanagi formula from our model, which shares many properties of the recent bit thread proposal. 
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