Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session S27: LandauerBennett Award Session: Quantum Error Correction Theory and Experiment IIIFocus

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Sponsoring Units: DQI Chair: Markus Kesselring Room: BCEC 160C 
Thursday, March 7, 2019 11:15AM  11:51AM 
S27.00001: Rolf Landauer and Charles H. Bennett Award in Quantum Computing talk: Repeated parity measurement and feedback in a mixedspecies trapped ion register Invited Speaker: Jonathan Home Quantum error correction is essential for realizing the full potential of largescale quantum information processing devices. Fundamental to its experimental realization is the repetitive detection of errors via projective measurements of quantum correlations among qubits, as well as corrections using conditional feedback. I will describe experiments in which we demonstrate up to 50 sequential measurements of correlations between two beryllium ion microwave qubits using an ancillary opticalfrequency qubit in a calcium ion, and implement feedback that allows us to stabilize twoqubit subspaces as well as maximally entangled Bell states [1]. The use of multiple ion species allows us to completely reset the ancilla after measurement and completely mitigate any unwanted effects. Looking towards further scaling, many apparent challenges appear to lie in the use of radiofrequency traps, including powerdissipation and the need to coalign microscopically varying potentials. I will describe how this might be mitigated using microfabricated arrays of Penning traps, which would also provide a powerful tool for implementing trappedion quantum simulation on a variety of twodimensional lattices. 
Thursday, March 7, 2019 11:51AM  12:03PM 
S27.00002: Optimality of GottesmanKitaevPreskill (GKP) Codes for Bosonic Quantum Error Correction Kyungjoo Noh, Victor Albert, Liang Jiang Bosonic quantum error correction has recently risen as a hardwareefficient alternative to the conventional multiqubitbased quantum error correction. We mainly focus on photon loss error, which is a dominant error source in microwave cavity modes. Previously, it was shown that GKP codes outperform many other bosonic quantum errorcorrecting codes in correcting photon loss errors, despite the fact that GKP codes are not designed to correct loss errors [1]. Here, we explain why GKP codes perform well against photon loss errors by providing a nearoptimal decoding scheme and analyzing its performance. Furthermore, we formulate a biconvex optimization to find the best singlemode bosonic errorcorrecting code for photon loss errors. In particular, we solve the biconvex optimization heuristically by an alternating semidefinite programming method and show that, starting from Haar random initial codes, our numerical optimization yields a hexagonal GKP code as an optimal encoding in a practically relevant regime [2]. 
Thursday, March 7, 2019 12:03PM  12:15PM 
S27.00003: Highthreshold fualttolerant quantum computation with GKP qubits and realistically noisy devices Kosuke Fukui, Akihisa Tomita, Keisuke Fujii To implement faulttolerant quantum computation with continuous variables, the GottesmanKitaevPreskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to realize large scale quantum computation with the GKP qubits [Phys. Rev. X. 8, 021054 (2018)]. Although our method can reduce the required squeezing level to less than 10 dB, which is within the reach of the current experimental technology, we have assumed that the CZ gate and an efficiency of the homodyne detection are ideal. In this work, we show that the required squeezing level is around 10 dB under the realistic assumption that the CZ gate and homodyne detection degrade the squeezing level of the GKP qubits, developing a method to reduce a noise on the GKP qubit by using postselection and maximumlikelihood methods. 
Thursday, March 7, 2019 12:15PM  12:27PM 
S27.00004: Grid states for encoding and stabilizing a logical qubit in superconducting circuits (Part 1) Alec Eickbusch, Steven Touzard, Phillipe CampagneIbarcq, Evan ZalysGeller, Nicholas Frattini, Volodymyr Sivak, Shruti Puri, Mazyar Mirrahimi, Shyam Shankar, Michel H. Devoret Quantum computation requires that systems preserve quantum information in the presence of noise. The impact of this noise can be mitigated by redundantly encoding a quantum bit of information within a space with a large number of dimensions. Stabilization is done by detecting noiseinduced transformations of the system state before the encoded information is lost. In 2001, Gottesman Kitaev and Preskill (GKP) proposed to encode a quantum bit in nonlocal grid states of a harmonic oscillator. Remarkably, GKP codes have the potential to protect quantum information against all known error channels. In this talk, I will review GKP code properties and present a protocol based on a tunable interaction with an ancillary twolevel system to create and stabilize GKP grid states using phaseestimation of the harmonic oscillator field. 
Thursday, March 7, 2019 12:27PM  12:39PM 
S27.00005: Grid states for encoding and stabilizing a logical qubit in superconducting circuits (Part 2) Steven Touzard, Alec Eickbusch, Phillipe CampagneIbarcq, Evan ZalysGeller, Nicholas Frattini, Volodymyr Sivak, Shruti Puri, Mazyar Mirrahimi, Shyam Shankar, Michel H. Devoret Protecting quantum information requires encoding a quantum bit of information into a space with a large number of dimensions. To this end, Gottesman Kitaev and Preskill (GKP) proposed to use a single harmonic oscillator as an alternative to an ensemble of many twolevel systems. In this scheme, the information is encoded in grid states of the oscillator. The dispersive interaction between the oscillator and an ancillary twolevel system is sufficient to create and stabilize these nonlocal states, provided that the interaction strength is periodically modulated in time. In this talk, I will show how to engineer such a modulated interaction and I will present our experimental progress towards the creation and stabilization of GKP grid states. 
Thursday, March 7, 2019 12:39PM  12:51PM 
S27.00006: Continuous symmetries and approximate quantum error correction Philippe Faist, Sepehr Ghazi Nezami, Victor Albert, Grant Salton, Fernando Pastawski, Patrick Hayden, John Preskill Quantum error correction and symmetries are relevant to many areas of physics, including many body quantum systems, holographic quantum gravity, and referenceframe errorcorrection [Hayden et al., arXiv:1709.04471]. Here, we show that any code is fundamentally limited in its ability to approximately errorcorrect against erasures at known locations if it is covariant with respect to a continuous local symmetry. Our bound vanishes either in the limit of large individual subsystems, or in the limit of a large number of subsystems, and is approximately tight in these regimes. Furthermore, we prove an approximate version of the EastinKnill theorem that quantifies a code’s ability to correct erasure errors if it admits a universal set of transversal logical gates. The bound is in terms of the local physical subsystem dimension. We provide a collection of example codes illustrating our bounds in different regimes. In the context of the AdS/CFT correspondence, our approach provides insight into how time evolution in the bulk corresponds to time evolution on the boundary without violating the EastinKnill theorem, and our fiverotor code can be stacked to form a covariant holographic code. 
Thursday, March 7, 2019 12:51PM  1:03PM 
S27.00007: Numerically optimized quantum errorcorrecting codes for a bosonic mode Matti Silveri, Kari Mäkinen Bosonic quantum errorcorrecting codes, such as cat and binomial codes, provide good performance against photon loss errors and are experimentally realizable e.g. with superconducting circuits. Motivated by this and aiming to broaden the spectrum of bosonic codes, we have numerically searched for bosonic singlemode codes. The codes are constructed from a finite superposition of Fock states. By utilizing numerical methods, the complex coefficients of the Fock states are chosen so that a code protects against L photon loss errors and minimizes the probability for the L+1:th error to occur. We have found codes that are protected up 9 photon loss errors. We present the structure and analyze the performance of these numerically optimized codes. 
Thursday, March 7, 2019 1:03PM  1:15PM 
S27.00008: Singlemode bosonic error correcting codes with rotation symmetry Arne Grimsmo, Joshua Combes, Ben Q Baragiola Bosonic mode error correcting codes, or mode codes for short, are error correcting codes where a qubit (or qudit) is encoded into one or multiple bosonic modes, i.e., quantum oscillators with an infinite Hilbert space. In this talk I focus on singlemode codes that obey rotation symmetry in phase space, such as the the well known Cat, Binomial and GKP codes. I will introduce a universal scheme for this class of codes based only on simple and experimentally wellmotivated interactions. The scheme is faulttolerant in the sense that small errors are guaranteed to remain small under the considered gates. I will also introduce a faulttolerant error correction scheme based on crossKerr interactions and destructive phase measurement (e.g., heterodyne). Remarkably, the error correction scheme approaches the optimal recovery map for Cat and Binomial codes when the ancilla modes are error free. We numerically compute breakeven thresholds under loss and dephasing, both with ideal and faulty ancillas. 
Thursday, March 7, 2019 1:15PM  1:27PM 
S27.00009: Simplified mixedstate encoding for quantum computation with continuousvariable systems Kevin Marshall, Daniel James, Alexandru Paler, HoiKwan Lau Recent development of mixedstate encoding (MSE) allows a purestate logical qubit to be encoded by a continuousvariable system in mixed physical state. Despite interest due to its counterintuitiveness, the utility of current MSE is limited due to several operational drawbacks, namely probabilistic initialisation, redundant information carrier, and requirement of discretevariable measurement. In this work, we present a simplified MSE that does not suffer from any of these drawbacks. Specifically, our protocol encodes each qubit by only one mixedstate harmonic oscillator, and the logical basis can be deterministically initialised by displacing a thermal equlibirum state. By using measurementbased quantum computation formalism, logical operations can be performed by only continuousvariable interaction and measurement. Without the necessity of ground state cooling, our proposal could broaden the candidate for quantum computation, and reduce the reinitialisation time of measured qubits. Additionally, the noise tolerance of logical quantum information can be enhanced by treating conventional purestate encoded qubits as MSE qubits. 
Thursday, March 7, 2019 1:27PM  1:39PM 
S27.00010: Faulttolerant gates on a logical qubit Serge Rosenblum, Philip Reinhold, Wenlong Ma, Liang Jiang, Luigi Frunzio, Robert J Schoelkopf A faulttolerant architecture based on errorcorrected qubits requires the implementation of logical gates that do not induce uncorrectable errors. Here, we present a faulttolerant construction for a gate on a cavityencoded logical qubit. The scheme uses the multilevel structure of a transmon ancilla, along with RFtunable transmoncavity interaction, to apply arbitrary phases to the cavity Fock states. This enables a broad range of gates on a variety of encodings, while protecting the logical qubit against photon loss, as well as ancilla decay and dephasing. Together with the previously demonstrated faulttolerant syndrome measurements [1], this result further expands the toolbox towards fully faulttolerant processing of logical qubits. 
Thursday, March 7, 2019 1:39PM  1:51PM 
S27.00011: Optimal condition for a cavity QEDbased faulttolerant quantum computation Rui Asaoka, Rina Kanamoto, Yuuki Tokunaga, Takao Aoki Cavity quantum electrodynamics (QED) has been extensively studied for decades as one of the promising candidates for the realization of quantum computing and quantum network. For example, the controlled phase flip gate between photons assisted by cavityQED systems was proposed in 2004[1] and demonstrated recently[2]. However, faulttolerant quantum computing is still difficult because of the infidelity and the losses originated from imperfections of the cavity QED system. 
Thursday, March 7, 2019 1:51PM  2:03PM 
S27.00012: Simulation of Gaussian channels via teleportation with applications to error correction and secretkey capacities. Spyros Tserkis, Josephine Dias, Riccardo Laurenza, Samuel L Braunstein, Stefano Pirandola, Timothy Ralph Gaussian channels are the typical way to model the decoherence in continuousvariable quantum states. It is known that those channels can be simulated by a teleportation protocol using as a resource state either a maximally entangled state passing through the same channel, i.e., the Choistate, or a state that is entangled at least as much as the Choistate. Since the construction of the Choistate requires infinite mean energy and entanglement, i.e. it is unphysical, we derive instead every physical state able to simulate a given channel through teleportation with finite resources. Finally, we use those states to generalize a previously known error correction protocol by making it able to correct noise coming from thermal loss channels, and we also show how finiteenergy resource states are able to provide tight upper bounds to the secretkey capacity of Gaussian channels. 
Thursday, March 7, 2019 2:03PM  2:15PM 
S27.00013: Recovering noisefree quantum observables Matthew Otten, Stephen K Gray We introduce a technique for recovering noisefree observables in noisy quantum systems by combining the results of many slightly different experiments. Our approach is applicable to a variety of quantum systems but we illustrate it with applications to quantum computing and quantum sensing. The approach corresponds to repeating the same quantum evolution many times with known variations on the underlying systems' error properties, e.g. the spontaneous emission and dephasing times, T1 and T2. As opposed to standard quantum error correction methods, which have an overhead in the number of qubits, our method has only an overhead in number of evaluations, allowing the overhead to, in principle, be hidden via parallelization. We show that the effective spontaneous emission, T1, and dephasing, T2, times can be increased using this method in both simulation and experiments on an actual quantum computer. We also show how to correct more complicated entangled states and how Ramsey fringes relevant to quantum sensing can be signicantly extended in time. This work was performed at the Center for Nanoscale Materials, a U.S. Department of Energy Office of Science User Facility, and supported by the U.S. Department of Energy, Oce of Science, under Contract No. DEAC0206CH11357. 
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