Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session N37: Bosonic Codes and New Quantum Error Correction SchemesFocus Recordings Available

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Sponsoring Units: DQI Chair: Yariv Yanay, Laboratory for Physical Sciences Room: McCormick Place W194B 
Wednesday, March 16, 2022 11:30AM  11:42AM 
N37.00001: Preparation and Stabilization of GKP states with KerrCat Qubit Ancilla Shivnag Sista, Shraddha Singh, Shruti Puri The GottesmanKitaevPreskill (GKP) code is a promising bosonic error correction code that provides protection against small displacement errors of an oscillator. Preparation and stabilization of GKP states have recently been demonstrated in trappedion and circuitQED platforms. The key component in these experiments is a twolevelancillacontrolled displacement of the highQ cavity mode. In the circuitQED implementation, the main factor limiting the fidelity of GKP preparation and stabilization is the propagation of relaxation or T_{1} errors from the ancilla to a large, uncorrectable error in the GKP state. Remarkably, the contagious relaxation errors are highly suppressed in a Kerrcat qubit, potentially making it an excellent twolevel ancilla. Here, we characterize the performance of the GKP preparation and stabilization protocol with Kerrcat ancilla. We consider dominant sources of errors in the system and identify the parameter regimes where the use of a Kerr cat ancilla results in better performance compared to a conventional twolevel ancilla. 
Wednesday, March 16, 2022 11:42AM  11:54AM 
N37.00002: Extending the logical lifetime of a stabilized GottesmanKitaevPreskill qubit with reinforcement learning Volodymyr Sivak, Alec W Eickbusch, Baptiste Royer, Ioannis Tsioutsios, Robert J Schoelkopf, Michel H Devoret GottesmanKitaevPreskill (GKP) encoding of a qubit in an oscillator is a promising candidate for quantum error correction (QEC) in bosonic systems. We introduce a novel QEC protocol for the GKP encoding, and experimentally implement it with a superconducting microwave cavity coupled to a transmon ancilla qubit. The protocol contains 33 tunable parameters which we optimize insitu using a reinforcement learning agent. We demonstrate that the agent learns interpretable directions in parameter landscape, which would be difficult and timeconsuming to discover and optimize for a human experimentalist. The learned QEC protocol for GKP has process fidelity on par with that of the simplest uncorrectable Fock encoding, and yields X & Z logical Pauli operator lifetimes approaching 1 ms. Our experiment clearly demonstrates the advantage of closedloop optimization for quantum control over the limited modelbased tuneup. 
Wednesday, March 16, 2022 11:54AM  12:06PM 
N37.00003: Demonstration of Heralded Optical Attenuation by Zero Photon Subtraction Cory M Nunn, Todd B Pittman, James D Franson Photon subtraction is widely employed for optical quantum state engineering with potential applications in quantum communication, and it can be accomplished by conditional measurements of single photons at the outputs of a beam splitter. Interestingly, conditioning on the detection of zero photons in a similar way also transforms optical states. In particular, this socalled "zero photon subtraction" reduces the mean photon number of any superposition of Fock states. Here we experimentally demonstrate this counterintuitive type of attenuation and observe an interesting dependence on the photon number statistics of the input state. These effects are analogous to that of typical singlephoton subtraction and provide some additional insight into physical implementations of creation and annihilation operators in quantum optics. 
Wednesday, March 16, 2022 12:06PM  12:18PM 
N37.00004: Automated discovery of autonomous quantum error correction schemes Zhaoyou Wang, Taha Rajabzadeh, Nathan R Lee, Amir SafaviNaeini We can encode a qubit in the energy levels of a quantum system. Relaxation and other dissipation processes lead to decay of the fidelity of this stored information. Is it possible to preserve the quantum information for a longer time by introducing additional drives and dissipation? The existence of autonomous quantum error correcting codes answers this question in the positive. Nonetheless, discovering these codes for a real physical system, i.e., finding the encoding and the associated driving fields and bath couplings, remains a challenge that has required intuition and inspiration to overcome. In this work, we develop and demonstrate a computational approach based on adjoint optimization for discovering autonomous quantum error correcting codes given a description of a physical system. We implement an optimizer that searches for a logical subspace and control parameters to better preserve quantum information. We demonstrate our method on a system of a harmonic oscillator coupled to a lossy qubit, and find that varying the Hamiltonian distance in Fock space  a proxy for the control hardware complexity  leads to discovery of different and new error correcting schemes. We discover what we call the \sqrt{3} code, realizable with a Hamiltonian distance d=2, and propose a hardwareefficient implementation based on superconducting circuits. 
Wednesday, March 16, 2022 12:18PM  12:30PM 
N37.00005: Hardware efficient autonomous error correction protocol (Part I) Tanay Roy, Ziqian Li, David Rodriguez Perez, Eliot Kapit, David Schuster Quantum error correction (QEC) would be indispensable when scaling up qubits for building a fullfledged quantum computer. Autonomous quantum error correction (AQEC) is a hardwareefficient way to realize QEC without fast digital feedback control. The Very Small Logical Qubit (VSLQ) is one of the AQEC protocols which requires two qutrits and two lossy resonators for protection against relaxation errors [1]. We propose a new scheme to implement the VSLQ Hamiltonian, which we call the star code, that requires only twophoton processes. The star code can be implemented using any linear coupler that can parametrically drive qutritqutrit red and blue sidebands, making the code more flexible and easier to realize than the original design. Our simulations show a significant improvement in logical qubit lifetimes and suppression of dephasing noise. We also discuss other constraints that must be addressed while designing the device for successful implementation. 
Wednesday, March 16, 2022 12:30PM  12:42PM 
N37.00006: Hardware efficient autonomous error correction protocol (Part II) Ziqian Li, Tanay Roy, David Rodriguez Perez, Eliot Kapit, David Schuster A crucial component of our scheme to implement the Very small Logical Qubit (VSLQ) Hamiltonian is an interqutrit coupling mechanism capable of generating strong interactions between various twoqutrit levels while maintaining a small crossKerr interaction. We discuss our design of a tunable inductive coupler that can produce relevant blue and red sidebands with rates greater than 6 MHz and suppresses ZZ coupling at the operating DC flux point. We also achieve qutritresonator blue sideband rates above 1 MHz which is more than sufficient for the VSLQ protocol. We demonstrate our preliminary results of the logical state stabilization and corresponding improvements in the logical relaxation times. Finally, we discuss the challenges behind realizing the full autonomous quantum error correction where six microwave drives are needed to stabilize an unknown logical superposition state. 
Wednesday, March 16, 2022 12:42PM  1:18PM 
N37.00007: Faulttolerant quantum computing with bosonic qubits Invited Speaker: Kyungjoo Noh A popular approach for realizing a faulttolerant quantum computer is to construct logical qubits encoded in a surface code (or its variants) with bare twolevel qubits (e.g., superconducting qubits or trappedion qubits) as underlying physical qubits. Recently, various alternative approaches have been proposed, such as using bosonic qubits (e.g., GKP qubits and cat qubits) as underlying qubits instead of bare twolevel qubits. Bosonic qubits are distinguished from bare twolevel qubits as they are themselves protected via bosonic quantum error correction (bosonic QEC). Moreover, bosonic QEC provides bosonic qubits with special structures that are absent in bare twolevel qubits. In this talk, I will provide an overview of various proposals for bosonicqubit architectures and explain how the unique properties of underlying bosonic qubits (e.g., extra analog information for GKP qubits and noise bias for some cat qubits) may be utilized to reduce the hardware resource overhead for building a faulttolerant quantum computer. 
Wednesday, March 16, 2022 1:18PM  1:30PM 
N37.00008: Encoding qubits in multimode grid states  Part 1 Shraddha Singh, Baptiste Royer, Steven M Girvin Bosonic errorcorrection codes leverage the continuous variables of the Hilbert space to design lowerror quantum memories. The GottesmanKitaevPreskill (GKP) code is an example of a bosonic code that provides logical encoding of qubit in a phase space lattice of an oscillator mode. Recent experiments in microwave cavities and trapped ions show promising realization of these codes. In order to further improve over single mode codes, one can concatenate such codes with a qubit code. In this talk, we take a different approach, studying codes based on lattices in the 2ndimensional phase space of n oscillators. We highlight the advantages of this approach with the specific example of a twomode code based on a hypercubic lattice. Compared to single mode codes, this code consists of shorter stabilizers and longer logical operators which consequently provides increased protection against errors while reducing ancillainduced faults during stabilizer measurements. We also discuss the gate set for this code, as well as more general relations between lattice symmetries and logical gates. 
Wednesday, March 16, 2022 1:30PM  1:42PM 
N37.00009: Encoding qubits in multimode grid states  Part 2 Baptiste Royer, Shraddha Singh, Steven M Girvin Bosonic errorcorrection codes are emerging as an attractive and hardwareefficient alternative to qubitbased encodings. In particular, the GottesmanKitaevPreskill (GKP) grid codes have generated interest due to predicted long logical lifetimes and the fact that Clifford operations can be implemented using Gaussian circuits. Moreover, they have recently been implemented in microwave cavities and in the motion of trapped ions. However, one recurring challenge with practical implementations of bosonic codes, including the GKP code, is that errors in the ancilla used for quantum control of the oscillator modes propagate as logical errors, limiting the information lifetime. In this talk, we show how this limitation can be overcome using multimode GKP codes. First, we will introduce general qubit ancillabased errorcorrection circuits to stabilize the code space of multimode grid codes. Then, we show that stabilizing the code space of a twomode hypercubic code, ancilla errors mostly propagate as correctable errors. Our new errorcorrection circuits promise the extension of the logical lifetime orders of magnitude beyond the ancilla lifetime. 
Wednesday, March 16, 2022 1:42PM  1:54PM 
N37.00010: Optimized error correction with repetition cat qubits. FrançoisMarie Le Régent, Jérémie Guillaud, Mazyar Mirrahimi, Zaki Leghtas, Camille Berdou Repetition cat qubits constitute a viable solution for lowoverhead faulttolerant quantum computation. We present an optimized error correction circuit for such an encoding. We perform numerical simulations of this optimized error correction protocol using a circuitbased error model. The error models are carefully derived from the analysis of the master equation associated to twophoton driven dissipation and in presence of typical physical noise sources. We demonstrate an enhancement of the threshold for phaseflip error correction and a better scaling below the threshold. 
Wednesday, March 16, 2022 1:54PM  2:06PM 
N37.00011: Quantifying Qubit Magic with GottesmanKitaevPreskill Encoding Oliver Hahn, Alessandro Ferraro, Lina Hultquist, Giulia Ferrini, Laura GarcíaÁlvarez Quantum resource theories are a powerful framework to characterize and quantify relevant quantum phenomena and identify processes that optimize their use for different tasks. In this work [1], we define a resource measure for magic, the soughtafter property in most faulttolerant quantum computers. In contrast to previous literature, our formulation is based on bosonic codes, wellstudied tools in continuousvariable quantum computation. With this new methodology, we are able to prove its properties and connect it to the stnorm, a quantity previously only known to be a onesided magic witness in qubit systems. In particular, we use the GottesmanKitaevPreskill code to represent multiqubit states and employ the resource theory of Wigner negativity. The analytical expression of our magic measure allows us to extend current analysis limited to small dimensions, easily addressing systems of up to 12 qubits. 
Wednesday, March 16, 2022 2:06PM  2:18PM 
N37.00012: Saving the cat: Approximate quantum error correction using squeezed Schrödinger cat states David S Schlegel, Fabrizio Minganti, Vincenzo Savona A promising road to quantum error correction is that of bosonic codes, whereby a logical quantum bit is robustly encoded in wellchosen states of a quantum harmonic oscillator. Schrödinger cat codes in particular can correct phaseflip errors in the limit of large displacement of the boson field, while they are still vulnerable to bitflip errors induced by photon loss. Other bosonic codes  such as the fourlegged cat code, the binomial code, or the GKP code  have been studied. A bosonic code that can correct both bitflip and phaseflip errors within an experimentally viable and scalable scheme is still however a challenge. Here we show that adding squeezing as a resource, squeezedcat states allow a partial correction of the bitflip error, therefore suppressing the logical error rate, while improving the protection against phaseflip errors. We develop a full paritycheck and recovery protocol that is suitable to be implemented on currently available superconducting architectures. With parameters typical of the experimental stateoftheart, the code can suppress the logical bitflip error rate by more than one order of magnitude, already with a moderate amount of squeezing. 
Wednesday, March 16, 2022 2:18PM  2:30PM 
N37.00013: Constructing resource theories of nonclassicality for continuous and discretevariable hybrid systems Tomohiro Shitara, Kazuki Koshino Most of the physical systems used for quantum information processing consist of harmonic oscillators, described by continuous variables (CV), and effectively finite dimensional systems, described by discrete variables (DV). We propose a method of constructing a resource theory of nonclassicality for such a hybrid CV+DV system from that for a CV system. A monotone measure for the hybrid system can be obtained by performing an appropriate measurement on the DV system and then taking the average of the monotone measure for the conditional state of the CV system over measurement outcomes. As an example, we analyze the metrological power of a partially decohered Schrödinger's catlike state. Our construction provides a general method of generalizing a convex resource theory defined on a subsystem to an extended system. 
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