Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 510)
Virtual (March 2022); Time Zone: Pacific Time
Session N64: Quantum Error Correction Foundations and Theory IFocus

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Sponsoring Units: DQI Chair: Michael Vasmer, Perimeter Inst for Theo Phys Room: Room 415 
Wednesday, March 8, 2023 11:30AM  11:42AM 
N64.00001: Entanglement Purification with Quantum LDPC Codes and Iterative Decoding Narayanan Rengaswamy, Nithin Raveendran, Ankur Raina, Bane Vasic Recent constructions of quantum LDPC (QLDPC) codes provide optimal scaling of the code parameters, enabling faulttolerant quantum systems with minimal resource overhead. However, the hardware path to longrangeinteractiondemanding QLDPC codes is likely a challenging one. Given the practical difficulty in building a monolithic architecture for quantum systems, such as computers, based on optimal QLDPC codes, it is worth considering a distributed implementation of such codes over a network of interconnected mediumsized quantum processors. In such a setting, all syndrome measurements and logical operations must be performed through the use of highfidelity shared entangled states between the processing nodes. Since probabilistic manyto1 distillation schemes for purifying entanglement are inefficient, we investigate quantum error correction based entanglement purification in this work. Specifically, we employ QLDPC codes to distill GHZ states, as the resulting highfidelity logical GHZ states can interact directly with the code used to perform distributed quantum computing (DQC), e.g. for faulttolerant Steane syndrome extraction. We use the minsum decoder for distilling 3qubit GHZ states using a rate 0.118 family of lifted product QLDPC codes and obtain a threshold of 10.7% under depolarizing noise. Our results can be extended to larger size GHZ states as well. 
Wednesday, March 8, 2023 11:42AM  11:54AM 
N64.00002: Quantum twoblock nonabelian group codes Hsiang Ku Lin, Leonid P Pryadko We study numerically and analytically a class of quantum twoblock CSS codes with generator matrices H_{X} = (A,B), H_{Z} = (B^{T},A^{T}), where commuting square matrices A, B of size m × m are associated with elements of the group algebra F_{2}G, and G is a group of order m. These codes are the shortest liftedproduct codes [1] that can be obtained from the group G. Also, they contain all generalizedbicycle (GB) codes obtained when G is the (abelian) group of cyclic permutations. The twoblock group code (TBGC) ansatz is of interest as a method to construct short quantum LDPC codes without the upper distance bound of more regular GB codes [2]. Analytically, we show that nontrivial TBGCs with stabilizer generators of weight w = 4 can be always expressed as direct sums of GB codes. We also compute optimal parameters of TBGCs associated with nonabelian groups of orders m ≤ 50 by exhaustive enumeration of all such codes. 
Wednesday, March 8, 2023 11:54AM  12:30PM 
N64.00003: ConstantOverhead Quantum Error Correction with Thin Planar Connectivity Invited Speaker: Nicolas G Delfosse The surface code is the most popular quantum error correction code for the design of largescale faulttolerant quantum computers. However, it leads to a huge overhead because each logical qubit is encoded into hundreds of physical qubits. In this talk, I will discuss our proposal for a low overhead quantum error correction scheme based on quantum LDPC codes and a few layers of longrange connections. 
Wednesday, March 8, 2023 12:30PM  12:42PM 
N64.00004: Spacetime topological defect networks and floquet codes Dominic J Williamson I propose an extension of the topological defect network construction from groundstate wave functions to spacetime partition functions as a unifying framework to describe static fracton topological orders and dynamical topological floquet codes. 
Wednesday, March 8, 2023 12:42PM  12:54PM 
N64.00005: Qutritbased topological subsystem codes Joseph M Sullivan, Scott Jensen, Tyler D Ellison We introduce a topological subsystem code based on a generalization of Kitaev's honeycomb model to qutrits. The code exhibits a number of beneficial properties, including a realization on a lowdegree graph in a planar geometry, twobody checks, and high biasednoise error thresholds. We further demonstrate that topological twist defects can be constructed by twobody measurements, and the full Clifford group can be implemented fault tolerantly by braiding twist defects. Through a mapping to a statistical mechanical model, we compute the optimal error thresholds of the subsystem code. We also establish a mapping of the error thresholds to those of a Z_{3} surface code with anisotropic pure Pauli X noise. 
Wednesday, March 8, 2023 12:54PM  1:06PM 
N64.00006: Pauli topological subsystem codes from Abelian anyon theories Tyler D Ellison, YuAn Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, Dominic J Williamson We construct Pauli topological subsystem codes characterized by arbitrary twodimensional Abelian anyon theories  this includes nonmodular anyon theories and those without a Lagrangian subgroup. We exemplify the construction with topological subsystem codes based on the nonmodular Z_{4}^{(1)} anyon theory and the chiral semion theory, both of which cannot be captured by topological stabilizer codes. The construction proceeds by "gauging out" certain anyon types of a topological stabilizer code. This amounts to defining a gauge group generated by the stabilizer group of the topological stabilizer code and a set of anyonic string operators for the anyon types that are gauged out. The resulting topological subsystem code is characterized by an anyon theory that is a proper subset of the anyons of the topological stabilizer code. We thereby show that every Abelian anyon theory is a subtheory of a stack of toric codes and a certain family of twisted quantum doubles that generalize the double semion anyon theory. Our work thus extends the classification of twodimensional Pauli topological subsystem codes to systems of compositedimensional qudits and shows that the classification is at least as rich as that of twodimensional Abelian anyon theories. We further prove a number of general statements about the logical operators of translation invariant topological subsystem codes and define their associated anyon theories in terms of higherform symmetries. 
Wednesday, March 8, 2023 1:06PM  1:18PM 
N64.00007: Quantum error correction in a timedependent transverse field Ising model Yifan Hong, Jeremy T Young, Adam M Kaufman, Andrew Lucas We describe a simple quantum error correcting code built out of a timedependent transverse field Ising model. The code is similar to a repetition code, but has two advantages: an Nqubit code can be implemented with a finitedepth spatially local unitary circuit, and it can subsequently protect against both X and Z errors if N≥10 is even. We propose an implementation of this code with 10 ultracold Rydberg atoms in optical tweezers, along with further generalizations of the code. 
Wednesday, March 8, 2023 1:18PM  1:30PM 
N64.00008: Homomorphic Logical Measurements Shilin Huang, Tomas JochymO'Connor, Theodore J Yoder Shor and Steane ancilla are two wellknown methods for faulttolerant logical measurements, 
Wednesday, March 8, 2023 1:30PM  1:42PM 
N64.00009: Hyperbolic Floquet Quantum Error Correcting Codes Ali Fahimniya, Sheryl Mathew, Hossein Dehghani, Kishor Bharti, Alicia Kollar, Alexey V Gorshkov, Michael J Gullans Largescale universal quantum computation requires protecting quantum information against quantum noise which can be performed using quantum errorcorrecting codes. Recently, Hastings and Haah [1] introduced a faulttolerant dynamical subsystem code on a honeycomb lattice using twoqubit check measurements. Despite having zero logical qubits when viewed as a static subsystem code, the sequence of twoqubit measurements protects two dynamical logical qubits. On the other hand, hyperbolic surface codes are known as a generalization of toric code on a negatively curved manifold. Since the genus of such manifolds increases with the system size, it has been demonstrated that these codes possess a constant encoding rate. In this work, we introduce hyperbolic Floquet codes, where twoqubit check operators are measured in a periodic sequence. Using this measurement scheme, first, we show that the number of dynamically protected logical qubits grows with the system size. Next, we numerically demonstrate the existence of a threshold for the error rate of physical qubits that our code can protect against. Finally, we propose a planar version of these codes with open boundary conditions which are experimentally more feasible to be realized using current platforms. 
Wednesday, March 8, 2023 1:42PM  1:54PM 
N64.00010: Quantum Perspectives on the Clifford Group William R Munizzi, Cynthia Keeler, Jason Pollack The Clifford group, a multiplicative group generated by the Hadamard, phase, and CNOT gates, defines a set of unitary operations which normalize the Pauli group. The finite structure of this group promotes a graphtheoretic description, known as a Cayley graph, with vertices indicating each group element and edges representing the particular generators that transform Clifford operations into each other. Acting with the Clifford group on a computational basis state generates the complete set of stabilizer states, the set of all nqubit quantum states invariant under some 2^{n}element subset of the nqubit Pauli group. Stabilizer states and stabilizer circuits, those quantum circuits exclusively composed of Clifford operations and stabilizer measurements, are famously known to be simulable on a classical computer. The Hilbert space of nqubit stabilizer states also admits a natural description as a mathematical graph, known as a reachability graph, which can be constructed as a quotient space of the overall Cayley graph after identifying group elements which act trivially on each stabilizer state. When considering the action of some Clifford subgroup this quotient space separates into multiple disconnected subgraphs, which we term restricted graphs. We introduce this definition of reachability graphs as Cayley graph quotient spaces and demonstrate how operator identities on stabilizer states completely describe the identifications that produce restricted graphs. Motivated by an understanding of stabilizer state entropies, we provide a complete description of the Clifford subgroup generated by the Hadamard and CNOT gates acting on any pair of qubits in an nqubit system, and present some physical insights gained from studying the associated set of restricted graphs. 
Wednesday, March 8, 2023 1:54PM  2:06PM 
N64.00011: Multi spin Clifford code for higher order angular momentum errors in spin systems Sivaprasad T Omanakuttan, Jonathan A Gross The physical symmetries of a system play a central role in quantum error correction. In this work we encode a qubit in a collection of systems with angularmomentum symmetry (spins), extending the tools developed in [1] for single large spins. By considering large spins present in atomic systems and focusing on their collective symmetric subspace, we develop new codes with octahedral symmetry capable of correcting errors up to second order in angularmomentum operators. These errors include the most physically relevant noise sources such as microwave control errors and optical pumping. We additionally explore new qubit codes that exhibit distance scaling commensurate with the surface code while permitting transversal singlequbit Clifford operations. 
Wednesday, March 8, 2023 2:06PM  2:18PM 
N64.00012: Preparing the XY surface code with high threshold under biased noise PeiKai Tsai, Yue Wu, Shruti Puri Tailoring quantum surface codes by local Clifford deformation can increase their thresholds under biased noise. A specific example is the XYsurface code, which reduces to a repetition code under pure dephasing noise and achieves code capacity threshold of 50%. However, it is crucial to analyze the performance of the code during logical operations such as state preparation. In the standard approach, a logical X (or Y) state is prepared by initializing each physical qubit in the +> (or +i>) state, followed by measuring all stabilizers. However, this technique breaks the underlying symmetry of the XY code under pure dephasing noise, which limits the logical state preparation threshold. In this work, we propose a new logical initialization protocol which maintains the effectiveness of the XY code against dephasing noise. In this protocol, physical qubits are first locally entangled into two or fourbody Bell states, following which all the stabilizers are measured. We prove that in this procedure dephasing errors can be decoded as a repetition code, which guarantees a 50% state preparation threshold. Our analysis is supported by numerical simulations, which also show an overall improvement in threshold when dephasing errors is accompanied by small amount of bitflip noise. 
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