Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Z40: Towards Fault Tolerance and Realization of Quantum Error CorrectionFocus Recordings Available

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Sponsoring Units: DQI Chair: Kevin Satzinger, Google Room: McCormick Place W196B 
Friday, March 18, 2022 11:30AM  11:42AM 
Z40.00001: Towards Demonstrating Fault Tolerance in Small Circuits Using BaconShor Codes Ariel Shlosberg, Anthony M Polloreno, Graeme Smith Quantum error correction is necessary to perform largescale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily studies of quantum memory, an important first step towards quantum computation, where the objective is to increase the lifetime of the encoded quantum information. Additionally, several works have explored the implementation of logical gates. In this work we study a next step  faulttolerantly implementing quantum circuits. We choose the $[[4, 1, 2]]$ BaconShor subsystem code, which has a particularly simple errordetection circuit. Through both numerics and sitecounting arguments, we compute pseudothresholds for the Pauli error rate $p$ in a depolarizing noise model, below which the encoded circuits outperform the unencoded circuits. These pseudothreshold values are shown to be as high as $p=3\%$ for short circuits, and $p=0.6\%$ for circuits of moderate depth. Additionally, we see that multiple rounds of stabilizer measurements give an improvement over performing a single round at the end. This provides a concrete suggestion for a smallscale faulttolerant demonstration of a quantum algorithm that could be accessible with existing hardware. 
Friday, March 18, 2022 11:42AM  11:54AM 
Z40.00002: High threshold faulttolerant measurementbased quantum computing with biased noise qubits Jahan Claes, Eli Bourassa, Shruti Puri Measurementbased quantum computing (MBQC) is an alternative model of quantum computation that is equivalent to the standard gatebased model and is the preferred approach for several optical quantum computing architectures. In MBQC, a quantum computation is executed by preparing an entangled cluster state and then selectively measuring qubits. MBQC can be made faulttolerant by creating an MBQC computation that executes the standard surface code, an approach known as "foliation." 
Friday, March 18, 2022 11:54AM  12:06PM 
Z40.00003: Faulttolerant logical gates in holographic stabilizer codes are severely restricted Sam Cree We evaluate the usefulness of holographic stabilizer codes for practical purposes by studying their allowed sets of faulttolerantly implementable gates. We treat them as subsystem codes and show that the set of transversally implementable logical operations is contained in the Clifford group for sufficiently localized logical subsystems. As well as proving this concretely for several specific codes, we argue that this restriction naturally arises in any stabilizer subsystem code that comes close to capturing certain properties of holography. We extend these results to approximate encodings, localitypreserving gates, certain codes whose logical algebras have nontrivial centers, and discuss cases where restrictions can be made to other levels of the Clifford hierarchy. A few auxiliary results may also be of interest, including a general definition of entanglement wedge map for any subsystem code, and a thorough classification of different correctability properties for regions in a subsystem code. 
Friday, March 18, 2022 12:06PM  12:18PM 
Z40.00004: Tailored rotated Toric codes for biased noise Qian Xu, Nam Mannucci, Alireza Seif, Aleksander Kubica, Steve T Flammia, Qian Xu, Liang Jiang Quantum error correction lies at the heart of faulttolerant quantum computing. The performance of errorcorrecting codes can be greatly boosted when tailored for realistic types of noise, such as noise biased towards dephasing. We consider a family of generalized rotated toric codes (RTCs) that are defined on a square lattice whose plaquettes represent the XZZX type of check operators, with periodic boundary conditions specified by two (not necessarily orthogonal) periodicity vectors. We show that by adaptively choosing the code layout and tailoring the decoder, the RTCs exhibit high threshold and favorable subthreshold resource scaling in the biasednoise regime. With perfect measurements, the code threshold saturates the hashing bound. Furthermore, the RTCs have a remarkable faulttolerant threshold using practical decoders under a phenomenological noise model. We show that the optimallychosen RTCs, encoding a single logical qubit, can outperform the planar surface codes when using the same amount of qubit resource across different bias regimes, therefore enabling more efficient quantum error correction. 
Friday, March 18, 2022 12:18PM  12:30PM 
Z40.00005: Mitigating leakageinduced correlated errors for superconducting quantum error correction Kevin Miao, Matthew J McEwen, Juan Atalaya, Yu Chen, Andre Petukhov, Alexander N Korotkov, Rami Barends Leakage into noncomputational states threatens the stability of quantum error correction. We present the operation of a multilevel reset protocol [1] in the context of quantum error correction, and discuss how the removal of otherwise longlived leakageinduced correlated errors improves error correction performance. The multilevel reset protocol prepares the qubit ground state with high fidelity after starting in any of the first three excited states, thereby providing an efficient sink for leakage states. By reducing the reset error of this protocol and optimizing the gate duration, we position this gate to be highly compatible with superconducting quantum error correction codes. 
Friday, March 18, 2022 12:30PM  1:06PM 
Z40.00006: Progress with stabilized cat qubits towards hardwareefficient faulttolerance Invited Speaker: Mazyar Mirrahimi Cat qubits are bosonic encodings of quantum information that promise a significant reduction in hardware overhead towards faulttolerance. By confining the state of a quantum harmonic oscillator — a superconducting cavity mode for instance — to the 2D manifold of the Schrödinger cat states, one obtains a biased noise qubit where one error component (bitflips) is exponentially suppressed with the cat size. It is then possible to perform an extensive set of biaspreserving gates paving the way towards a hardwareefficient concatenation with another encoding for suppressing the other error component (phaseflips). So far, two types of confinements have been considered for such cat qubits each with its own advantages: a dissipative confinement based on an engineered nonlinear dissipation, and a Hamiltonian confinement based on a driven Kerr nonlinearity. In this work, we analyze the possibility of combining these two types of confinements and the benefits of such a combination. We also discuss the optimization of the phaseflip error correction process in view of simplifying the experimental requirements to reach the faulttolerance threshold. 
Friday, March 18, 2022 1:06PM  1:18PM 
Z40.00007: Distancefour quantum codes with combined postselection and error correction Prithviraj Prabhu, Ben Reichardt When storing encoded qubits, if single faults can be corrected and double faults postselected against, logical errors only occur due to at least three faults. At current noise rates, having to restart when two errors are detected prevents very longterm storage, but this should not be an issue for lowdepth computations. We consider distancefour, efficient encodings of multiple qubits into a modified planar patch of the 16qubit surface code. We simulate postselected error correction for up to 12000 rounds of parallel stabilizer measurements, and subsequently estimate the cumulative probability of logical error for up to twelve encoded qubits. 
Friday, March 18, 2022 1:18PM  1:30PM 
Z40.00008: Quantum Error Correction in the Surface Code (Part I): Stabilizer Measurements and State Initialization Nathan Lacroix, Sebastian Krinner, Ants Remm, Christoph Hellings, Stefania Lazar, Christian Kraglund Andersen, Francois Swiadek, Johannes Herrmann, Graham J Norris, Elie Genois, Agustin Di Paolo, Catherine Leroux, Markus Müller, Alexandre Blais, Christopher Eichler, Andreas Wallraff Quantum error correction codes offer ways to compensate errors in quantum systems to a level which enables solving classically intractable problems. The surface code [A. G. Fowler, et al., Phys. Rev. A 86, 032324 (2012)] is one of the major candidates for a scalable quantum computing architecture because of its high tolerance to errors and its simple 2Dgrid qubitarrangement. In this talk, we discuss our progress towards the experimental realization of a distance3 surface code on a 17qubit superconducting qubit device. We verify the performance of essential components of the surface code including the realization of weight2 stabilizers and weight4 stabilizers, and the initialization of logicalqubit states. We discuss which type of errors are most prominent and whether or not they are correctable. 
Friday, March 18, 2022 1:30PM  1:42PM 
Z40.00009: Quantum Error Correction in the Surface Code (Part II): Logical State Preservation Experiments Sebastian Krinner, Nathan Lacroix, Ants Remm, Christoph Hellings, Stefania Lazar, Christian Kraglund Andersen, Francois Swiadek, Johannes Herrmann, Graham J Norris, Elie Genois, Agustin Di Paolo, Catherine Leroux, Markus Muller, Alexandre Blais, Christopher Eichler, Andreas Wallraff Quantum error correction is an approach for preserving quantum information in the presence of decoherence and control errors. The surface code is unique in its high tolerance to errors. However, so far only error detection has been demonstrated in the surface code. Here, we report on progress towards realizing a distance3 surface code, capable of correcting any singlequbit error on its 17 physical qubit constituents. We repeatedly measure all stabilizers of the code, extract bit and phaseflip error syndromes, and characterize the overall performance in terms of the probability with which errors occur. Furthermore, we present a leakage detection scheme, allowing us to identify sequences in which any of the qubits was measured in a leakage state. Error correction is expected to be an essential ingredient in the realization of faulttolerant universal quantum information processing. 
Friday, March 18, 2022 1:42PM  1:54PM 
Z40.00010: Quantum Error Correction in the Surface Code (Part III): Realistic Simulation of the Experimental Code Performance Elie Genois, Agustin Di Paolo, Catherine Leroux, Sebastian Krinner, Nathan Lacroix, Ants Remm, Christoph Hellings, Stefania Lazar, Christian Kraglund Andersen, Francois Swiadek, Johannes Herrmann, Graham J Norris, Markus Muller, Christopher Eichler, Andreas Wallraff, Alexandre Blais The surface code is a prominent candidate for the realization of quantum error correction with superconducting qubits due to its suitable 2Dgrid qubitarrangement and its relatively high error tolerance. To guide efforts in improving the code ability to preserve logical states, it is necessary to perform realistic modeling of the system based on experimentally informative device characteristics such as individual qubit coherence times, crossKerr interactions, and gate fidelities. Here, we solve the complete timeevolution of a 17qubit device implementing a distance3 surface code using a Monte Carlo wave function approach. We also implement an effective model that captures all the desired dynamics while significantly reducing the computational requirements. Using this approach, we analyze the expected code performance as a function of experimentally relevant qubit parameters and their nonuniform distribution on the device. We also investigate the optimal parameter improvements needed to enhance logical state preservation and to reach the threshold. 
Friday, March 18, 2022 1:54PM  2:06PM 
Z40.00011: Faulttolerance for a universal nonAbelian topological quantum computer at finite temperature Alexis Schotte, Lander Burgelman, Guanyu Zhu We study a quantum memory constructed as a twodimensional phenomenological model of Fibonacci anyons on a torus, in the presence of thermal noise represented by paircreation processes and measurement errors. The correction procedure is based on the cellular automaton decoders originating in the works of Gács and Harrington. Through numerical simulations, we obtain a faulttolerant threshold for this code and hence provide strong evidence for the existence of faulttolerant universal nonAbelian codes. 
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