Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session A31: Theory of Quantum Error CorrectionFocus Live
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Sponsoring Units: DQI Chair: Shruti Puri, Yale University |
Monday, March 15, 2021 8:00AM - 8:12AM Live |
A31.00001: The surface code on the rhombic dodecahedron Andrew Landahl I present a jaunty little [[14, 3, 3]] non-CSS surface code that can be |
Monday, March 15, 2021 8:12AM - 8:24AM Live |
A31.00002: Continuous-variable error correction for general Gaussian noises Jing Wu, Quntao Zhuang Quantum error correction mainly concerns the protection of quantum information encoded in discrete-variable systems modelled as qubits. However, many applications, e.g. quantum sensing and communication, require continuous-variable systems modelled as oscillators. Recently, Gottesman-Kitaev-Preskill (GKP) states are shown to enable the protection of continuous-variable systems, via encoding a single oscillator into multiple oscillators. Here we extend the study to multiple oscillators under independent but inhomogeneous Gaussian noises. To get the minimum reduced noise, we optimize over the code structure in terms of the ordering of the multiple oscillators. Asymptotic analyses and numerical simulations show that both the GKP-two-mode-squeezing code and GKP-squeezing-repetition code can reduce the noise standard deviation to the order of the geometric mean of the standard deviations of the heterogeneous noises, under global optimization of the codes. Our approach applies to general correlated Gaussian noises, which can be unraveled to independent Gaussian noises through Gaussian operations. As an example, we apply our strategies to memory channels. |
Monday, March 15, 2021 8:24AM - 8:36AM Live |
A31.00003: Quantum LDPC codes from SAT instances Maxime Tremblay, Stefanos Kourtis Quantum computing is promising a big leap in computing power. However, building a scalable quantum computer is not an easy task. One major limitation is the imperfect nature of qubits and the presence of noise in the system. To circumvent this problem, we need to design fault tolerant architectures for quantum computers. However, as of today, the most studied fault tolerant protocols are based upon surface codes and topological codes which do not scale well. |
Monday, March 15, 2021 8:36AM - 8:48AM Live |
A31.00004: Statistical Mechanics of Quantum Error-Correcting Codes Yaodong Li, Matthew P A Fisher We study stabilizer quantum error-correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension. Building upon a general formula relating the error-susceptibility of a subregion to its entanglement properties, and a previously established mapping between entanglement entropies and domain wall free energies of an underlying spin model, we propose a statistical mechanical description of the QECC in terms of "entanglement domain walls". Such domain walls are most easily accounted for by capillary-wave theory of liquid-gas interfaces, which we use as an illustrative tool. We show that the information-theoretic decoupling criterion corresponds to a geometric decoupling of domain walls when transverse fluctuations dominate over the surface tension. It follows that the "contiguous code distance" diverges with the system size, and a finite code rate is protected against local undetectable errors. We support these correspondences with numerical evidences, where we find capillary-wave theory describes many qualitative features of the QECC; we also discuss when and why it fails to do so. |
Monday, March 15, 2021 8:48AM - 9:00AM Live |
A31.00005: Non-abelian topological error correction with Turaev-Viro codes and the estimation of the error threshold Alexis Schotte, Guanyu Zhu, Lander Burgelman, Frank Verstraete Non-abelian topological codes are of great interest, since they provide the opportunity to achieve a universal fault-tolerant logical gate set through braiding, without the need for magic state distillation. So far results concerning thresholds of such ECCs have been obtained exclusively using phenomenological anyon models. Here, we present the first error-correction threshold for a microscopic model supporting anyons of which the braid group representation is universal. |
Monday, March 15, 2021 9:00AM - 9:36AM Live |
A31.00006: Conservation laws and quantum error correction Invited Speaker: Benjamin Brown Quantum error-correcting codes are essential to the realisation of scalable quantum computation. They defend encoded quantum information by making stabilizer measurements to identify the occurrence of errors. A quantum error-correcting code depends on a classical decoding algorithm that uses the outcomes of stabilizer measurements to determine the error that needs to be repaired. Likewise, the design of a decoding algorithm depends on the underlying physics of the quantum error-correcting code that it needs to decode. The surface code, for instance, can make use of the minimum-weight perfect-matching decoding algorithm to pair the defects that are measured by its stabilizers due to its underlying charge parity conservation symmetry. In this talk I will argue that this perspective on decoding gives us a unifying principle to design decoding algorithms for exotic codes, as well as new decoding algorithms that are specialised to the noise that a code will experience. I will describe new decoders for exotic three-dimensional fracton codes, as well as classical fractal codes we have designed using these principles. I will also discuss how the symmetries of a code change if we focus on restricted noise models, and how we have leveraged this observation to design high-threshold decoders for biased noise models. |
Monday, March 15, 2021 9:36AM - 9:48AM Live |
A31.00007: Quantum error correction with bosonic-Bacon-Shor codes Stefanus Tanuarta, Arne Grimsmo In this talk, we present numerical results for error correction where single-mode bosonic codes are concatenated with a Bacon-Shor code. We compare different bosonic codes, including cat- and binomial codes, to conventional two-level systems at the ground level. Break-even points and logical error rates are computed for small codes and a circuit level noise model that includes photon loss and dephasing. |
Monday, March 15, 2021 9:48AM - 10:00AM Live |
A31.00008: Master Equations for Error-Suppressed Hamiltonian Quantum Computing Humberto Munoz-Bauza, Daniel Lidar Error suppression and coherent diabatic evolution have emerged as important features of Hamiltonian quantum computation that are likely to be necessary for quantum speedup. We derive Markovian master equations for systems encoded with an error detecting code protecting the code space against interactions with the environment. This protection is enforced with a penalty Hamiltonian consisting of the generators of the stabilizer group of the error detecting code, splitting the Hilbert space into stabilizer subspaces. When the gap of the penalty Hamiltonian is larger than the frequencies of the encoded system Hamiltonian as well as the inverse of the bath correlation time, transitions out of the code space can be expressed in Davies-Lindblad form, while logical errors that occur in transitions across degenerate stabilizer subspaces can be treated with coarse graining for diabatic quantum annealing. |
Monday, March 15, 2021 10:00AM - 10:12AM Live |
A31.00009: Minimal distances for certain quantum product codes and tensor products of chain complexes Weilei Zeng, Leonid P Pryadko We use a map to quantum error-correcting codes and a subspace projection to get lower bounds for minimal homological distances in a tensor product of two chain complexes of vector spaces over a finite field. Homology groups of such a complex are described by the Künneth theorem. We give an explicit expression for the distances when one of the complexes is a linear map between two spaces. The codes in the construction, subsystem product codes and their gauge-fixed variants, generalize several known families of quantum error-correcting codes. |
Monday, March 15, 2021 10:12AM - 10:24AM Live |
A31.00010: Autonomous Stabilization of Finite-energy Gottesman-Kitaev-Preskill States Baptiste Royer, Shraddha Singh, Steven Girvin Bosonic error-correction codes are emerging as an attractive and hardware-efficient alternative to qubit-based encodings. In particular, the Gottesman-Kitaev-Preskill (GKP) code has been shown in simulations to protect logical information better than other known bosonic codes against typical error channels. However, in their ideal form, GKP codewords contain an infinite amount of energy, making the stabilization of their realistic, finite-energy version challenging. More specifically, stabilization strategies for GKP states need to take into account the amount of energy injected at each error-correction step. |
Monday, March 15, 2021 10:24AM - 10:36AM Live |
A31.00011: Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead Oscar Higgott, Nikolas P Breuckmann We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained, and we introduce a new method for decoding which uses this information to improve performance. Applied to the subsystem toric code with three-qubit check operators, we increase the threshold under circuit-level depolarising noise from 0.67% to 0.81%. The threshold increases further under a circuit-level noise model with small finite bias, up to 2.22% for infinite bias. Furthermore, we construct families of finite-rate subsystem LDPC codes with three-qubit check operators and optimal-depth parity-check measurement schedules. To the best of our knowledge, these finite-rate subsystem codes outperform all known codes at circuit-level depolarising error rates as high as 0.2%, where they have a qubit overhead that is 4.3× lower than the most efficient version of the surface code and 5.1× lower than the subsystem toric code. Their threshold and pseudo-threshold exceeds p=0.42% for circuit-level depolarising noise, increasing to p=2.4% under infinite bias using gauge fixing. |
Monday, March 15, 2021 10:36AM - 10:48AM Live |
A31.00012: Topological quantum error correction in fractal dimensions I: code construction and logical gates Guanyu Zhu, Arpit Dua, Tomas Jochym-O'Connor Topological error correcting codes and topological orders in integer spatial dimensions have been widely studied in the fields of quantum information and condensed matter physics. In this work, we consider topological codes defined on a wide class of fractal lattices, which can be considered as a usual d-dimensional lattice with holes at all length scales and correspond to fractal (Hausdorff) dimension $d-\delta$ ($\delta>0$). For simplicity, we call these lattices d-dimensional fractal lattices. We first prove a no-go theorem that topological orders on 2D fractals with Hausdorff dimension $2-\delta$ do not exist in nature. We further construct topological codes on three and higher-dimensional fractals. An important application of these codes is to reduce the space overhead for implementing non-Clifford logical gates. Based on the results of Bravyi and Koenig, there is a trade-off between dimensionality and universality in topological stabilizer codes, i.e., only higher-dimensional codes can implement fault-tolerant logical gates in higher levels of the Clifford hierarchy via local constant depth circuits. By constructing fractal topological codes, we can lower the Hausdorff dimension of the codes and hence reduce the number of qubits needed for a given logical non-Clifford gate. |
Monday, March 15, 2021 10:48AM - 11:00AM Live |
A31.00013: Topological quantum error correction in fractal dimensions II: decoding and threshold estimation Arpit Dua, Guanyu Zhu, Tomas Jochym-O'Connor We investigate quantum error correction with topological codes on 3D fractal lattices with Hausdorff dimension 3-δ. We show concrete decoding schemes for correcting the bit-flip and phase errors. For the phase errors, we have developed both a minimum-weight-perfect-matching decoder and a cluster decoder on the 3D fractal lattice. For the bit-flip errors, we have developed a particular type of local cellular-automaton decoder, the sweep decoder, for the 3D fractal code. We also show that bit-flip errors can be corrected in a single shot. For all these decoders, we have numerically estimated the corresponding error threshold using Monte Carlo simulations. |
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