Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session R27: Quantum Error Correction Theory and Experiment IIFocus

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Sponsoring Units: DQI Chair: Christopher Chamberland, IBM Thomas J Watson Research center Room: BCEC 160C 
Thursday, March 7, 2019 8:00AM  8:36AM 
R27.00001: The boundaries and topological defects of the color code Invited Speaker: Markus Kesselring We give a thorough exploration of the color code phase to find all of its boundaries and domain walls. 
Thursday, March 7, 2019 8:36AM  8:48AM 
R27.00002: Connecting discrete and continuous variable quantum codes Linshu Li, Victor Albert, Kyungjoo Noh, Liang Jiang We consider the connection between discrete variable (DV) codes based on qubit/qudit systems and continuous variable (CV) codes based on bosonic systems. Specifically, we study generalization of quantum parity codes (QPCs) that allows multiple excitations in each mode and fills in the gap between DV quantum parity codes and singlemode binomial codes. The connection offers an alternative perspective to understand these two types of quantum codes, and can hopefully shed light upon generic connections between the two regimes. 
Thursday, March 7, 2019 8:48AM  9:00AM 
R27.00003: Braiding via symmetry transformation: universal transversal gate set for topological codes Guanyu Zhu, Maissam Barkeshli Recent studies of the relationship between symmetry and topology have stimulated a series of new discoveries. A recently developed theory of ``quantum origami" revealed the deep relation between mapping glass group, topological symmetry and transversal gates in faulttolerant quantum computation (arXiv:1711.05752). Motivated by this finding, here we show that elements in the spherical braid group with n punctures (anyons) can be completely generated with two isometries related to different rotational symmetries of the punctured surface. By folding the surface to 2n layers connected with gapped boundaries, we acquire a ``folded fan" model for quantum computers in reminiscence of the ``pancake" model consisting of multiple disconnected layers. The two isometries in the unfolded manifold can be mapped into onsite symmetry in the folded fan, corresponding to faulttolerant transversal logical gates which can be used to perform quantum computation. For the nonabelian FibonacciTuraevViro code, these transversal gates form a universal set, along with a constantdepth circuit switching the symmetry. In contrast to the code switching approach to circumvent the EastinKnill nogo theorem, we achieve the circumvention using a symmetry switching approach with constant time overhead. 
Thursday, March 7, 2019 9:00AM  9:12AM 
R27.00004: Depth reduction for quantum Clifford circuits through Pauli measurements YiCong Zheng, ChingYi Lai, Todd Brun, LeongChuan Kwek Clifford circuits play an important role in quantum computation. Gottesman and Chuang proposed a gate teleportation protocol so that a quantum circuit can be implemented by the teleportation circuit with specific ancillary qubits. In particular, an nqubit Clifford circuit U can be implemented by preparing an ancillary stabilizer state $I \otimes U \Psi\rightangle^{\otimes n}$^{ }for teleportation and doing a Pauli correction conditioned on the measurement. In this paper, we provide an alternative procedure to implement a Clifford circuit through Pauli measurements, by preparing O(1) ancillas that are CalderbankShorSteane (CSS) stabilizer states. That is to say, O(1) CSS states are sufficient to implement any Clifford circuit. As an application to faulttolerant quantum computation, any Clifford circuit can be implemented by O(1) steps of Steane syndrome extraction if clean CSS stabilizer states are available. 
Thursday, March 7, 2019 9:12AM  9:24AM 
R27.00005: A Systematic Construction of Clifford Perfect Tensors Mengzhen Zhang, Liang Jiang Perfect tensors are essential building blocks for holographic quantum states, which provide an intriguing platform of combining quantum information theory and physics of spacetime. Network of perfect tensors generated from stabilizer codes can be efficiently analyzed. To our knowledge, the full classification of such perfect tensors is still unknown. In this work, we demonstrate a systematic approach of constructing a large class of perfect tensors, with some existing construction schemes as special cases. Moreover, we investigate their operator generalization to continuous variable systems and identify the differences between the construction schemes in discrete variable and continuous variable systems. 
Thursday, March 7, 2019 9:24AM  9:36AM 
R27.00006: CalderbankSteaneShor Holographic Quantum Error Correcting Codes Thomas Stace We expand the class of holographic quantum error correcting codes by developing the notion of block perfect tensors, a wider class that includes previously defined perfect tensors. The relaxation of this constraint opens up a range of other holographic codes. We demonstrate this by introducing the selfdual CSS heptagon holographic code, based on the 7qubit Steane code. Finally we show promising thresholds for the erasure channel by applying a straightforward, optimal erasure decoder to the heptagon code and benchmark it against existing holographic codes. 
Thursday, March 7, 2019 9:36AM  9:48AM 
R27.00007: Good quantum subsystem codes in 2dimensions Theodore Yoder Given any two classical codes with parameters [n1, k, d1] and [n2, k, d2], we show how to construct a quantum subsystem code in 2dimensions with parameters [[N, K, D]] with N <= 2 n1 n2, K=k, and D = min(d1, d2). These quantum codes are in the class of generalized BaconShor codes introduced by Bravyi. Then, using constructions of good families of classical expander codes, we give constructive families of good quantum subsystem codes in 2dimensions, that is, families saturating Bravyi's bound KD = O(N). While such codes were known to exist via counting arguments, this is the first explicit construction of them. Additionally, we provide a lineartime decoder for these subsystem codes. 
Thursday, March 7, 2019 9:48AM  10:00AM 
R27.00008: Dynamically protected qubit based on highimpedance superconducting circuits Phillipe CampagneIbarcq, Mazyar Mirrahimi, Michel H. Devoret Quantum information encoded in a physical system is submitted to decoherence induced by interaction with uncontrolled degrees of freedom in the environment of the system. However, these interactions are local in the sense that they only induce continuous evolutions of the system in its phase space. One can thus protect quantum information by storing it “nonlocally”, i.e. in the correlations between distant phase space regions. Here, we propose to combine a high impedance superconducting resonator with a Josephson junction whose energy is stroboscopically modulated. This system simulates the dynamics of a LC oscillator combined with a Josephson junction and a Quantum Phase Slip element. In presence of these two nonlocally acting noiseless elements, the ground states are degenerate nonlocal grid states of the resonator and are expected to provide a fully protected logical qubit. 
Thursday, March 7, 2019 10:00AM  10:12AM 
R27.00009: Natural quantum errorcorrection in manybody dynamics implies stability of volumelaw entangled states against projective measurements Soonwon Choi, Yimu Bao, Xiaoliang Qi, Ehud Altman In a generic isolated quantum manybody system, entanglement entropy of any subsystem grows linearly in time until saturated to a value proportional to its volume. Random projective measurements, however, can severely affect such dynamics by disentangling the measured parts from the rest of the system. In this work, we investigate this interplay between entangling dynamics and projective measurements from the perspective of quantum information theory. We show that volumelaw entangled states can remain stable even when a substantial fraction of the system is measured in every time unit. Our key observation, based on the quantum decoupling theorem, is that a sufficiently scrambling unitary can hide quantum correlations in a nonlocal form such that local measurements cannot decrease entanglement. Such dynamics is generic and can be explicitly demonstrated in a toy model involving random local unitary gates acting on a chain of qubit clusters followed by probabilistic measurements. Our work suggests that the stability of the volumelaw entangling phase originates from the effective quantum error correcting feature of scrambling dynamics, which protects quantum entanglement from the noisy environment. 
Thursday, March 7, 2019 10:12AM  10:24AM 
R27.00010: Quantum simulation of fermions: geometric locality and error mitigation Zhang Jiang, Jarrod McClean, Ryan Babbush, Hartmut Neven We consider mappings from fermionic systems to spin systems that preserve geometric locality in more than one spatial dimension. Such mappings are useful for simulating lattice fermion models (e.g., the Hubbard model) on a quantum computer. Localitypreserving mappings avoid the overhead associated with nonlocal parity terms in conventional mappings, such as the JordanWigner transformation. As a result, they often provide solutions with lower circuit depth. Moreover, localitypreserving mappings are likely to be more resistant to qubit noises by avoiding encoding the fermionic correlation functions in nonlocal Pauli operators. Here, we discuss how to detect/correct singlequbit errors with two known localitypreserving maps. We then go beyond that by constructing new mappings with better error detecting/correcting performance than the existing ones. Our methods do no introduce extra physical qubits beyond those required by the original mappings. Being able to detect/correct errors in initial state preparations is crucial to the success of nearterm quantum algorithms such as the variational quantum eigensolver. Our results also provide systematic methods to constructing quantum errordetecting/correcting codes with Majorana fermion operators. 
Thursday, March 7, 2019 10:24AM  10:36AM 
R27.00011: Approximate stabilizer rank and improved weak simulation of Clifforddominated circuits for qudits Yifei Huang, Peter J Love Bravyi and Gosset recently gave classical simulation algorithms for quantum circuits dominated by Clifford operations. These algorithms scale exponentially with the number of Tgate in the circuit, but polynomially in the number of qubits and Clifford operations. Here we extend their algorithm to qudits of odd prime dimensions. We generalize their approximate stabilizer rank method for weak simulation to qudits and obtain the scaling of the approximate stabilizer rank with the number of singlequdit magic states. We also relate the canonical form of qudit stabilizer states to Gauss sum evaluations. We give an O(n^{3}) algorithm to calculating the inner product of two nqudit stabilizer states. 
Thursday, March 7, 2019 10:36AM  10:48AM 
R27.00012: Direct Measurement of a Very Small Logical Qubit's Observables Nicholas Materise, Eliot Kapit We extend recent longitudinal readout schemes to the very small logical qubit (VSLQ) architecture. The two photon Xoperators in the VSLQ are read out by borrowing principles from the longitudinal approach, although the operator itself is transverse. Our results follow those of previous studies of coupling between a single cavity mode and superconducting qubit, where high measurement fidelities are realized for shorter measurement pulses compared to dispersive readout. In the interest of minimizing microwave circuit resources per VSLQ unit cell, we have investigated the use of the higher modes of the same resonator for error correction. We demonstrate use of the fundamental resonator mode for fast readout of an inductively coupled VSLQ with improved fidelities compared to the dispersive case. By measuring along the Xaxis, we benefit from the added protection of the passive error correction during readout, reducing potential state preparation and measurement error. 
Thursday, March 7, 2019 10:48AM  11:00AM 
R27.00013: Graph convolutional network for topological stabilizer codes Yasunari Suzuki, Amarsanaa Davaasuren, Keisuke Fujii, Masato Koashi, Yasunobu Nakamura As quantum computers are close to realization, a fast, versatile, and highperformance decoder for quantum error correction is demanded. In recent years, several machinelearningbased decoders have been proposed, and are expected to enable fast decoding with nearoptimal performance for an arbitrary topological code. Since local Pauli errors only flip local syndromes in topological codes, a convolutional neural network is used for explicitly extracting local features in topological codes. However, the filter shapes for the convolution only match to the qubit allocation of [2d^22d+1, 1, d]surface code. It has been not known how we can naturally extract local features of other topological codes. 
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