Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session T73: Quantum Error Correction Foundations and Theory II |
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Sponsoring Units: DQI Chair: Arne Grimsmo, University of Sydney Room: Room 405 |
Thursday, March 9, 2023 11:30AM - 11:42AM |
T73.00001: Topological order subject to local errors I: a systematic study of error-induced phases Yimu Bao, Ruihua Fan, Ashvin Vishwanath, Ehud Altman Topologically ordered ground states can serve as a quantum memory that is robust against local errors. The encoded information can be protected using a specific quantum error correction algorithm up to a finite error threshold. In this talk, we show the mixed state describing topologically ordered states corrupted by local errors can exhibit distinct phases characterized by its capability to encode information. Remarkably, these error-induced phases cannot be detected by observables in a single-copy density matrix and instead are only probed by nonlinear functions of the density matrix. To characterize such phases, we introduce an errorfield double formalism that identifies the density matrix with a pure state in the double Hilbert space. We further use the path-integral formulation of this pure state and map the error-induced phases to (1+1)D boundary phases of a topologically ordered system. In the concrete examples of the Abelian topological order, the Toric code and the double semion model, subject to incoherent errors, we provide a systematic study of the possible phases. |
Thursday, March 9, 2023 11:42AM - 11:54AM |
T73.00002: Topological order subject to local errors II: diagnostics of error-induced phases Yimu Bao, Ruihua Fan, Ehud Altman, Ashvin Vishwanath Topologically ordered ground states can encode information nonlocally and protect it from local errors up to a finite error threshold. The capability of encoding information defines distinct error-induced phases. In this talk, we propose three complementary information-theoretic diagnostics of such phases intrinsic to the corrupted mixed state: (1) quantum relative entropy between an error-corrupted ground state and excited state; (2) coherent quantum information; (3) topological entanglement negativity. In the example of 2D Toric code with local incoherent errors, three diagnostics simultaneously undergo the transition and consistently probe the error-induced phases. We analytically establish this result by mapping the three diagnostics to observables in a series of 2D classical statistical mechanics models. These observables all detect the ferromagnetic transitions in the classical models and thus exhibit singular behaviors at the same error threshold. We numerically verify our results using Monte-Carlo simulations. |
Thursday, March 9, 2023 11:54AM - 12:06PM |
T73.00003: Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories Arshag Danageozian The recovery of fragile quantum states from decoherence is the basis of building a quantum memory. Many recovery techniques, such as quantum error correction, rely on the prior knowledge of the environment noise parameter to achieve their best performance. However, such parameters are likely to drift in time in the context of implementing long-time quantum memories. This necessitates the use of a ``spectator'' system, which makes an estimate of the noise parameter in real time, then feeds the outcome back to the recovery protocol as a classical side-information. In this article, I present information-theoretic bounds on the performance of such a spectator-based recovery. First, I show that there is a fundamental bound in the performance of any recovery operation, as a function of the entanglement fidelity of the overall dynamics. Then, I provide information-theoretic characterizations of the incomplete knowledge of the noise parameter to the lower bound. Finally, I provide fundamental bounds for multicycle recovery in the form of recurrence inequalities. The latter suggests that incomplete knowledge could be an advantage. These results are illustrated for the approximate [4,1] code of the amplitude-damping channel. |
Thursday, March 9, 2023 12:06PM - 12:18PM |
T73.00004: Quantum Error-Correction Properties of Hyperinvariant Tensor Networks Matthew A Steinberg Hyperinvariant tensor networks were developed in order to provide simulations of Conformal Field-Theoretic states in the context of the AdS/CFT correspondence. We show that the original construction is generalizable using the quantum Fourier transform and k-Uniform maximally-entangled quantum states. Additionally, we show that a hyperinvariant tensor network can be modified as a quantum error-correction code, and that the rate of many example code families are finite. Finally, we report on the practical applicability of these new quantum error-correction code families by performing analytical and numerical threshold studies. Our work is anticipated to stimulate a larger conversation on holographic quantum error correction, as well as simulations of conformal field theory in the context of hyperbolic tensor-network constructions. |
Thursday, March 9, 2023 12:18PM - 12:30PM |
T73.00005: Error-correcting codes for fermionic quantum simulation Yu-An Chen, Yijia Xu, Alexey V Gorshkov We provide ways to simulate fermions by qubits on 2d lattices using $mathbb{Z}_2$ gauge theories (stabilizer codes). By studying the symplectic automorphisms of the Pauli module over the Laurent polynomial ring, we develop a systematic way to increase the code distances of stabilizer codes. We identify a family of stabilizer codes that can be used to simulate fermions with code distances of $d=2,3,4,5,6,7$ such that any $lfloor frac{d-1}{2} floor$-qubit error can be corrected. In particular, we demonstrate three stabilizer codes with code distances of $d=3$, $d=4$, and $d=5$, respectively, with all stabilizers and logical operators shown explicitly. The syndromes for all Pauli errors are provided. Finally, we introduce a syndrome-matching method to compute code distances numerically. |
Thursday, March 9, 2023 12:30PM - 12:42PM |
T73.00006: Measurement-free Quantum Error Correction for Gaussian Noise using Gottesman-Kitaev-Preskill States En-Jui Chang, Ching-Yi Lai Gaussian noise is common in bosonic systems; however, No-Go theorems state that we require non-Gaussian resources such as Gottesman-Kitaev-Preskill (GKP) States to correct Gaussian noise. Here, we bypass the No-Go results by using the phase conjugation to reduce dependence on non-Gaussian states. In particular, we propose a measurement-free bosonic quantum error correction (QEC) scheme and a measurement-free bosonic quantum error distillation (QED) scheme to reduce the number of required GKP states and the required squeezing ability. Furthermore, we can arbitrarily suppress the quadrature noise variance if the squeezing ability is strong. In addition, we show a trade-off between finite squeezing ability and finite number of required GKP states. Thus, we can resource-efficiently correct Gaussian Noise if the squeezing ability is sufficiently large. |
Thursday, March 9, 2023 12:42PM - 12:54PM |
T73.00007: Optimized four-qubit quantum error correcting code for amplitude damping channel Xuanhui Mao, Qian Xu, Liang Jiang Quantum error correction (QEC) is essential for reliable quantum information processing. Targeting a particular error channel, both the encoding and the recovery channel can be optimized through a biconvex optimization to give a high-performance, noise-adapted QEC scheme. We solve the biconvex optimization by the technique of alternating semi-definite programming and identify a new four-qubit code for amplitude damping channel, one major noise in superconducting circuits and a good model for spontaneous emission and energy dissipation. We also construct analytical encoding and recovery channels that are close to the numerically optimized ones. We show that the new code notably outperforms the Leung-Nielsen-Chuang-Yamamoto four-qubit code in terms of the entanglement fidelity over an amplitude damping channel. |
Thursday, March 9, 2023 12:54PM - 1:06PM |
T73.00008: Stability of k-local phases of matter Ali Lavasani, Michael J Gullans, Victor V Albert, Maissam Barkeshli It is well known that Hamiltonians associated to topological phases of matter on Euclidean geometries are stable against local noise, meaning that local noise can not close their gap or lift their ground state degeneracy in the thermodynamic limit. In this work, we relax the assumption about the existence of an underlying Euclidean geometry and ask whether k-local Hamiltonians associated to (not necessarily geometric) qLDPC error correcting codes are robust against local noise, where locality of noise is now defined with respect to the interaction graph. We find that if there exists constants $varepsilon_1,varepsilon_2>0$ such that the size of balls of radius $r$ on the interaction graph is upper bounded by $O(exp(r^{1-varepsilon_1}))$ and balls of radius $O(log(N)^{1+varepsilon_2})$ are locally correctable, then the associated Hamiltonian is stable against local noise. As a non-trivial example, we show that the semi-Hyperbolic surface code Hamiltonian has a finite perturbation strength threshold. |
Thursday, March 9, 2023 1:06PM - 1:18PM |
T73.00009: Continuous quantum error correction on non-Markovian models Juan Garcia Nila We study quantum error correction by a continuous quantum-jump process, comparing performance with a Markovian error model to two different non-Markovian models: an interaction Hamiltonian between the system and an environment qubit coupled to a “cooling” bath—a model that has been shown to have abrupt transitions between Makovian and non-Markovian behavior—and the post-Markovian master equation (PMME). For the PMME, we consider an exponential kernel with underdamped and overdamped behavior. We compare these two non-Markovian error models both to the Markovian case and to each other. |
Thursday, March 9, 2023 1:18PM - 1:30PM |
T73.00010: Quantum phase diagram of the three-dimensional subsystem toric code Yaodong Li, Curt von Keyserlingk, Guanyu Zhu, Tomas Jochym-O'Connor We study the phase diagram of the Hamiltonian of the three-dimensional subsystem toric code (3d STC), as recently constructed by Kubica and Vasmer [arXiv:2106.02621]. In the sector with no stabilizer violations, we show that the effective Hamiltonian describes two copies of decoupled 3d Z2 lattice gauge theories, where the stabilizer constraints act as local gauge invariance. |
Thursday, March 9, 2023 1:30PM - 1:42PM |
T73.00011: Candidate for a passively protected quantum memory in two dimensions Simon Lieu, Yu-Jie Liu, Alexey V Gorshkov An interesting problem in the field of quantum error correction involves finding a physical system that hosts a ``passively-protected quantum memory,'' defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is only known in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model which appears to passively correct against both bit-flip and phase-flip errors in two dimensions: A square lattice composed of photonic ``cat qubits'' coupled via dissipative terms which tend to fix errors locally. Inspired by the presence of two distinct $mathbb{Z}_2$-symmetry-broken phases, our scheme relies on Ising-like dissipators to protect against bit flips and on a driven-dissipative photonic environment to protect against phase flips. We also connect the ability to store the quantum memory to the existence of a non-equilibrium phase in the photonic-Ising model, hinting a perturbative stability under more general noise channels. At the end, we discuss possible ways to realize the photonic-Ising model. |
Thursday, March 9, 2023 1:42PM - 1:54PM |
T73.00012: Evaluating Surface Code Schemes for Neutral Atom Devices Joshua Viszlai, Jonathan M Baker, Frederic T Chong With quantum computers beginning to scale to hundreds of qubits and beyond, error correction is a necessary step to reach the error rates required for large-scale applications. Understanding the performance of various error correcting codes on different hardware technologies will be needed to fully characterize these technologies and their potential. We evaluate surface code operations in the context of a neutral atom architecture using recently realized dual atom species arrays. We propose a novel embedding of surface code qubits into small clusters to exploit unique neutral atom properties such as long-distance interactions and flexible atom positioning which enables transversal CNOT gates. We perform numerical simulations to estimate logical error rates of our design and compare with corresponding lattice surgey operations. To better characterize the performance of the surface code on neutral atom devices, our analysis includes errors stemming from atom loss, reloading, and movement, in addition to typical qubit initialization, gate, and readout errors. |
Thursday, March 9, 2023 1:54PM - 2:06PM |
T73.00013: Algorithmic-level Error Correction: Arbitrarily Accurate Recovery Of Noisy Quantum Signal Processing Andrew K Tan, Yuan Liu, Minh C Tran, Isaac L Chuang The fundamentally stochastic behavior of quantum systems means that error correction and noise mitigation strategies are crucial for quantum computation. Most popular existing methods are fine-grained approaches, providing techniques to make more perfect gates from imperfect ones. Remarkably, modern classical computers almost completely eschew such fine-grained error correction, and in their place employ strategies which correct errors at the level of algorithms and protocols. Here we introduce the concept of algorithm-level error correction (ALEC) for quantum information processing, the defining feature of which is the design of subroutines that allow gate-level errors to cancel; therefore requiring a sophisticated understanding of how gate-level errors propagate to the output of algorithms. We demonstrate the first example ALEC for quantum signal processing (QSP) under the simple noise model of a consistent multiplicative under or over rotation in the signal processing operator by a fixed but unknown amount. We construct a recovery sequence, subject to the same noise, capable of suppressing the error to an arbitrary degree. Importantly, our method fits squarely within the noisy QSP model and does not require any additional resources. Finally, we provide an analysis of the query complexity of our recovery procedure. |
Thursday, March 9, 2023 2:06PM - 2:18PM |
T73.00014: Surface code error correction in a modular quantum computer Denis Sedov, Renyu Wang, Leonid P Pryadko We consider error correction in a quantum computer formed by planar |
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