Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session K44: Quantum Error Correction, Control & Simulation |
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Sponsoring Units: GQI Chair: Todd Brun, University of Southern California Room: 347 |
Wednesday, March 16, 2016 8:00AM - 8:12AM |
K44.00001: Hamiltonian Engineering for High Fidelity Quantum Operations Hugo Ribeiro, Alexandre Baksic, Aashish Clerk High-fidelity gates and operations are crucial to almost every aspect of quantum information processing. In recent experiments~[1], fidelity is mostly limited by unwanted couplings with states living out of the logical subspace. This results in both leakage and phase errors. Here, we present a general method to deal simultaneously with both these issues and improve the fidelity of quantum gates and operations. Our method is applicable to a wide variety of systems. As an example, we can correct gates for superconducting qubits~[1], improve coherent state transfer between a single NV centre electronic spin and a single nitrogen nuclear spin~[2], improve control over a nuclear spin ensemble~[3], etc. Our method is intimately linked to the Magnus expansion. By modifying the Magnus expansion of an initially given Hamiltonian $H_{\mathrm{i}}$, we find analytically additional control Hamiltonians $H_{\mathrm{ctrl}}$ such that $H_{\mathrm{i}} + H_{\mathrm{ctrl}}$ leads to the desired gate while minimizing both leakage and phase errors. \newline \vskip\baselineskip \noindent [1] Zijun Chen, \emph{et al.}, arXiv:1509.05470. \newline [2] G. D. Fuchs, \emph{et al.}, Nat. Phys. \textbf{7}, 789–793 (2011). \newline [3] Mathieu Munsch, \emph{et al.}, Nat. Nano. 9, 671–675 (2014). [Preview Abstract] |
Wednesday, March 16, 2016 8:12AM - 8:24AM |
K44.00002: Method for generating all uniform $\pi$-pulse sequences used in deterministic dynamical decoupling Haoyu Qi, Jonathan Dowling Dynamical decoupling has been actively investigated since Viola first suggested using a pulse sequence to protect a qubit from decoherence. Since then, many schemes of dynamical decoupling have been proposed to achieve high-order suppression, both analytically and numerically. However, hitherto, there has not been a systematic framework to understand all existing uniform $\pi$-pulse dynamical decoupling schemes. In this report, we use the projection pulse sequences as basic building blocks and concatenation as a way to combine them. We derived a concatenated-projection dynamical decoupling, a framework in which we can systematically construct pulse sequences to achieve arbitrary high suppression order. All previously known uniform dynamical decoupling sequences using $\pi$ pulse can be fit into this framework. Understanding uniform dynamical decoupling as successive projections on the Hamiltonian will also give insights on how to invent new ways to construct better pulse sequences. [Preview Abstract] |
Wednesday, March 16, 2016 8:24AM - 8:36AM |
K44.00003: Quantum gates with optimal bandwidth in noisy environments Guang Hao Low, Yoder Theodore, Isaac Chuang The traditional approach of open-loop quantum error correction suppresses certain systematic imperfections $\epsilon$ in quantum control to higher orders $\epsilon^{\mathcal{O}(L)}$ by a well-designed sequence of $L$ imperfect quantum gates. However, this philosophy of maximal flatness leads to an $\epsilon$-bandwidth that scales poorly with length and a residual that is easily overwhelmed by unaccounted sources of noise. We advance the paradigm of equiripple compensated gates that directly optimize for bandwidth given the limitations imposed by noise of magnitude $\delta$, leading to dramatically improved performance. Where $\epsilon$ represent amplitude errors, we provide a formalism that generalizes both approaches and is effective at finding such gates. With it, we provide in closed-form the phase angles for an optimal family of population inversion gates with an $\bar{\epsilon}$-bandwidth of $\mathcal{O}(\frac{\log\delta^{-1}}{L})$ -- a quadratic improvement over optimal maximally flat variants. We also construct optimal NOT gates and discuss extensions to other gates and error models. [Preview Abstract] |
Wednesday, March 16, 2016 8:36AM - 8:48AM |
K44.00004: Engineering autonomous error correction in stabilizer codes at finite temperature C. Daniel Freeman, Chris Herdman, Birgitta Whaley We present an error correcting protocol that enhances the lifetime of stabilizer code based qubits which are susceptible to string-like error modes at finite temperature, such as the toric code. The primary tool employed is dynamic application of the CSWAP operator, a local, unitary operator which exchanges defects and thereby translates quasiparticles. Crucially, the protocol does not require any information about the locations of quasiparticles, and can be used to enhance the lifetime of an encoded qubit in the absence of stabilizer measurement. This work was supported by the NSF grant DGE-1106400. [Preview Abstract] |
Wednesday, March 16, 2016 8:48AM - 9:00AM |
K44.00005: New class of photonic quantum error correction codes Matti Silveri, Marios Michael, R. T. Brierley, Juha Salmilehto, Victor V. Albert, Liang Jiang, S. M. Girvin We present a new class of quantum error correction codes for applications in quantum memories, communication and scalable computation. These codes are constructed from a finite superposition of Fock states and can exactly correct errors that are polynomial up to a specified degree in creation and destruction operators. Equivalently, they can perform approximate quantum error correction to any given order in time step for the continuous-time dissipative evolution under these errors. The codes are related to two-mode photonic codes[1] but offer the advantage of requiring only a single photon mode to correct loss (amplitude damping), as well as the ability to correct other errors, e.g.\ dephasing. Our codes are also similar in spirit to photonic "cat codes" but have several advantages including smaller mean occupation number and exact rather than approximate orthogonality of the code words. We analyze how the rate of uncorrectable errors scales with the code complexity and discuss the unitary control for the recovery process. These codes are realizable with current superconducting qubit technology[2] and can increase the fidelity of photonic quantum communication and memories. [1] I.Chuang et al., Phys. Rev. A 56, 1114 (1997).[2] R.Heeres et al., Phys. Rev. Lett. 115, 137002 (2015). [Preview Abstract] |
Wednesday, March 16, 2016 9:00AM - 9:12AM |
K44.00006: Non-commuting two-local Hamiltonians for quantum error suppression Eleanor Rieffel, Zhang Jiang Physical constraints make it challenging to implement and control multi-body interactions. Designing quantum information processes with Hamiltonians consisting of only one- and two-local terms is a worthwhile challenge. A common approach to robust storage of quantum information is to encode in the ground subspace of a Hamiltonian. Even allowing particles with high Hilbert-space dimension, it is not possible to protect quantum information from single-site errors by encoding in the ground subspace of any Hamiltonian containing only commuting two-local terms [1]. We demonstrate how to get around this no-go result by encoding in the ground subspace of a Hamiltonian consisting of non-commuting two-local terms arising from the gauge operators of a subsystem code. Specifically, we show how to protect stored quantum information against single-qubit errors using a Hamiltonian consisting of sums of the gauge generators from Bacon-Shor codes [2] and generalized-Bacon-Shor code [3]. Thus, non-commuting two-local Hamiltonians have more error-suppressing power than commuting two-local Hamiltonians. Finally, we comment briefly on the robustness of the whole scheme. [1] I. Marvian and D. A. Lidar, PRL 113, 260504 (2014) [2] D. Bacon, PRA 73, 012340 (2006) [3] S. Bravyi, PRA 83, 012320 (2011) [Preview Abstract] |
Wednesday, March 16, 2016 9:12AM - 9:24AM |
K44.00007: Error threshold for the surface code in a superohmic environment Daniel A. Lopez-Delgado, E. Novais, Eduardo R. Mucciolo, Amir O. Caldeira Using the Keldysh formalism, we study the fidelity of a quantum memory over multiple quantum error correction cycles when the physical qubits interact with a bosonic bath at zero temperature. For encoding, we employ the surface code, which has one of the highest error thresholds in the case of stochastic and uncorrelated errors. The time evolution of the fidelity of the resulting two-dimensional system is cast into a statistical mechanics phase transition problem on a three-dimensional spin lattice, and the error threshold is determined by the critical temperature of the spin model. For superohmic baths, we find that time does not affect the error threshold: its value is the same for one or an arbitrary number of quantum error correction cycles. [Preview Abstract] |
Wednesday, March 16, 2016 9:24AM - 9:36AM |
K44.00008: Fidelity of a quantum state protected by the surface code in the presence of a finite-temperature bosonic bath E. Novais, A. J. Stanforth, Eduardo R. Mucciolo We evaluate the fidelity of a multi-qubit quantum state protected by the surface code during a single quantum error correction cycle when qubits couple to a gapless bosonic environment. We discuss the protection of the state for different spectral functions and bath temperatures. Analytical results are supported by finite-size scaling analyses based on Monte Carlo and exact numerical calculations. Our results demonstrate a finite threshold that explicitly depends on the bath-mediated qubit-qubit interaction range and bath spectral function and temperature. [Preview Abstract] |
Wednesday, March 16, 2016 9:36AM - 9:48AM |
K44.00009: Repeated quantum error correction by real-time feedback on continuously encoded qubits Julia Cramer, Norbert Kalb, M. Adriaan Rol, Bas Hensen, Machiel S. Blok, Matthew Markham, Daniel J. Twitchen, Ronald Hanson, Tim H. Taminiau Because quantum information is extremely fragile, large-scale quantum information processing requires constant error correction. To be compatible with universal fault-tolerant computations, it is essential that quantum states remain encoded at all times and that errors are actively corrected. I will present such active quantum error correction in a hybrid quantum system based on the nitrogen vacancy (NV) center in diamond [1]. We encode a logical qubit in three long-lived nuclear spins, detect errors by multiple non-destructive measurements using the optically active NV electron spin and correct them by real-time feedback. By combining these new capabilities with recent advances in spin control, multiple cycles of error correction can be performed within the dephasing time. We investigate both coherent and incoherent errors and show that the error-corrected logical qubit can indeed store quantum states longer than the best spin used in the encoding [1]. Furthermore, I will present our latest results on increasing the number of qubits in the encoding, required for quantum error correction for both phase- and bit-flip. [1] J. Cramer et al. 2015; arXiv:1508.01388v1 [Preview Abstract] |
Wednesday, March 16, 2016 9:48AM - 10:00AM |
K44.00010: Serialized Quantum Error Correction Protocol for High-Bandwidth Quantum Repeaters Andrew Glaudell, Edo Waks, Jacob Taylor Advances in single-photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have low enough losses to be overcome using quantum error correction. Such error-corrected communication is equivalent to a novel quantum repeater scheme, but crucial questions regarding implementation and system requirements remain open. In this talk, I will show that long-range entangled bit generation with rates approaching $10^8$ entangled bits per second may be possible using a completely serialized protocol, in which photons are generated, entangled, and error corrected via sequential, one-way interactions with as few matter qubits as possible. Provided loss and error rates of the required elements are below the threshold for quantum error correction, this scheme demonstrates improved performance over transmission of single photons. We find improvement in entangled bit rates at large distances using this serial protocol and various quantum error correcting codes. [Preview Abstract] |
Wednesday, March 16, 2016 10:00AM - 10:12AM |
K44.00011: Spectroscopy of cross-correlations of environmental noises with two qubits Lukasz Cywinski, Piotr Szankowski, Marek Trippenbach A single qubit driven by an appropriate sequence of control pulses can serve as a spectrometer of local noise affecting its energy splitting. We show that by driving and observing two spatially separated qubits, it is possible to reconstruct the spectrum of cross-correlations of noises acting at various locations. When the qubits are driven by the same sequence of pulses, real part of cross-correlation spectrum can be reconstructed, while applying two distinct sequence to the two qubits allows for reconstruction of imaginary part of this spectrum [1]. The latter quantity contains information on either causal correlations between environmental dynamics at distinct locations, or on the occurrence of propagation of noisy signals through the environment. While entanglement between the qubits is not necessary, its presence enhances the signal from which the spectroscopic information is reconstructed. [1] P. Szankowski, M. Trippenbach, and L. Cywinski, arXiv:1507.03897. [Preview Abstract] |
Wednesday, March 16, 2016 10:12AM - 10:24AM |
K44.00012: 1D quantum simulation using a solid state platform Megan Kirkendall, Patrick Irvin, Mengchen Huang, Jeremy Levy, Hyungwoo Lee, Chang-Beom Eom Understanding the properties of large quantum systems can be challenging both theoretically and numerically. One experimental approach--quantum simulation--involves mapping a quantum system of interest onto a physical system that is programmable and experimentally accessible. A tremendous amount of work has been performed with quantum simulators formed from optical lattices; by contrast, solid-state platforms have had only limited success. Our experimental approach to quantum simulation takes advantage of nanoscale control of a metal-insulator transition at the interface between two insulating complex oxide materials\footnote{C. Cen \textit{et al.}, Nat. Mater. \textbf{7}, 298 (2008)}. This system naturally exhibits a wide variety of ground states (e.g., ferromagnetic, superconducting) and can be configured into a variety of complex geometries. We will describe initial experiments that explore the magnetotransport properties of one-dimensional superlattices with spatial periods as small as 4 nm, comparable to the Fermi wavelength. The results demonstrate the potential of this solid-state quantum simulation approach, and also provide empirical constraints for physical models that describe the underlying oxide material properties. [Preview Abstract] |
Wednesday, March 16, 2016 10:24AM - 10:36AM |
K44.00013: Classical Emulation of a Two-Qubit Quantum Computer with Analog Electronics Brian La Cour, Corey Ostrove, Granville Ott, Michael Starkey, Gary Wilson Abstract: The Hilbert space mathematical structure of a gate-based quantum computer may be reproduced by mapping the computational basis states to corresponding functions in the space of complex exponentials and identifying an inner product between any two such functions. The span of these complex basis exponentials may then identified with the finite-dimensional Hilbert space of a gate-based quantum computer. By using classical analog electronic components, such as four-quadrant multipliers and operational amplifiers, voltage signals representing arbitrary four-dimensional quantum states, along with the equivalent gate and measurement operations of a quantum computer have been physically realized through the corresponding circuitry. The fidelity of the emulation is measured using both a direct evaluation of the signal as well as through an emulation of quantum state tomography to infer the quantum state. We demonstrate that for both state synthesis and gate operations, our quantum emulation device is capable of achieving over 99\% fidelity. [Preview Abstract] |
Wednesday, March 16, 2016 10:36AM - 10:48AM |
K44.00014: Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field Arzu Kurt, Resul Eryigit Using Krylov averaging method, we have derived a fourth-order master equation for a charged harmonic oscillator weakly coupled to an electromagnetic field. Interaction is assumed to be of velocity coupling type which also takes into account the diagmagnetic term. Exact analytical expressions have been obtained for the second, the third and the fourth-order corrections to the diffusion and the drift terms of the master equation. We examined the validity range of the second order master equation in terms of the coupling constant and the bath cutoff frequency and found that for the most values of those parameters, the contribution from the third and the fourth order terms have opposite signs and cancel each other. Inclusion of the third and the fourth-order terms is found to not change the structure of the master equation. [Preview Abstract] |
Wednesday, March 16, 2016 10:48AM - 11:00AM |
K44.00015: A Numerical Study of Entanglement Entropy of the Heisenberg Model on a Bethe Cluster Barry Friedman, Greg Levine Numerical evidence is presented for a nearest neighbor Heisenberg spin model on a Bethe cluster, that by bisecting the cluster, the generalized Renyi entropy scales as the number of sites in the cluster. This disagrees with spin wave calculations and a naive application of the area law but agrees with previous results for non interacting fermions on the Bethe cluster. It seems this scaling is not an artifact of non interacting particles. As a consequence, the area law in greater then one dimension is more subtle then generally thought and applications of the density matrix renormalization group to Bethe clusters face difficulties at least as a matter of principle. [Preview Abstract] |
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