Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session G27: Quantum Error Correction and Quantum Control |
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Sponsoring Units: GQI Chair: Leonid Pryadko, University of Californa, Riverside Room: 329 |
Tuesday, March 19, 2013 11:15AM - 11:27AM |
G27.00001: Towards Fault-Tolerant Dynamical Decoupling Gregory Quiroz, Daniel Lidar Dynamical Decoupling (DD) is a error suppression technique which combats decoherence by applying strong and fast pulses to a quantum system to effectively average system-environment interactions. Although many DD constructions have been designed which exhibit suppression of interactions to high orders in time-dependent perturbation theory, this result is predominately in the ideal pulse limit as DD effectiveness degrades significantly in the presence of additional errors generated by faulty pulses. Here, we present a decoupling scheme which provides robustness to certain forms of pulse errors and utilizes concatenation to attain high order error suppression. Using numerical simulations, we convey the advantages of this scheme over additional robust DD constructions and provide evidence for the possibility of arbitrary order error suppression in the presence of pulse errors. [Preview Abstract] |
Tuesday, March 19, 2013 11:27AM - 11:39AM |
G27.00002: Fault-Tolerant Storage of Quantum Information by Large Block Codes Ching-Yi Lai, Todd Brun An important issue in the implementation of a quantum computer is to protect quantum information from decoherence. Concatenated quantum codes and topological quantum codes are extensively studied for fault-tolerant quantum computation. However, there is not much research on large block codes in any fault-tolerant scheme. Here we propose a method for storage of quantum information by a large block code, which has a high code rate and high distance. To access or protect the quantum information stored in a large block code requires only the fault-tolerant implementation of the gates from the Clifford group. We derive the lifetime of the quantum information stored in a large block code by CSS code construction. [Preview Abstract] |
Tuesday, March 19, 2013 11:39AM - 11:51AM |
G27.00003: Progress in analytical investigations of the achievement of fault tolerance in quantum computing Gerald Gilbert, Yaakov Weinstein We describe progress made in understanding and assuring fault tolerance in quantum computation. We introduce and explore analytical techniques for explicitly determining the logical state of a quantum computer undergoing dynamical evolution according to an arbitrary quantum algorithm. We carry out detailed analyses of the effects of errors, paying special attention to the general case of non-equiprobable errors, i.e., the important and realistic situation in which the probabilities for sigma\textunderscore x, sigma\textunderscore y and sigma\textunderscore z errors are not necessarily the same (sigma\textunderscore x, sigma\textunderscore y and sigma\textunderscore z are the Pauli operators). [Preview Abstract] |
Tuesday, March 19, 2013 11:51AM - 12:03PM |
G27.00004: Simulating the Transverse Ising Model on a Quantum Computer: Error Correction with the Surface Code Hao You, Michael Geller, Phillip Stancil We estimate the resource requirements for the quantum simulation of the ground state energy of the one-dimensional quantum transverse Ising model (TIM), based on the surface code implementation of a fault-tolerant quantum computer. The surface code approach has one of the highest known tolerable error rates ($\sim$1\%) which makes it currently one of the most practical quantum computing schemes. Compared to results of the same model using the concatenated Steane code, the current results indicate that the simulation time is comparable but the number of physical qubits for the surface code is 1-2 orders of magnitude larger than that of the concatenation code. Considering that the error threshold requirements of the surface code is four orders of magnitude higher than the concatenation code, building a quantum computer with a surface code implementation appears more promising given current physical hardware capabilities. We would like to acknowledge valuable discussions with Joydip Ghosh, Matteo Mariantoni, Andrew Sornborger, James Whitfield and Zhongyuan Zhou. This work was supported by the National Science Foundation through grant CDI 1029764. [Preview Abstract] |
Tuesday, March 19, 2013 12:03PM - 12:15PM |
G27.00005: Multi-Run Quantum Error Correction in Coupled Electron-Nuclear Systems Robabeh Rahimi Darabad, Daniel K. Park, Jonathan Baugh, Raymond Laflamme It has been a milestone in realizing quantum computing, to enhance our control over physical systems so that making quantum processors performing accurately and precisely in presence of environmental noise. For practical uses, quantum error correction should be employed in multi-run cycles in order to keep the encoded qubit, that is carrying the information, safe from noise. We have been working towards implementing multi-run quantum error correction in molecular systems that involve electron and nuclear spins. Electron spins of a molecular sample are used for pumping up the nuclear spin polarizations, in addition to addressing and manipulating the nuclear spins. The required experimental conditions for having access to refreshable ancilla qubits are very much enhanced by a careful design of the molecular sample. We report the progress and prospects towards overcoming the experimental challenges in terms of sample preparation; irradiation imposed free electron samples, free radical molecular spin systems, and triplet state photoexcitable co-crystal samples. [Preview Abstract] |
Tuesday, March 19, 2013 12:15PM - 12:27PM |
G27.00006: Resilience of topological error-correction codes to concurrent qubit and measurement errors Ruben S. Andrist, Hector Bombin, Miguel Angel Martin-Delgado, Helmut G. Katzgraber Topologically-protected quantum computing schemes avert decoherence by storing quantum information in nonlocal degrees of freedom while actively correcting for local errors. To date, the effects of individual error sources, such as, for example, bit flips, phase flips, or measurement errors have been studied. A more realistic assessment of the error stability is given by studying the combination of different error sources, such as bit flips and measurement errors. So far this has only been accomplished under the assumption that both bit-flip and measurement errors occur with the same probability [New J. Phys. 13, 083006 (2011)]. Here we study in detail the interplay between bit-flip and measurement errors, and analyze the resilience of topological error-correction codes to concurrent, nonsymetric bit flips and measurement errors. The error threshold is determined by mapping the problem onto classical, disordered lattice gauge theories, that are investigated using large-scale Monte Carlo simulations and improved estimators for systems with local gauge symmetries. [Preview Abstract] |
Tuesday, March 19, 2013 12:27PM - 12:39PM |
G27.00007: Quantum error correction with soft-pulse dynamically corrected gates with always-on qubit couplings on bipartite lattices Amrit De, Leonid P. Pryadko We suggest a scalable implementation of a universal set of high fidelity quantum gates on a bipartite lattice with always-on Ising couplings using dynamical decoupling (DD) sequences with second-order self-refocusing pulses. In addition to decoupling the unwanted parts of the inter-qubit interaction, the constructed gates also protect the qubits against low-frequency phase noise. This allows heterogeneous concatenation of DD and quantum error correction. We illustrate the technique by simulating the encoding/decoding and repeated ancilla based measurements for 4- and 5-qubit quantum error detecting/correcting codes on a spin chain and on a star graph. [Preview Abstract] |
Tuesday, March 19, 2013 12:39PM - 12:51PM |
G27.00008: Protecting OAM states of light from the decoherence effects of a turbuent atmosphere Jose Raul Gonzalez Alonso, Todd Brun While there are many advantages to using the polarization of photons to encode quantum information, a major disadvantage is that the limited dimension of the Hilbert space that describes the polarization state allows only the encoding of one qubit per photon. However, if one uses the the orbital angular momentum (OAM) of photons then the Hilbert space that describes the OAM state of a photon is infinite dimensional. Thus, it is possible to encode more than one qubit per photon. This advantage can be exploited in quantum key distribution (QKD) and in quantum secure direct communications. However, unlike the polarization of a photon, the OAM is prone to the decoherence effects produced by interactions with a turbulent atmosphere. In this work, we derive an expression for these decohering effects, and numerically simulate them to find a Kraus error map. We then theoretically demonstrate encoding and information recovery methods that could mitigate such unwanted effects. [Preview Abstract] |
Tuesday, March 19, 2013 12:51PM - 1:03PM |
G27.00009: Unitary Transformations in a Large Hilbert Space Brian Anderson, Hector Sosa Martinez, Aaron Smith, Carlos Riofrio, Charlie Baldwin, Ivan Deutsch, Poul Jessen Quantum systems with Hilbert space dimension greater than two (qudits) provide an alternative to qubits as carriers of quantum information, and may prove advantageous for quantum information tasks if good laboratory tools for qudit manipulation and readout can be developed. We have implemented a protocol for arbitrary unitary transformations in the 16 dimensional hyperfine ground manifold of Cesium 133 atoms, using phase modulated rf and microwave magnetic fields to drive the atomic evolution. Our phase modulation waveforms are designed numerically using a variant of the highly efficient GRAPE algorithm. The fidelity of the resulting transformations is verified experimentally through randomized benchmarking, which indicates an average fidelity better than 97\% across a sample of random unitaries. Our toolbox for quantum control is in principle applicable for a broad class of physical systems, such as large spins or anharmonic oscillators. [Preview Abstract] |
Tuesday, March 19, 2013 1:03PM - 1:15PM |
G27.00010: Resonant Microwave Control of a Symmetric Exchange-Only Spin Qubit J. Medford, J. Beil, J. M. Taylor, H. Lu, A. C. Gossard, C. M. Marcus We demonstrate two-axis control of an exchange-only spin qubit in a GaAs triple quantum dot using a resonant microwave excitation. The qubit is operated in a regime where two separate exchange interactions are active simultaneously, suppressing leakage out of the qubit subspace and providing some immunity to charge noise. Spectroscopic probes of the qubit reveal that the resonance frequency can be adjusted between 100 MHz and 1.5 GHz with a voltage applied to the middle quantum dot. We find a coherence time $T_2\sim20~ \mu$s for a 64 pulse Carr-Purcell-Meiboom-Gill dynamical decoupling sequence. Finally, analysis of the coherence time for multiple sequences reveals a power spectrum $S(\omega)\sim \omega^{-0.9}$, which suggests that the fluctuating Overhauser fields are not the dominant source of dephasing in this system. [Preview Abstract] |
Tuesday, March 19, 2013 1:15PM - 1:27PM |
G27.00011: Decay of the rotating-frame spin echo and its application to sensing the local environment of a NV center Vagharsh Mkhitaryan, Xiao-Xuan Huang, Viatcheslav Dobrovitski We study a NV electron spin subjected to a strong driving field, which reverses its sign with the period $\tau$ (multi-pulse Solomon echo), and analyze the rotating-frame echo decay at long times (large number of reversals). The form and the rate of the echo decay is calculated analytically and numerically, by modelling the decohering spin environment as a magnetic noise. For short $\tau$ the decay is strongly suppressed, being of the 4th order in $\tau$ (vs. 3rd order in the regular Carr-Purcell decoupling, and 2nd order in the standard continuous-wave decoupling). This ensures exceptional decoupling stability with respect to the slow fluctuations of the external magnetic field. Moreover, we find that the decay rate depends non-monotonically on the correlation time of the environment, decreasing for both very fast and very slow spin baths. Using these results, we demonstrate how the multi-pulse version of the Solomon echo can be harnessed to sense and analyze in detail the local spin environment of the NV center. [Preview Abstract] |
Tuesday, March 19, 2013 1:27PM - 1:39PM |
G27.00012: Sudden Decoherence Transitions for Quantum Discord Hyungjun Lim, Robert joynt We formulate the computation of quantum discord in terms of the generalized Bloch vector, focusing on the case of 2 qubits. This provides useful insights on the time evolution of quantum coherence for the open stem, particularly the comparison of entanglement and discord. We introduce a numerical method for calculating quantum discord for a special class of multipartite states. In agreement with previous work in low-dimensional cases (L. Mazzola et al., Phys. Rev. Lett. 104, 200401 (2010), we find situations in which there is a sudden transition from classical to quantum decoherence characterized by the discord remaining relatively robust (classical decoherence) until a certain point from where it begins to decay quickly whereas the classical correlation decays more slowly (quantum decoherence). We propose a general condition to observe this phenomenon. [Preview Abstract] |
Tuesday, March 19, 2013 1:39PM - 1:51PM |
G27.00013: Correlation Dynamics of Qubit-Qutrit Systems in a Classical Dephasing Environment Goktug Karpat, Baris Cakmak, Zafer Gedik We study the time evolution of classical and quantum correlations for hybrid qubit-qutrit systems in independent dephasing environments. Our discussion involves a comparative analysis of the Markovian dynamics of negativity, quantum discord, geometric measure of quantum discord and classical correlation. In the presence of multilocal dephasing noise, we demonstrate the phenomenon of frozen quantum discord for qubit-qutrit states. We show that geometric discord can also get frozen for a class of separable states in this case. On the other hand, when only the qutrit is under the action of a dephasing channel, we observe that the partial coherence left in the system might enable quantum discord to remain invariant throughout the whole dynamics even though the entanglement in the qubit-qutrit state disappears in a finite time interval. [Preview Abstract] |
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