nuclear magnetic resonance

Robustness of dynamical decoupling sequences | Phys. Rev. A 87, 042309 (2013)

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Robustness of dynamical decoupling sequences

Mustafa Ahmed Ali Ahmed [1,2], Gonzalo A. Álvarez [1,3], and Dieter Suter [1]
1Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
2Department of Physics, International University of Africa, Khartoum, Sudan
3Department of Chemical Physics, Weizmann Institute of Science, Rehovot, Israel

Active protection of quantum states is an essential prerequisite for the implementation of quantum computing. Dynamical decoupling (DD) is a promising approach that applies sequences of control pulses to the system in order to reduce the adverse effect of system-environment interactions. Since every hardware device has finite precision, the errors of the DD control pulses can themselves destroy the stored information rather than protect it. We experimentally compare the performance of different DD sequences in the presence of an environment that was chosen such that all relevant DD sequences can equally suppress its effect on the system. Under these conditions, the remaining decay of the qubits under DD allows us to compare very precisely the robustness of the different DD sequences with respect to imperfections of the control pulses.

©2013 American Physical Society

via Phys. Rev. A 87, 042309 (2013): Robustness of dynamical decoupling sequences.

Average error per pulse for different DD sequences with delay τ =100μs. The average decay per pulse for different sequences is plotted against the number of pulses. The most conspicuous feature is that CP performs very badly and CPMG very well. The compensated sequences lie between these two extremes, and we find that the higher order sequences (XY8, KDD perform better than the lower order sequences (XY4). For unknown initial conditions, KDD shows the best performance. Under the present conditions, sequences that differ only with respect to time reversal symmetry perform quite similarly.
Average error per pulse for different DD sequences with delay τ =100μs.
The average decay per pulse for different sequences is plotted against the number of pulses. The most conspicuous feature is that CP performs very badly and CPMG very well. The compensated sequences lie between these two extremes, and we find that the higher order sequences (XY8, KDD perform better than the lower order sequences (XY4). For unknown initial conditions, KDD shows the best performance. Under the present conditions, sequences that differ only with respect to time reversal symmetry perform quite similarly.
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Experimental protection of quantum gates against decoherence and control errors | Phys. Rev. A 86, 050301(R) 2012

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 Experimental protection of quantum gates against decoherence and control errors

Alexandre M. Souza, Gonzalo A. Álvarez, and Dieter Suter
Fakultät Physik, Technische Universität Dortmund, D-44221, Dortmund, Germany

One of the biggest challenges for implementing quantum devices is the requirement to perform accurate quantum gates. The destructive effects of interactions with the environment present some of the most difficult obstacles that must be overcome for precise quantum control. In this work we implement a proof of principle experiment of quantum gates protected against a fluctuating environment and control pulse errors using dynamical decoupling techniques. We show that decoherence can be reduced during the application of quantum gates. High-fidelity quantum gates can be achieved even if the gate time exceeds the free evolution decoherence time by one order of magnitude and for protected operations consisting of up to 330 individual control pulses.

©2012 American Physical Society

via Phys. Rev. A 86, 050301 2012: Experimental protection of quantum gates against decoherence and control errors.

Gate fidelity as a function of gate time for different gate operations protected by different dynamical decoupling (DD) sequences. “Simple” indicates gates that were implemented by unprotected rotations. BB1 means that the gates are only protected by BB1 composite pulses which does not protect against decoherence. The delay between the pulses for the NOOP was ≈ 3μs.
Gate fidelity as a function of gate time for different gate operations protected by different dynamical decoupling (DD) sequences. “Simple” indicates gates that were implemented by unprotected rotations. BB1 means that the gates are only protected by BB1 composite pulses which does not protect against decoherence. The delay between the pulses for the NOOP was ≈ 3μs.

Iterative rotation scheme for robust dynamical decoupling | Phys. Rev. A 85, 052324 (2012)

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Gonzalo A. Álvarez, Alexandre M. Souza, and Dieter Suter

Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
Received 1 March 2012; published 29 May 2012

The loss of quantum information due to interactions with external degrees of freedom, which is known as decoherence, remains one of the main obstacles for large-scale implementations of quantum computing. Accordingly, different measures are being explored for reducing its effect. One of them is dynamical decoupling DD which offers a practical solution because it only requires the application of control pulses to the system qubits. Starting from basic DD sequences, more sophisticated schemes were developed that eliminate higher-order terms of the system-environment interaction and are also more robust against experimental imperfections. A particularly successful scheme, called concatenated DD CDD, gives a recipe for generating higher-order sequences by inserting lower-order sequences into the delays of a generating sequence. Here, we show how this scheme can be improved further by converting some of the pulses to virtual and thus ideal pulses. The resulting scheme, called (XY4)^n, results in lower power deposition and is more robust against pulse imperfections than the original CDD scheme.

©2012 American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevA.85.052324
DOI: 10.1103/PhysRevA.85.052324

via Phys. Rev. A 85, 052324 2012: Iterative rotation scheme for robust dynamical decoupling.

 

Normalized spin-signal after about 100 pulses for different DD sequences as a function of the RF frequency of the DD pulses and the delay between them. All sequences have 100 pulses except (XY4)^2, which contains 96. The labels (a) and (s) refers the the asymmetric and symmetric version of the sequences. The plot shows that our concatenation scheme with virtual pulses (XY4)^2 outperforms the concatenation scheme with real pulses CDD_2. Following a similar procedure we introduce a new sequence KDD^2 that outperforms the other DD sequences shown in the plot. This new sequence is based on the KDD sequence [PRL 106, 240501 (2011)].
Normalized spin-signal after about 100 pulses for different DD sequences as a function of the RF frequency of the DD pulses and the delay between them. All sequences have 100 pulses except (XY4)^2, which contains 96. The labels (a) and (s) refers the the asymmetric and symmetric version of the sequences. The plot shows that our concatenation scheme with virtual pulses (XY4)^2 outperforms the concatenation scheme with real pulses CDD_2. Following a similar procedure we introduce a new sequence KDD^2 that outperforms the other DD sequences shown in the plot. This new sequence is based on the KDD sequence [PRL 106, 240501 (2011)].

Shift-driven modulations of spin-echo signals | Proc. Natl. Acad. Sci. U. S. A. 109, 5958 (2012).

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Pieter E. S. Smith, Guy Bensky, Gonzalo A. Álvarez, Gershon Kurizki, and Lucio Frydman

Abstract:

Since the pioneering works of Carr-Purcell and Meiboom-Gill [Carr HY, Purcell EM (1954) Phys Rev 94:630; Meiboom S, Gill D (1985) Rev Sci Instrum 29:688], trains of π-pulses have featured amongst the main tools of quantum control. Echo trains find widespread use in nuclear magnetic resonance spectroscopy (NMR) and imaging (MRI), thanks to their ability to free the evolution of a spin-1/2 from several sources of decoherence. Spin echoes have also been researched in dynamic decoupling scenarios, for prolonging the lifetimes of quantum states or coherences. Inspired by this search we introduce a family of spin-echo sequences, which can still detect site-specific interactions like the chemical shift. This is achieved thanks to the presence of weak environmental fluctuations of common occurrence in high-field NMR—such as homonuclear spin-spin couplings or chemical/biochemical exchanges. Both intuitive and rigorous derivations of the resulting “selective dynamical recoupling” sequences are provided. Applications of these novel experiments are given for a variety of NMR scenarios including determinations of shift effects under inhomogeneities overwhelming individual chemical identities, and model-free characterizations of chemically exchanging partners.chemical exchange dynamic decoupling magnetic field inhomogeneity magnetic resonance quantum control

via Proc. Natl. Acad. Sci. U. S. A. 109, 5958 (2012): Shift-driven modulations of spin-echo signals.

Behavior observed for the illustrated compound (Cynnamic acid) upon implementing the proposed selective dynamical recoupling (SDR) sequence, as mediated by homonuclear 1H-1H couplings, for the indicated parameters. Experiments (black traces) are compared against simulations (red) using the indicated parameters, and analytical curves (blue) arise from the two-site modulation predicted by our results. (A) x-dependence observed for the isolated olefinic proton pair of Cynnamic acid at high-resolution. (B) Idem but for the Cynnamic acid placed in a grossly inhomogeneous magnetic field (shimming coils off), illustrating SDR’s ability to retrieve high resolution shift modulations. While it relies on fully refocused π-pulse trains that normally cancel also the shift modulations, by the assistance of slowly fluctuations due to the homonuclear 1H-1H couplings the shift modulation are selectively reintroduced.
Behavior observed for the illustrated compound (Cynnamic acid) upon implementing the proposed selective dynamical recoupling (SDR) sequence, as mediated by homonuclear 1H-1H couplings, for the indicated parameters. Experiments (black traces) are compared against simulations (red) using the indicated parameters, and analytical curves (blue) arise from the two-site modulation predicted by our results. (A) x-dependence observed for the isolated olefinic proton pair of Cynnamic acid at high-resolution. (B) Idem but for the Cynnamic acid placed in a grossly inhomogeneous magnetic field (shimming coils off), illustrating SDR’s ability to retrieve high resolution shift modulations. While it relies on fully refocused π-pulse trains that normally cancel also the shift modulations, by the assistance of slowly fluctuations due to the homonuclear 1H-1H couplings the shift modulation are selectively reintroduced.

Copyright ©2012 by the National Academy of Sciences

Controlling Spin-Spin Network Dynamics by Repeated Projective | Phys. Rev. Lett. 108, 140403 (2012)

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Christian O. Bretschneider (1), Gonzalo A. Álvarez (2), Gershon Kurizki (1), and Lucio Frydman (1)

(1) Department of Chemical Physics, Weizmann Institute of Science, Rehovot, 76100, Israel

(2) Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany

Received 13 September 2011; published 3 April 2012

We show that coupled-spin network manipulations can be made highly effective by repeated projections of the evolving quantum states onto diagonal density-matrix states (populations). As opposed to the intricately crafted pulse trains that are often used to fine-tune a complex network’s evolution, the strategy hereby presented derives from the “quantum Zeno effect” and provides a highly robust route to guide the evolution by destroying all unwanted correlations (coherences). We exploit these effects by showing that a relaxationlike behavior is endowed to polarization transfers occurring within a N-spin coupled network. Experimental implementations yield coupling constant determinations for complex spin-coupling topologies, as demonstrated within the field of liquid-state nuclear magnetic resonance.

© 2012 American Physical Society

via Phys. Rev. Lett. 108, 140403 (2012): Controlling Spin-Spin Network Dynamics by Repeated Projective Measurements.

Polarization evolutions in Pyridine. Different symbols are different spins. a) Free evolution (symbols: experiments, lines: simulations). b) Repetitively measured evolution for different delays between measurements. This experimental data  illustrate the switch of the dynamics shown in (a) to quasimonotonic polarization transfers, as a result of introducing repeated projective measurements that involve instantaneous erasements of the off-diagonal density-matrix terms at intervals tau. This tailored dynamics allows for a simple determination of the spin-spin coupling network topology.
Polarization evolutions in Pyridine. Different symbols are different spins. a) Free evolution (symbols: experiments, lines: simulations). b) Repetitively measured evolution for different delays between measurements. This experimental data illustrate the switch of the dynamics shown in (a) to quasimonotonic polarization transfers, as a result of introducing repeated projective measurements that involve instantaneous erasements of the off-diagonal density-matrix terms at intervals tau. This tailored dynamics allows for a simple determination of the spin-spin coupling network topology.