Quantum computing gates via optimal control

Atia, Yosi; Elias, Yuval; Mor, Tal; Weinstein, Yossi

doi:10.1142/s0219749914500312

Cited by 9 publications

(16 citation statements)

References 46 publications

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“…In order to implement AC and multiple-cycle AC on liquid-state TCE we utilized (following [34]) Gradient Ascent Pulse Engineering (GRAPE) [35], an optimal control algorithm, to generate high fidelity pulses for obtaining the compression gate and the PE gate [36]. Here we present various algorithms for cooling liquid TCE.…”

Section: Methodsmentioning

confidence: 99%

“…In the experiment, the measured relaxation times (see table I), were obtained by inversion recovery as in [23,36]. Adding a paramagnetic reagent to the TCE, improved the relaxation time ratios as suggested in [37].…”

Section: Wait For Duration D3 (H Regains Polarization)mentioning

confidence: 99%

“…The pulses were designed to be robust to deviations up to ±15% in RF power [36]. The pulses were not designed to apply a spe- cific unitary gate, but to apply a less constraining stateto-state transformation.…”

Section: Fig 2: (Color Online) Visualization Of Process 1 Basedmentioning

confidence: 99%

“…However the state of the system changes with each cooling cycle. Therefore, among two pulses that apply PE, even though one pulse performs better in equilibrium [36], we used another pulse, which yielded better cooling for the entire process. Let {{.…”

Section: Fig 2: (Color Online) Visualization Of Process 1 Basedmentioning

confidence: 99%

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Algorithmic cooling in liquid-state nuclear magnetic resonance

et al. 2016

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Algorithmic cooling is a method that employs thermalization to increase qubit purification level, namely it reduces the qubit-system's entropy. We utilized gradient ascent pulse engineering (GRAPE), an optimal control algorithm, to implement algorithmic cooling in liquid state nuclear magnetic resonance. Various cooling algorithms were applied onto the three qubits of 13 C2-trichloroethylene, cooling the system beyond Shannon's entropy bound in several different ways. In particular, in one experiment a carbon qubit was cooled by a factor of 4.61. This work is a step towards potentially integrating tools of NMR quantum computing into in vivo magnetic resonance spectroscopy.

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Section: Methodsmentioning

confidence: 99%

Section: Wait For Duration D3 (H Regains Polarization)mentioning

confidence: 99%

Section: Fig 2: (Color Online) Visualization Of Process 1 Basedmentioning

confidence: 99%

Section: Fig 2: (Color Online) Visualization Of Process 1 Basedmentioning

confidence: 99%

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Algorithmic cooling in liquid-state nuclear magnetic resonance

et al. 2016

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“…Highly efficient 3-bit compression was achieved in the solid state using quantum optimal control theory (the GRAPE algorithm) [31,32]. We have recently [29,30,60] adopted this approach in the liquid state, and achieved short optimized 3-bit compression shaped pulses (around 15 ms) for TCE; the high efficiency of the compression (∼ 90%) allowed us to cool one carbon of TCE by about 4.5-fold, beyond Shannon's bound, following several rounds of algorithmic cooling.…”

Section: Compression and Ac Of Tcementioning

confidence: 99%

Experimental heat-bath cooling of spins

et al. 2014

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Abstract. Algorithmic cooling (AC) is a method to purify quantum systems, such as ensembles of nuclear spins, or cold atoms in an optical lattice. When applied to spins, AC produces ensembles of highly polarized spins, which enhance the signal strength in nuclear magnetic resonance (NMR). According to this cooling approach, spin-half nuclei in a constant magnetic field are considered as bits, or more precisely quantum bits, in a known probability distribution. Algorithmic steps on these bits are then translated into specially designed NMR pulse sequences using common NMR quantum computation tools. The algorithmic cooling of spins is achieved by alternately combining reversible, entropy-preserving manipulations (borrowed from data compression algorithms) with selective reset, the transfer of entropy from selected spins to the environment. In theory, applying algorithmic cooling to sufficiently large spin systems may produce polarizations far beyond the limits due to conservation of Shannon entropy. Here, only selective reset steps are performed, hence we prefer to call this process "heat-bath" cooling, rather than algorithmic cooling. We experimentally implemented two consecutive steps of selective reset, thus transferring entropy from two selected spins to the environment. We performed such cooling experiments, with commercially available labeled molecules, on standard liquid-state NMR spectrometers. We report in particular on our original experiment, unpublished until now except on the arXiv (quant-ph/0511156) in 2005, which was, to the best of our knowledge, the world's first experiment that yielded polarizations results that bypassed Shannon's entropy-conservation bound, so that the entire spin-system was cooled.

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Rapid convergence of optimal control in NMR using numerically-constructed toggling frames

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Anklin

Massefski

et al. 2017

Journal of Magnetic Resonance

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We present a numerical method for rapidly solving the Bloch equation for an arbitrary time-varying spin-1/2 Hamiltonian. The method relies on fast, vectorized computations such as summation and quaternion multiplication, rather than slow computations such as matrix exponentiation. A toggling frame is constructed in which the Hamiltonian is time-invariant, and therefore has a simple analytical solution. The key insight is that constructing this frame is faster than solving the system dynamics in the original frame. Rapidly solving the Bloch equations for an arbitrary Hamiltonian is particularly useful in the context of NMR optimal control. Optimal control theory can be used to design pulse shapes for a range of tasks in NMR spectroscopy. However, it requires multiple simulations of the Bloch equations at each stage of the algorithm, and for each relevant set of parameters (e.g. chemical shift frequencies). This is typically time consuming. We demonstrate that by working in an appropriate toggling frame, optimal control pulses can be generated much faster. We present a new alternative to the well-known GRAPE algorithm to continuously update the toggling-frame as the optimal pulse is generated, and demonstrate that this approach is extremely fast. The use and benefit of rapid optimal pulse generation is demonstrated for 19F fragment screening experiments.

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Quantum computing gates via optimal control

Cited by 9 publications

References 46 publications

Algorithmic cooling in liquid-state nuclear magnetic resonance

Algorithmic cooling in liquid-state nuclear magnetic resonance

Experimental heat-bath cooling of spins

Rapid convergence of optimal control in NMR using numerically-constructed toggling frames

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