Observations of quantum dynamics by solution-state NMR spectroscopy

Pravia, Marco A.; Fortunato, Evan M.; Weinstein, Yaakov S.; Price, Mark D.; Teklemariam, G.; Nelson, R. J.; Sharf, Yehuda; Somaroo, Shyamal; Tseng, Ching-Hsiang; Havel, Timothy F.; Cory, David G.

doi:10.1002/(sici)1099-0534(1999)11:4<225::aid-cmr3>3.0.co;2-e

Cited by 28 publications

(30 citation statements)

References 17 publications

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“…The state of the two-qubit spin ensemble can be represented in the high temperature expansion as ρ = I/4 + ε∆ρ, where ε = ω L /4k B T is the ratio between the magnetic and thermal energies [7][8][9] and I is the identity operator. The state of the spins system is highly mixed, however it can encompass coherent evolutions, interference [6,8,9], and also supporting general quantum correlations without entanglement [10][11][12][13].…”

Section: Jmentioning

confidence: 99%

Experimental analysis of the quantum complementarity principle

et al. 2012

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One of the milestones of quantum mechanics is Bohr's complementarity principle. It states that a single quantum can exhibit a particle-like or a wave-like behaviour, but never both at the same time. These are mutually exclusive and complementary aspects of the quantum system. This means that we need distinct experimental arrangements in order to measure the particle or the wave nature of a physical system. One of the most known representations of this principle is the single-photon Mach-Zehnder interferometer. When the interferometer is closed an interference pattern is observed (wave aspect of the quantum) while if it is open, the quantum behaves like a particle. Here, using a molecular quantum information processor and employing nuclear magnetic resonant (NMR) techniques, we analyze the quantum version of this principle by means of an interferometer that is in a quantum superposition of being closed and open, and confirm that we can indeed measure both aspects of the system with the same experimental apparatus. More specifically, we observe with a single apparatus the interference between the particle and the wave aspects of a quantum system. One of the most striking departure from the classical lines of thought is the double-slit experiment with a single quantum (from here now named qubit for simplicity). This experiment, which is an example of Bohr's complementarity principle, tells us that we have to choose either to observe interference fringes (wave-like behaviour) or to know which path has been taken by the qubit (particlelike behaviour). This fact, that has been experimentally verified in many different contexts [1], means that these two knowledges (wave-like and particle-like behaviour) are mutually exclusive.A possible realization of this experiment is the singlequbit Mach-Zehnder interferometer, schematically shown in Fig. 1. After crossing the first beam splitter, BS 1 , the qubit is in a coherent superposition state of been taken both paths a and b at the same time. The second beam splitter, BS 2 , if present, recombines the qubit paths that is, then, detected by D a or D b . If we perform this experiment by varying the phase shift θ between the two paths, the result will be an interference pattern in the probability of the qubit detection by D a or D b , indicating that the it behaves like a wave (for α = π). However, if we remove BS 2 (α = 0), the interference between both paths disappears and the particle character of the qubit is observed.An important feature of classical complementarity experiment is the fact that, we can only say something about the behaviour of the system (particle or wave) after the measurement has been carried out. We then must choose beforehand what phenomenon we want to observe. This means that the two experimental arrangements are complementary. This characteristics, which is the essence of Bohr's principle, led Wheeler to formu- late his delayed-choice gedanken experiment [2]. Wheeler speculated whether the qubit could "know", before entering in the interferometer, wha...

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Section: Jmentioning

confidence: 99%

Experimental analysis of the quantum complementarity principle

et al. 2012

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“…This can be compared to conventional spatial averaging method where η ≈ 6.12 (point A 5 in Fig. 1(a)) [31] and line-selective pulse approach where unitary bound can be achieved η ≈ 6.67 (point A 4 in Fig. 1(a)) [32].…”

Section: Arxiv:14124146v2 [Quant-ph] 4 Aug 2015mentioning

confidence: 99%

Approximation of reachable sets for coherently controlled open quantum systems: Application to quantum state engineering

Luo

et al. 2016

Phys. Rev. A

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Precisely characterizing and controlling realistic open quantum systems is one of the most challenging and exciting frontiers in quantum sciences and technologies. In this Letter, we present methods of approximately computing reachable sets for coherently controlled dissipative systems, which is very useful for assessing control performances. We apply this to a two-qubit nuclear magnetic resonance spin system and implement some tasks of quantum control in open systems at a near optimal performance in view of purity: e.g., increasing polarization and preparing pseudo-pure states. Our work shows interesting and promising applications of environment-assisted quantum dynamics.PACS numbers: 03.67. Lx,03.65.Yz Recent years have seen immense advances in active and precise manipulation of a broad variety of quantum systems. The subject of quantum system control has been developed into a rapidly growing area [1] attracting substantial interests from the community of quantum information physicists. One of the fundamental tasks is to design reliable control techniques for systems that are exposed to a dissipative environment [2]. As dissipation tends to irreversibly affect the system dynamics, it is recognized as one dominant source for information loss and hence must be suppressed. Only recently was it realized that open system engineering may exhibit surprising advantages in some important aspects [3, 3, 5]. For example, it was shown that the purification efficiency of heatbath algorithmic cooling protocol can surpass the closed system limit [3]. In other researches [5], there emerged great interests in environment-assisted entangled state engineering. Dissipative production of entangled steady states has already been realized in various experimental setups like trapped ions [6], superconducting circuit [7] and double quantum dot [8].Although some ideas borrowed from classical control theory (e.g., time optimal control) have been successfully extended to construct methods for steering closed quantum systems [9], it turns out to be more challenging for open quantum systems. The major reason comes from the fact proved in [1] that for a finite dimensional Markovian quantum system, coherent means of control cannot fully compensate the irreversibility of the dynamics. In fact, to what extent can the system evolving tendency be changed depends upon not only the external operations but also the structure of the relaxation mechanisms. This certainly forms an obstacle in devising of general control methodology. Previous research results have been able to characterize the reachable set on the states of a single qubit both qualitatively [1] and quantitatively [6,12]. However, to generalize these results to higher dimensional systems is not easy [13].Realising the lack of exact theory for the reachability problem, we propose to use approximation techniques. Basically the idea is to approximate the reachable set, usually in terms of simple geometric objects (e.g., convex polytopes [14], ellipsoids [15]), from both externally (ov...

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“…In heteronuclear spin systems the controlled-transfer approach gate approach can give even larger improvements in effective purity compared with the conventional spatial averaging techniques, firstly because some conventional spatial averaging methods [13] trade simplicity for efficiency, and secondly because such methods usually begin with an initial sequence that equalizes the polarization of the two spins. Although an efficient method for doing this in a two spin system is known [13], the simplest general method in larger spin systems is just to reduce the polarization of the more highly polarized spins to that of the least polarized spins, inevitably wasting polarization in the process.…”

Section: Heteronuclear Spin Systemsmentioning

confidence: 99%

“…Hadamard gates can be replaced by pseudo-Hadamard gates as usual [1], while controlled-phase-shift gates correspond to a combination of evolution under the spinspin coupling for some appropriate time, with undesired interactions being suppressed by spin echoes [16], and local z rotations. If desired, extraneous z rotations and couplings can be absorbed into the spin reference frames [17,18], and any such rotations remaining when the gra- 13 C FIG. 1: Experimental demonstration of pseudo-pure states prepared using a conventional approach and our new approach.…”

Section: Implementationsmentioning

confidence: 99%

Preparing pseudopure states with controlled-transfer gates

2010

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The preparation of pseudo-pure states plays a central role in the implementation of quantum information processing in high temperature ensemble systems, such as nuclear magnetic resonance. Here we describe a simple approach based on controlled-transfer gates which permits pseudo-pure states to be prepared efficiently using spatial averaging techniques.PACS numbers: 03.67. Lx, Nuclear Magnetic Resonance (NMR) spin systems provide a simple approach for demonstrating techniques for quantum information processing [1]. Because of the difficulty in preparing pure spin states almost all experiments have used pseudo-pure states [2, 3], sometimes called effective pure states [4,5]. These are mixed states of the formwhere |0 = |00 . . . 0 is the desired ground state and 1/2 n is the maximally mixed state. The effective purity δ of these states is very low if prepared from hightemperature thermal systems [6], but the pseudo-pure state approach remains useful for simple demonstrations, and may also find applications in systems prepared at spin temperatures which are low enough to substantially enhance the ground state population but not low enough to generate a true pure state.A range of methods for preparing pseudo-pure states have been described [1], which can usually be divided into temporal averaging approaches, in which the final result is averaged over a number of repetitions of the experiment with different starting states, and spatial averaging approaches, in which magnetic field gradients are used to average the spin system over a macroscopic sample. Spatial averaging has the advantage that only a single experiment is required, but suffers from a number of practical disadvantages: in particular it can be difficult to design experiments which prepare pseudo-pure states with the highest possible purity, and to avoid the generation of zero-quantum coherence terms [7], which are not averaged by field gradients. Here we describe a simple spatial averaging approach which prepares pseudo-pure states with the highest possible purity. * Electronic address: jonathan.jones@qubit.org I. CONTROLLED-TRANSFER GATESThe thermal state of an NMR spin system is diagonal in the computational basis with a pattern of populations determined by Boltzmann factors. Although details vary greatly, all methods for preparing pseudo pure states fundamentally work by averaging the populations of states other than the ground state, ideally leaving the ground state untouched [8,9].Averaging of this kind can be achieved using a controlled-transfer gate, which comprises a controlledrotation gate with a rotation angle of θ, followed by the application of a magnetic field crush gradient which removes all off-diagonal terms (if the system's density matrix is diagonal before the gate zero-quantum terms will not be generated). The controlled rotation occurs around some axis in the xy plane; the choice of axis is unimportant as the off-diagonal terms, which depend on the choice of axis, are removed by the field gradient. For definiteness the rotation can be ...

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Observations of quantum dynamics by solution-state NMR spectroscopy

Cited by 28 publications

References 17 publications

Experimental analysis of the quantum complementarity principle

Experimental analysis of the quantum complementarity principle

Approximation of reachable sets for coherently controlled open quantum systems: Application to quantum state engineering

Preparing pseudopure states with controlled-transfer gates

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