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High Resolution non-Markovianity in NMR

View Article: PubMed Central - PubMed

ABSTRACT

Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.

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Related in: MedlinePlus

Quantum circuit representing the NMR pulse sequence for implementing the second collision.The input state is the resulting state from the first collision ρt(1). The boxes with the symbols Rα(θ) indicate that a rotation of the angle θ on that particular spin was performed around the α direction and . The boxes with the symbol τ1 represent a free evolution of the system and environment for a period of time τ1. τ1 is the time needed such that a rotation of π/2 occurs in the system and here it will be given by  s.
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f5: Quantum circuit representing the NMR pulse sequence for implementing the second collision.The input state is the resulting state from the first collision ρt(1). The boxes with the symbols Rα(θ) indicate that a rotation of the angle θ on that particular spin was performed around the α direction and . The boxes with the symbol τ1 represent a free evolution of the system and environment for a period of time τ1. τ1 is the time needed such that a rotation of π/2 occurs in the system and here it will be given by  s.

Mentions: The NMR implementation of the collisions between the system and particles of the environment are shown in Figs 4 and 5. The boxes with the symbols Rα(θ) indicate that a rotation of the angle θ on that particular spin was performed around the α direction. The big boxes are free evolution of the system for the time τ. The angles θ are related to the parameter η of the collisional model, and they are of the order of 1°. For the steps used in the experiment the differences between them were approximately of 0.5°. The system we have used is homonuclear, which means that all of the spins are of the same species (fluorine in this case), and implementing single rotations were hard because they are close in frequency. Then, the length of the pulses for exciting only one spin (qubit) are long. This causes undesired evolutions of the quantum state due to the interactions between the spins, leading the whole system to evolve while the individual operations are applied. Furthermore, the rf pulses are also imperfect and they may affect others spins, besides the one which it is intended for. This means that at the end of the quantum algorithm lots of errors due to these undesirable evolutions and pulse imperfections will have been accumulated. In order to correct the state of the system the method described in ref. 33 was used.


High Resolution non-Markovianity in NMR
Quantum circuit representing the NMR pulse sequence for implementing the second collision.The input state is the resulting state from the first collision ρt(1). The boxes with the symbols Rα(θ) indicate that a rotation of the angle θ on that particular spin was performed around the α direction and . The boxes with the symbol τ1 represent a free evolution of the system and environment for a period of time τ1. τ1 is the time needed such that a rotation of π/2 occurs in the system and here it will be given by  s.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037399&req=5

f5: Quantum circuit representing the NMR pulse sequence for implementing the second collision.The input state is the resulting state from the first collision ρt(1). The boxes with the symbols Rα(θ) indicate that a rotation of the angle θ on that particular spin was performed around the α direction and . The boxes with the symbol τ1 represent a free evolution of the system and environment for a period of time τ1. τ1 is the time needed such that a rotation of π/2 occurs in the system and here it will be given by  s.
Mentions: The NMR implementation of the collisions between the system and particles of the environment are shown in Figs 4 and 5. The boxes with the symbols Rα(θ) indicate that a rotation of the angle θ on that particular spin was performed around the α direction. The big boxes are free evolution of the system for the time τ. The angles θ are related to the parameter η of the collisional model, and they are of the order of 1°. For the steps used in the experiment the differences between them were approximately of 0.5°. The system we have used is homonuclear, which means that all of the spins are of the same species (fluorine in this case), and implementing single rotations were hard because they are close in frequency. Then, the length of the pulses for exciting only one spin (qubit) are long. This causes undesired evolutions of the quantum state due to the interactions between the spins, leading the whole system to evolve while the individual operations are applied. Furthermore, the rf pulses are also imperfect and they may affect others spins, besides the one which it is intended for. This means that at the end of the quantum algorithm lots of errors due to these undesirable evolutions and pulse imperfections will have been accumulated. In order to correct the state of the system the method described in ref. 33 was used.

View Article: PubMed Central - PubMed

ABSTRACT

Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.

No MeSH data available.


Related in: MedlinePlus