Theoretical considerations and simulation models related to the method of Sonquist and Morgan

Reichardt, Robert; Schmeikal, Bernd

doi:10.1007/bf00172374

Cited by 7 publications

(9 citation statements)

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“…This is similar to what is normally done for quantum gates [30,31]. Provided that errors are mainly introduced by random jitter, both threshold and protection time τ will play a fundamental role on the interpretation of the results presented here.…”

Section: Udd With Power-law Spectral Densitysupporting

confidence: 79%

Performance of dynamical decoupling in bosonic environments and under pulse-timing fluctuations

et al. 2016

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We study the suppression of qubit dephasing through Uhrig dynamical decoupling (UDD) in nontrivial environments modeled within the spin-boson formalism. In particular, we address the case of (i) a qubit coupled to a bosonic bath with power-law spectral density, and (ii) a qubit coupled to a single harmonic oscillator that dissipates energy into a bosonic bath, which embodies an example of a structured bath for the qubit. We then model the influence of random time jitter in the UDD protocol by sorting pulse-application times from Gaussian distributions centered at appropriate values dictated by the optimal protocol. In case (i) we find that, when few pulses are applied and a sharp cutoff is considered, longer coherence times and robust UDD performances (against random timing errors) are achieved for a super-Ohmic bath. On the other hand, when an exponential cutoff is considered a super-Ohmic bath is undesirable. In case (ii) the best scenario is obtained for an overdamped harmonic motion. Our study provides relevant information for the implementation of optimized schemes for the protection of quantum states from decoherence.

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Section: Udd With Power-law Spectral Densitysupporting

confidence: 79%

Performance of dynamical decoupling in bosonic environments and under pulse-timing fluctuations

et al. 2016

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“…In many-copy form, this is a problem of resource transformation ρ ⊗n O − → |φ φ|, where |φ is a magic state. This task has been coined magic state distillation (Anwar et al, 2012;Bravyi and Kitaev, 2005;Campbell and Browne, 2009;Reichardt, 2005), and it is an analog to the task of ebit distillation in the QRT of entanglement.…”

Section: Stabilizer Computation and "Magic" Statesmentioning

confidence: 99%

Quantum resource theories

2019

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Quantum resource theories (QRTs) offer a highly versatile and powerful framework for studying different phenomena in quantum physics. From quantum entanglement to quantum computation, resource theories can be used to quantify a desirable quantum effect, develop new protocols for its detection, and identify processes that optimize its use for a given application. Particularly, QRTs have revolutionized the way we think about familiar properties of physical systems like entanglement, elevating them from being just interesting fundamental phenomena to being useful in performing practical tasks. The basic methodology of a general QRT involves partitioning all quantum states into two groups, one consisting of free states and the other consisting of resource states. Accompanying the set of free states is a collection of free quantum operations arising from natural restrictions placed on the physical system, restrictions that force the free operations to act invariantly on the set of free states. The QRT then studies what information processing tasks become possible using the restricted operations. Despite the large degree of freedom in how one defines the free states and free operations, unexpected similarities emerge among different QRTs in terms of resource measures and resource convertibility. As a result, objects that appear quite distinct on the surface, such as entanglement and quantum reference frames, appear to have great similarity on a deeper structural level. This article reviews the general framework of a quantum resource theory, focusing on common structural features, operational tasks, and resource measures. To illustrate these concepts, an overview is provided on some of the more commonly studied QRTs in the literature.

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“…It is well established that a ratio of around 1000 is good enough for FTQC, and recent estimates of this have been a low as 100 [27]. We have demonstrated that an entangling gate can be performed in real systems in around 5 ps, which is around 200 times shorter than the longest measurements of decoherence times [12].…”

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confidence: 69%

Creating excitonic entanglement in quantum dots through the optical Stark effect

2004

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We show that two initially non-resonant quantum dots may be brought into resonance by the application of a single detuned laser. This allows for control of the inter-dot interactions and the generation of highly entangled excitonic states on the picosecond timescale. Along with arbitrary single qubit manipulations, this system would be sufficient for the demonstration of a prototype excitonic quantum computer. [5,6,7].In this paper, we shall analyze the behaviour of two adjacent self-assembled QD's addressed by an external classical laser field, with the aim of controlling the electronic interactions between them. We shall demonstrate that it is possible to generate and maintain long-lived entangled excitonic states in such QD's through the inter-dot resonant (Förster) energy transfer [5,8]. This is achieved with a single laser that dynamically Stark shifts the exciton ground states in and out of resonance, effectively switching the inter-dot interaction on and off.Our model considers only the ground state (no exciton) and first excited state (single exciton) in each dot, and these two states define our qubit as |0 and |1 respectively. Each QD is assumed to be within the strong-confinement regime where their typical sizes are much smaller than the corresponding bulk exciton radius, which is determined by the electron-hole Coulomb interaction. As a result, the confinement energy due to QD size dominates and mixing of the single-particle electron and hole states due to their Coulomb interactions may be neglected [9]. Any associated energy shift can be absorbed into the exciton creation energy; this shift is important as it ensures that the resonance condition for single-particle tunneling is not the same as that for resonant exciton transfer. Additionally, we consider only weak inter-dot interaction strengths (∼ 0.1 meV) which would be expected for two dots with relatively large spacing (∼ 10 nm) [10]. Therefore, we may neglect inter-dot tunneling of electrons and holes.The Hamiltonian for two coupled dots in the presence * Electronic address: ahsan.nazir@materials.ox.ac.uk † Electronic address: brendon.lovett@materials.ox.ac.uk of a single laser of frequency ω l may be written in the computational basis {|00 , |01 , |10 , |11 } as (h = 1):(1) where ω 0 is the ground state energy, ω 1(2) the exciton creation energy for dot 1(2), and ω T = ω 0 + ω 1 + ω 2 . The coupling terms V F and V XX are the Förster (transition dipole-dipole) and biexciton [6,7] (static dipole-dipole) interaction strengths respectively.We have assumed that each dot may couple to the laser with a different strength, governed by the respective Rabi frequency Ω 1 or Ω 2 , with Ω i (t) ≡ −2d i ·E(r, t), for i = 1, 2. Here, d i is the inter-band ground state transition dipole moment for dot i, and E(r, t) is the laser amplitude at time t and position r. Natural size and composition fluctuations in self-assembled dot samples (for example in InGaAs QD's [11]) lead to a large range of possible transition dipole moments for each dot. The size of the g...

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Theoretical considerations and simulation models related to the method of Sonquist and Morgan

Cited by 7 publications

References 1 publication

Performance of dynamical decoupling in bosonic environments and under pulse-timing fluctuations

Performance of dynamical decoupling in bosonic environments and under pulse-timing fluctuations

Quantum resource theories

Creating excitonic entanglement in quantum dots through the optical Stark effect

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