Dynamics of noisy quantum systems in the Heisenberg picture: Application to the stability of fractional charge

Rahmani, Armin

doi:10.1103/physreva.92.042110

Cited by 9 publications

(7 citation statements)

References 33 publications

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“…This is due to the linearity of the dynamical equation (8). A decoherence operator F β can represent either noise in the Hamiltonian parameters (in which case, F β is Hermitian [38,39]) or an engineered bath [40]. In the former case, f β 's are constant rates of noise processes and in the latter, f β (t)'s are control knobs that the Pontryagin's minimum principle says should vary in bang-bang form for an optimal protocol.…”

Section: B Presence Of Decoherencementioning

confidence: 99%

Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle

et al. 2017

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We use Pontryagin's minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed Quantum Approximate Optimization Algorithm. Focusing on the Sherrington-Kirkpatrick spin-glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale of the pulses provide an efficient parameterization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. For the particular systems we study, we find numerically that the optimal nonadiabatic bang-bang protocols outperform conventional quantum annealing in the presence of weak white additive external noise and weak coupling to a thermal bath modeled with the Redfield master equation.

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Section: B Presence Of Decoherencementioning

confidence: 99%

Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle

et al. 2017

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“…Note that white noise is a good approximation to ubiquitous colored noise with exponentially decaying correlations. We set W as a small value for the stochastic perturbation, which ensures the validity of noise-average density matrix technique 49 . We consider the system Hamiltonian containing two parts in a general form 48…”

Section: Anti-kz Behavior Of a Noisy Transverse-field Xy Chainmentioning

confidence: 99%

Anti-Kibble-Zurek behavior of a noisy transverse-field XY chain and its quantum simulation with two-level systems

Gao

Zhang

et al. 2017

Phys. Rev. B

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We study the dynamics of a transverse-field XY chain driven across quantum critical points by noisy control fields. We characterize the defect density as a function of the quench time and the noise strength, and demonstrate that the defect productions for three quench protocols with different scaling exponents exhibit the anti-Kibble-Zurek behavior, whereby slower driving results in more defects. The protocols are quenching through the boundary line between paramagnetic and ferromagnetic phases, quenching across the isolated multicritical point and along the gapless line, respectively. We also show that the optimal quench time to minimize defects scales as a universal power law of the noise strength in all the three cases. Furthermore, by using quantum simulation of the quench dynamics in the spin system with well-designed Landau-Zener crossings in pseudo-momentum space, we propose an experimentally feasible scheme to test the predicted anti-Kibble-Zurek behavior of this noisy transverse-field XY chain with two-level systems under controllable fluctuations.

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“…where |1 ≡ c † |0 , yielding the initial density matrix ρ 0 = 1 2 (|0 0| + |0 1| + |1 0| + |1 1|), which is then evolved and averaged over noise to obtain ρ(τ), by solving the master equation 38,43,44 ,…”

Section: Random White Noisementioning

confidence: 99%

Optimal diabatic dynamics of Majorana-based quantum gates

2017

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In topological quantum computing, unitary operations on qubits are performed by adiabatic braiding of nonAbelian quasiparticles, such as Majorana zero modes, and are protected from local environmental perturbations. In the adiabatic regime, with timescales set by the inverse gap of the system, the errors can be made arbitrarily small by performing the process more slowly. To enhance the performance of quantum information processing with Majorana zero modes, we apply the theory of optimal control to the diabatic dynamics of Majorana-based qubits. While we sacrifice complete topological protection, we impose constraints on the optimal protocol to take advantage of the nonlocal nature of topological information and increase the robustness of our gates. By using the Pontryagin's maximum principle, we show that robust equivalent gates to perfect adiabatic braiding can be implemented in finite times through optimal pulses. In our implementation, modifications to the device Hamiltonian are avoided. Focusing on thermally isolated systems, we study the effects of calibration errors and external white and 1/ f (pink) noise on Majorana-based gates. While a noise-induced antiadiabatic behavior, where a slower process creates more diabatic excitations, prohibits indefinite enhancement of the robustness of the adiabatic scheme, our fast optimal protocols exhibit remarkable stability to noise and have the potential to significantly enhance the practical performance of Majorana-based information processing.

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Dynamics of noisy quantum systems in the Heisenberg picture: Application to the stability of fractional charge

Cited by 9 publications

References 33 publications

Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle

Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle

Anti-Kibble-Zurek behavior of a noisy transverse-field XY chain and its quantum simulation with two-level systems

Optimal diabatic dynamics of Majorana-based quantum gates

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