Optimal state pairs for non-Markovian quantum dynamics

The memory effects in non-Markovian quantum dynamics can induce the revival of quantum coherence, which is believed to provide important physical resources for quantum information processing (QIP). However, no real quantum algorithms have been demonstrated with the help of such memory effects. Here, we experimentally implemented a non-Markovianity-assisted highfidelity refined Deutsch-Jozsa algorithm (RDJA) with a solid spin in diamond. The memory effects can induce pronounced nonmonotonic variations in the RDJA results, which were confirmed to follow a non-Markovian quantum process by measuring the non-Markovianity of the spin system. By applying the memory effects as physical resources with the assistance of dynamical decoupling, the probability of success of RDJA was elevated above 97% in the open quantum system. This study not only demonstrates that the non-Markovianity is an important physical resource but also presents a feasible way to employ this physical resource. It will stimulate the application of the memory effects in non-Markovian quantum dynamics to improve the performance of practical QIP.npj Quantum Information (2018) 4:3 ; doi:10.1038/s41534-017-0053-z INTRODUCTION Based on quantum phenomena, such as superposition, correlation and entanglement, quantum information processing (QIP) has provided great advantages over its classical counterpart 1-3 in efficient algorithms, 4,5 secure communication, 6,7 and highprecision metrology. [8][9][10][11][12][13][14][15][16] However, quantum superposition and correlation are fragile in an open quantum system. Notorious decoherence, [17][18][19] which is caused by interactions with noisy environments, is a major hurdle in the realization of fault-tolerant coherent operation 20,21 and scalable quantum computation. To further expand the implementation of QIP in open quantum systems, full understanding and control of environmental interactions are required. 17,[22][23][24] Many techniques have been developed to address this issue, including decoherence-free subspaces, 25 dynamical decoupling (DD) 13,26 and the geometric approach. 27 However, actively utilizing the environmental interactions would represent a significant achievement, compared with passively shielding them.Usually, the interaction of an open quantum system with a noisy environment exhibits memory-less dynamics with an irreversible loss of quantum coherence, that can be described by the Born-Markov approximation. 28 However, because of strong system-environment couplings, structured or finite reservoirs, low temperatures, or large initial system-environment correlations, the dynamics of an open quantum system may deviate substantially from the Born-Markov approximation and follow a non-Markovian process. [28][29][30][31][32] In such a process, the pronounced memory effect, which is the primary feature of a non-Markovian environment, can be used to revive the genuine quantum properties, 28-34 such as quantum coherence and correlations. Consequently, improving the performance of QIP by utilizing memo...

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“…When N > 0, the interaction process is non-Markovian. To experimentally characterize a non-Markovian quantum dynamics, optimal state pairs, 45 …”

Section: Resultsmentioning

confidence: 99%

Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond

et al. 2018

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“…For such cases, any pair of antipodal initial states living in the equatorial line in the Bloch sphere are expected to maximize σ(t) [25]. We checked this numerically.…”

Section: Figmentioning

confidence: 99%

Non-Markovian qubit dynamics in a circuit-QED setup

2015

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We consider a circuit-QED setup that allows the induction and control of non-Markovian dynamics of a qubit. Non-Markovianity is enforced over the qubit by means of its direct coupling to a bosonic mode which is controllably coupled to other qubit-mode system. We show that this configuration can be achieved in a circuit-QED setup consisting of two initially independent superconducting circuits, each formed by one charge qubit and one transmission-line resonator, which are put in interaction by coupling the resonators to a current-biased Josephson junction. We solve this problem exactly and then proceed with a thorough investigation of the emergent non-Markovianity in the dynamics of the qubits. Our study might serve the context for a first experimental assessment of non-Markovianity in a multi-element solid-state device.Comment: 8 pages, 7 figures, slightly changed titl

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“…The computational difficulty of performing such a maximisation can be reduced by taking into account recently proved conditions for initial-state pairs that maximise N BLP , 53 which state that the maximum occurs for initial states that are orthogonal and lie on the boundary of the state space (which is equivalent to having a zero eigenvalue). An alternative approach is to consider typical initial states of the system.…”

Section: A Measuring Non-markovianitymentioning

confidence: 99%

How Markovian is exciton dynamics in purple bacteria?

Vaughan

Linden

Manby

2017

The Journal of Chemical Physics

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We investigate the extent to which the dynamics of excitons in the light-harvesting complex LH2 of purple bacteria can be described using a Markovian approximation. To analyse the degree of non-Markovianity in these systems, we introduce a measure based on fitting Lindblad dynamics, as well as employing a recently introduced trace-distance measure. We apply these measures to a chromophore-dimer model of exciton dynamics and use the hierarchical equation-of-motion method to take into account the broad, low-frequency phonon bath. With a smooth phonon bath, small amounts of non-Markovianity are present according to the trace-distance measure, but the dynamics is poorly described by a Lindblad master equation unless the excitonic dimer coupling strength is modified. Inclusion of underdamped, high-frequency modes leads to significant deviations from Markovian evolution in both measures. In particular, we find that modes that are nearly resonant with gaps in the excitonic spectrum produce dynamics that deviate most strongly from the Lindblad approximation, despite the trace distance measuring larger amounts of non-Markovianity for higher frequency modes. Overall we find that the detailed structure in the high-frequency region of the spectral density has a significant impact on the nature of the dynamics of excitons.

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Optimal state pairs for non-Markovian quantum dynamics

Cited by 174 publications

References 25 publications

Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond

Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond

Non-Markovian qubit dynamics in a circuit-QED setup

How Markovian is exciton dynamics in purple bacteria?

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