Discrete-time controllability for feedback quantum dynamics

Viola

2017

Quantum Sci. Technol.

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Abstract. A variety of tasks in quantum control, ranging from purification and cooling, to quantum stabilization and open-system simulation, rely on the ability to implement a target quantum channel over a specified time interval within prescribed accuracy. This can be achieved by engineering a suitable unitary dynamics of the system of interest along with its environment -which, depending on the available level of control, is fully or partly exploited as a coherent quantum controller. After formalizing a controllability framework for completely positive trace-preserving quantum dynamics, we provide sufficient conditions on the environment state and dimension that allow for the realization of relevant classes of quantum channelsincluding extreme channels, stochastic unitaries, or simply any channel. The results hinge on generalizations of Stinespring's dilation via a subsystem principle. In the process, we show that a conjecture by Lloyd on the minimal dimension of the environment required for arbitrary open-system simulation, albeit formally disproved, can in fact be salvaged -provided that classical randomization is included among the available resources. Existing measurement-based feedback protocols for universal simulation, dynamical decoupling, and dissipative state preparation are recast within the proposed coherent framework as concrete applications, and the resources they employ discussed in the light of the general results.

Section: Arxiv:170401486v1 [Quant-ph] 5 Apr 2017supporting

confidence: 63%

“…in Ref. [30,48]. However, the first work addresses only state controllability via measurement-based feedback; in the second paper, which is specifically tailored to optical qudit channels, the implementation is nondeterministic in the sense that only a finite probability of success can be achieved in general.…”

Section: Probabilistic Unitary Designmentioning

confidence: 99%

Quantum and classical resources for unitary design of open-system evolutions

Viola

2017

Quantum Sci. Technol.

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“…One of the reasons for focusing on this class of evolutions stems directly from applications: methods for implementing unitary evolutions, as well as related unital channels with the aid of some ancillary systems, are available in a number of diverse experimental settings. On the other hand, constructing arbitrary quantum channels is a more challenging task [39], and can be generally done with good approximation only in the limit of fast control and/or short time scales [40]. The building block (14) can lead to different evolutions for the whole system, depending on neighborhood selection:…”

Section: Timing Of Operations and Evolution Typesmentioning

confidence: 99%

Consensus for Quantum Networks: Symmetry From Gossip Interactions

Mazzarella

Sarlette

IEEE Trans. Automat. Contr.

2015

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121

This paper extends the consensus framework, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. We define consensus situations on the basis of invariance and symmetry properties, finding four different probabilistic generalizations of classical consensus states. We then extend the gossip consensus algorithm to the quantum setting and prove its convergence properties, showing how it converges to symmetric states while preserving the expectation of permutation-invariant global observables.

“…Controllability and stabilizability for the resulting class of discrete-time, closed-loop dynamics have been studied in detail in [9,5,4,1]. In particular, from the results of [4,1], it is immediate to see that if the following control resources are available:…”

Section: Discrete-time Feedback Stabilizationmentioning

confidence: 99%

Quantum state preparation by controlled dissipation in finite time: From classical to quantum controllers

Baggio

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

Viola

2012

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We propose a general scheme for dissipatively preparing arbitrary pure quantum states on a multipartite qubit register in a finite number of basic control blocks. Our “splitting-subspace” approach relies on control resources that are available in a number of scalable quantum technologies (complete unitary control on the target system, an ancillary resettable qubit and controlled-not gates between the target and the ancilla), and can be seen as a “quantum-controller” implementation of a sequence of classical feedback loops. We show how a large degree of flexibility exists in engineering the required conditional operations, and make explicit contact with a stabilization protocol used for dissipative quantum state preparation and entanglement generation in recent experiments with trapped ions