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

Baggio, Giacomo; Ticozzi, Francesco; Viola, Lorenza

doi:10.1109/cdc.2012.6426787

Cited by 14 publications

(16 citation statements)

References 21 publications

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“…Furthermore, exact pure-state stabilization is only achievable provided that A may be perfectly refreshed, which in turn requires B to be perfectly initialized in a pure, two-level virtual subsystem. Remarkably, if these conditions are met, an arbitrary n -qubit pure state | ψ 〉 target may in fact be dissipatively prepared by using a finite number, n , of suitably defined control iterations 46 .…”

Section: Resultsmentioning

confidence: 99%

Quantum resources for purification and cooling: fundamental limits and opportunities

Ticozzi

Viola

2014

Sci Rep

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Preparing a quantum system in a pure state is ultimately limited by the nature of the system's evolution in the presence of its environment and by the initial state of the environment itself. We show that, when the system and environment are initially uncorrelated and arbitrary joint unitary dynamics is allowed, the system may be purified up to a certain (possibly arbitrarily small) threshold if and only if its environment, either natural or engineered, contains a “virtual subsystem” which has the same dimension and is in a state with the desired purity. Beside providing a unified understanding of quantum purification dynamics in terms of a “generalized swap process,” our results shed light on the significance of a no-go theorem for exact ground-state cooling, as well as on the quantum resources needed for achieving an intended purification task.

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Section: Resultsmentioning

confidence: 99%

Quantum resources for purification and cooling: fundamental limits and opportunities

Ticozzi

Viola

2014

Sci Rep

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“…It should be noted, that the operations forming our implementable set of gates shown in table 1 allow the realization of any completely positive map, which corresponds to a Markovian process [33][34][35]. The quality of the operations is affected by multiple physical parameters that are discussed in more detail in section 3.…”

Section: Tools Beyond Coherent Operationsmentioning

confidence: 99%

A quantum information processor with trapped ions

et al. 2013

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Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of 40 Ca + ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire

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“…For simplicity, our general proof is given (in Sec. A) for r = 2 which, from a control standpoint, may be seen as a QL generalization of the splitting-subspace scheme for FTS introduced in [67]. However, the construction may be easily modified to improve the efficiency of the cooling action implemented by W. If S consists of N qudits, with…”

Section: Proposition Iii4 (Unitary Generation Property)mentioning

confidence: 99%

Exact stabilization of entangled states in finite time by dissipative quantum circuits

2017

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Open quantum systems evolving according to discrete-time dynamics are capable, unlike continuous-time counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of sequences of quantum channels subject to specified quasi-locality constraints, and determine conditions under which stabilization of a pure multipartite entangled state of interest may be exactly achieved in finite time. Special emphasis is devoted to characterizing scenarios where finite-time stabilization may be achieved robustly with respect to the order of the applied quantum maps, as suitable for unsupervised control architectures. We show that if a decomposition of the physical Hilbert space into virtual subsystems is found, which is compatible with the locality constraint and relative to which the target state factorizes, then robust stabilization may be achieved by independently cooling each component. We further show that if the same condition holds for a scalable class of pure states, a continuous-time quasilocal Markov semigroup ensuring rapid mixing can be obtained. Somewhat surprisingly, we find that the commutativity of the canonical parent Hamiltonian one may associate to the target state does not directly relate to its finite-time stabilizability properties, although in all cases where we can guarantee robust stabilization, a (possibly non-canonical) commuting parent Hamiltonian may be found. Beside graph states, quantum states amenable to finite-time robust stabilization include a class of universal resource states displaying two-dimensional symmetry-protected topological order, along with tensor network states obtained by generalizing a construction due to Bravyi and Vyalyi. Extensions to representative classes of mixed graph-product and thermal states are also discussed.

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

Cited by 14 publications

References 21 publications

Quantum resources for purification and cooling: fundamental limits and opportunities

Quantum resources for purification and cooling: fundamental limits and opportunities

A quantum information processor with trapped ions

Exact stabilization of entangled states in finite time by dissipative quantum circuits

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