Quantum Algorithm for Universal Implementation of the Projective Measurement of Energy

A B S T R A C TSir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of modern physics to study the foundations and applications of quantum physics. He is leading an effort to develop new technologies from quantum mechanics. In this collection of essays, we recall the time we were working with him as a postdoc or a PhD student and look at how the time with him has influenced our research.

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“…Recently, I am also interested in developing new quantum algorithms based on higher order quantum operations [135].…”

Section: Analysis Of Entanglement -Muraomentioning

confidence: 99%

Journeys from quantum optics to quantum technology

Barnett

Beige

Ekert

et al. 2017

Progress in Quantum Electronics

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“…The task is to simulate another channel  x using the channel  x as a subroutine. For example, the black box could implement a unitary gate U x and the task could be to build the control-unitary gate [97][98][99][100].…”

Section: Transforming Quantum Channelsmentioning

confidence: 99%

Optimal quantum networks and one-shot entropies

Chiribella

Ebler

2016

New J. Phys.

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We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined operationally in terms of interative tests set up by a verifier. We show that the optimal performance is equal to a max relative entropy, which quantifies the informativeness of the test. Building on this result, we extend the notion of conditional min-entropy from quantum states to quantum causal networks. The optimization method is illustrated in a number of applications, including the inversion, charge conjugation, and controlization of an unknown unitary dynamics. In the non-causal setting, we show a proof-of-principle application to the maximization of the winning probability in a non-causal quantum game. IntroductionAdvances in quantum communication [1][2][3] and in the integration of quantum hardware [4-8] are pushing towards the realization of networked quantum information systems, such as quantum communication networks [9-13] and distributed quantum computing [14][15][16]. Networks of interacting quantum devices are attracting interest also at the theoretical level, providing a framework for quantum games [17] and protocols [18][19][20], insights on the foundations of quantum mechanics [18, 21-23], a starting point for a general theory of Bayesian inference [24-31] and for the development of models of higher-order quantum computation [32][33][34].The network scenario motivates a new set of optimization problems, where the goal is not to optimize individual devices, but rather to optimize how different devices interact with one another. In many situations, the devices operate in a well-defined causal order-this is the case, for example, in the circuit model of quantum computing, where computations are implemented by sequences of gates [35,36]. Recently, researchers have started to investigate more general situations, where the causal order can be in a quantum superposition [20,33,34,[37][38][39] or can be indefinite in other more exotic ways, in principle compatible with quantum mechanics [34,[40][41][42][43][44][45]. In these new situations, optimizing quantum networks is important, for at least three reasons: First, in order to establish an advantage, one has to first find the optimal performances achievable in a definite causal order. Second, finding the maximum advantage requires an optimization over all non-causal networks. This is an essential step for assessing the power of the new, non-causal models of information processing. Third, identifying the ultimate performances achieved in the absence of pre-defined causal structure is expected to shed light on the interplay between quantum mechanics and spacetime.In this paper we develop a semidefinite programming (SDP) approach to the optimization of quantum networks. We start by analyzing scenarios with definite causal order, choosing an operational measure of performance, quantified by how much the network scores in a giv...

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“…The condition is that the operation acts trivially on a subspace of the total Hilbert space. This condition allows the scheme to avoid the no-go theorems described and discussed in the references [40][41][42], as shown in detail in [43]. The work presented in [39] demonstrates the equivalence between such a controlled operation and a sequence of a controlled-X a gate followed by the quantum operation and the same controlled-X a gate afterwards.…”

Section: The X a Gatementioning

confidence: 74%

A cold-atoms based processor for deterministic quantum computation with one qubit in intractably large Hilbert spaces

Mansell

Bergamini

2014

New J. Phys.

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We propose the use of Rydberg interactions and ensembles of cold atoms in mixed state for the implementation of a protocol for deterministic quantum computation with one quantum bit that can be readily operated in high dimensional Hilbert spaces. We propose an experimental test for the scalability of the protocol and to study the physics of discord. Furthermore, we explore the possibility of extending to non-trivial unitaries, such as those associated to many-body physics. Finally develop a scheme to add control to cold atom unitaries in order to facilitate their implementation in our proposal.At present, no single feature of the quantum world has been identified as the source of the computational enhancement, efficiency and speed-up of quantum protocols. Whilst entanglement is widely recognized as a key resource in quantum technology [1], an advantage over classical computing could be achieved without it [2] in the presence of non-classical correlations (discord). Experiments using few photonic qubits [3] have shown that some computational tasks can be efficiently solved even with no entanglement. As entanglement is

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Quantum Algorithm for Universal Implementation of the Projective Measurement of Energy

Cited by 17 publications

References 21 publications

Journeys from quantum optics to quantum technology

Journeys from quantum optics to quantum technology

Optimal quantum networks and one-shot entropies

A cold-atoms based processor for deterministic quantum computation with one qubit in intractably large Hilbert spaces

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