arXiv subjects

Francesco Petruccione

Publications and source records attributed to Francesco Petruccione.

At least 73 records · Page 4Linked to original sources

arXiv2020

Convex combinations of CP-divisible Pauli channels that are not semigroups

We study the memory property of the channels obtained by convex combinations of Markovian channels that are not necessarily quantum dynamical semigroups (QDSs). In particular, we characterize the geometry of the region of (non-)Markovian channels obtained by the convex combination of the three Pauli channels, as a function of deviation from the semigroup form in a family of channels. The regions are highly convex, and interestingly, the measure of the non-Markovian region shrinks with greater deviation from the QDS structure for the considered family, underscoring the counterintuitive nature of (non-)Markovianity under channel mixing.

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arXiv2020

Collective heat capacity for quantum thermometry and quantum engine enhancements

The performances of quantum thermometry in thermal equilibrium together with the output power of certain class of quantum engines share a common characteristic: both are determined by the heat capacity of the probe or working medium. After noticing that the heat capacity of spin ensembles can be significantly modified by collective coupling with a thermal bath, we build on the above observation to investigate the respective impact of such collective effect on quantum thermometry and quantum engines. We find that the precision of the temperature estimation is largely increased at high temperatures, reaching even the Heisenberg scaling - inversely proportional to the number of spins. For Otto engines operating close to the Carnot efficiency, collective coupling always enhances the output power. Some tangible experimental platforms are suggested.

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arXiv2020

Quantum-enhanced analysis of discrete stochastic processes

Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number of realizations increases exponentially with the number of time steps, and importance sampling is often required to reduce the variance. We propose a quantum algorithm for calculating the characteristic function of a DSP, which completely defines its probability distribution, using the number of quantum circuit elements that grows only linearly with the number of time steps. The quantum algorithm takes all stochastic trajectories into account and hence eliminates the need of importance sampling. The algorithm can be further furnished with the quantum amplitude estimation algorithm to provide quadratic speed-up in sampling. Both of these strategies improve variance beyond classical capabilities. The quantum method can be combined with Fourier approximation to estimate an expectation value of any integrable function of the random variable. Applications in finance and correlated random walks are presented to exemplify the usefulness of our results. Proof-of-principle experiments are performed using the IBM quantum cloud platform.

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arXiv2020

Compressed Sensing Tomography for qudits in Hilbert spaces of non-power-of-two dimensions

The techniques of low-rank matrix recovery were adapted for Quantum State Tomography (QST) previously by D. Gross et al. [Phys. Rev. Lett. 105, 150401 (2010)], where they consider the tomography of $n$ spin-$1/2$ systems. For the density matrix of dimension $d = 2^n$ and rank $r$ with $r \ll 2^n$, it was shown that randomly chosen Pauli measurements of the order $O(dr \log(d)^2)$ are enough to fully reconstruct the density matrix by running a specific convex optimization algorithm. The result utilized the low operator-norm of the Pauli operator basis, which makes it `incoherent' to low-rank matrices. For quantum systems of dimension $d$ not a power of two, Pauli measurements are not available, and one may consider using SU($d$) measurements. Here, we point out that the SU($d$) operators, owing to their high operator norm, do not provide a significant savings in the number of measurement settings required for successful recovery of all rank-$r$ states. We propose an alternative strategy, in which the quantum information is swapped into the subspace of a power-two system using only $\textrm{poly}(\log(d)^2)$ gates at most, with QST being implemented subsequently by performing $O(dr \log(d)^2)$ Pauli measurements. We show that, despite the increased dimensionality, this method is more efficient than the one using SU($d$) measurements.

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arXiv2020

Influence of coincidence detection through free-space atmospheric turbulence using partial spatial coherence

The development of a quantum network relies on the advances of hybrid systems which includes ground to ground communication. However, the atmospheric turbulence of the environment poses a severe challenge to the optical quantum link. In this paper, we outline a theoretical and experimental investigation of the influence of atmospheric turbulence on the coincidence detection of the entangled photon pairs using a fully and partially spatially coherent pump beam. A spatial light modulator is encoded with Kolmogorov model to mimic the atmospheric turbulence strength. The results show that the photon pairs generated using a partially spatially coherent pump are more robust towards varying atmospheric turbulence strengths than the photon pairs produced by a fully spatially coherent pump beam.

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arXiv2020

Quantum Metamaterials: Applications in quantum information science

Metamaterials are artificially engineered periodic structures with exceptional optical properties that are not found in conventional materials. However, this definition of metamaterials can be extended if we introduce a quantum degree of freedom by adding some quantum elements (e.g quantum dots, cold atoms, Josephson junctions, molecules). Quantum metamaterials can then be defined as artificially engineered nanostructures made up of quantum elements. Furthermore, they exhibit controllable quantum states, maintain quantum coherence for times much higher than the transversal time of the electromagnetic signal. Metamaterials have been used to realised invisibility cloaking, super-resolution, energy harvesting, and sensing. Most of these applications are performed in the classical regime. Of recent, metamaterials have gradually found their way into the quantum regime, particularly to quantum sensing and quantum information processing. The use of quantum metamaterials for quantum information processing is still new and rapidly growing. In quantum information processing, quantum metamaterials have enabled the control and manipulation of quantum states, single photon generation, creating quantum entanglement, quantum states switching, quantum search algorithm, quantum state engineering tasks, and many more. In this work, we briefly review the theory, fabrication and applications of quantum metamaterials to quantum information processing.

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arXiv2020

Convex Combinations of Pauli Semigroups: Geometry, Measure and an Application

Finite-time Markovian channels, unlike their infinitesimal counterparts, do not form a convex set. As a particular instance of this observation, we consider the problem of mixing the three Pauli channels, conservatively assumed to be quantum dynamical semigroups, and fully characterize the resulting ``Pauli simplex.'' We show that neither the set of non-Markovian (completely positive indivisible) nor Markovian channels is convex in the Pauli simplex, and that the measure of non-Markovian channels is about 0.87. All channels in the Pauli simplex are P divisible. A potential application in the context of quantum resource theory is also discussed.

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arXiv2020

The theory of the quantum kernel-based binary classifier

Binary classification is a fundamental problem in machine learning. Recent development of quantum similarity-based binary classifiers and kernel method that exploit quantum interference and feature quantum Hilbert space opened up tremendous opportunities for quantum-enhanced machine learning. To lay the fundamental ground for its further advancement, this work extends the general theory of quantum kernel-based classifiers. Existing quantum kernel-based classifiers are compared and the connection among them is analyzed. Focusing on the squared overlap between quantum states as a similarity measure, the essential and minimal ingredients for the quantum binary classification are examined. The classifier is also extended concerning various aspects, such as data type, measurement, and ensemble learning. The validity of the Hilbert-Schmidt inner product, which becomes the squared overlap for pure states, as a positive definite and symmetric kernel is explicitly shown, thereby connecting the quantum binary classifier and kernel methods.

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arXiv2020

Lazy Open Quantum Walks

Open quantum walks (OQWs) describe a quantum walker on an underlying graph whose dynamics is purely driven by dissipation and decoherence. Mathematically, they are formulated as completely positive trace preserving (CPTP) maps on the space of density matrices for the walker on the graph. Any microscopically derived OQW must include the possibility of remaining on the same site on the graph when the map is applied. We extend the CPTP map to describe a lazy OQW. We derive a central limit theorem for lazy OQWs on a $d$-dimensional lattice, where the distribution converges to a Gaussian. We show that the properties of this Gaussian computed using conventional methods agree with the general formulas derived from our central limit theorem.

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arXiv2020

A Generalized Quantum Optical Scheme for Implementing Open Quantum Walks

Open quantum walks (OQWs) are a new type of quantum walks which are entirely driven by the dissipative interaction with external environments and are formulated as completely positive trace-preserving maps on graphs. A generalized quantum optical scheme for implementing OQWs that includes non-zero temperature of the environment is suggested. In the proposed quantum optical scheme, a two-level atom plays the role of the "walker", and the Fock states of the cavity mode correspond to the lattice sites for the "walker". Using the small unitary rotations approach the effective dynamics of the system is shown to be an OQW. For the chosen set of parameters, an increase in the temperature of the environment causes the system to reach the asymptotic distribution much faster compared to the scheme proposed earlier where the temperature of the environment is zero. For this case the asymptotic distribution is given by a steady Gaussian distribution.

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arXiv2020

Quantum classifier with tailored quantum kernel

Kernel methods have a wide spectrum of applications in machine learning. Recently, a link between quantum computing and kernel theory has been formally established, opening up opportunities for quantum techniques to enhance various existing machine learning methods. We present a distance-based quantum classifier whose kernel is based on the quantum state fidelity between training and test data. The quantum kernel can be tailored systematically with a quantum circuit to raise the kernel to an arbitrary power and to assign arbitrary weights to each training data. Given a specific input state, our protocol calculates the weighted power sum of fidelities of quantum data in quantum parallel via a swap-test circuit followed by two single-qubit measurements, requiring only a constant number of repetitions regardless of the number of data. We also show that our classifier is equivalent to measuring the expectation value of a Helstrom operator, from which the well-known optimal quantum state discrimination can be derived. We demonstrate the proof-of-principle via classical simulations with a realistic noise model and experiments using the IBM quantum computer.

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arXiv2020

Dynamics of quantum correlations in a Qubit-Oscillator system interacting via a dissipative bath

The entanglement dynamics in a bipartite system consisting of a qubit and a harmonic oscillator interacting only through their coupling with the same bath is studied. The considered model assumes that the qubit is coupled to the bath via the Jaynes-Cummings interaction, whilst the position of the oscillator is coupled to the position of the bath via a dipole interaction. We give a microscopic derivation of the Gorini-Kossakowski-Sudarshan-Lindblad equation for the considered model. Based on the Kossakowski Matrix, we show that non-classical correlations including entanglement can be generated by the considered dynamics. We then analytically identify specific initial states for which entanglement is generated. This result is also supported by our numerical simulations.

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arXiv2020

On quantum ensembles of quantum classifiers

Quantum machine learning seeks to exploit the underlying nature of a quantum computer to enhance machine learning techniques. A particular framework uses the quantum property of superposition to store sets of parameters, thereby creating an ensemble of quantum classifiers that may be computed in parallel. The idea stems from classical ensemble methods where one attempts to build a stronger model by averaging the results from many different models. In this work, we demonstrate that a specific implementation of the quantum ensemble of quantum classifiers, called the accuracy-weighted quantum ensemble, can be fully dequantised. On the other hand, the general quantum ensemble framework is shown to contain the well-known Deutsch-Jozsa algorithm that notably provides a quantum speedup and creates the potential for a useful quantum ensemble to harness this computational advantage.

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arXiv2019

Thermodynamics from indistinguishability: mitigating and amplifying the effects of the bath

Rich quantum effects emerge when several quantum systems are indistinguishable from the point of view of the bath they interact with. In particular, delocalised excitations corresponding to coherent superposition of excited states appear and change drastically the dynamics and steady state of the systems. Such phenomena, which are central mechanisms of superradiance, present interesting properties for thermodynamics and potentially other quantum technologies. Indeed, a recent paper [Phys. Rev. A 99, 052105 (2019)] studies these properties in a pair of indistinguishable two-level systems and points out surprising effects of mitigation and amplification of the bath's action on the energy and entropy of the pair. Here, we generalise the study to ensembles of arbitrary number of spins of arbitrary size (i.e. dimension). We confirm that the previously uncovered mitigation and amplification effects remain, but also that they become more and more pronounced with growing number of spins and growing spin size. Moreover, we find that the free energy variation and the entropy production associated with the bath-driven dissipation are systematically reduced, formalising the idea of mitigation of the bath's action. Most remarkably, the combination of mitigation effects from two baths at different temperatures can result in amplifying their action. This is illustrated with cyclic thermal machines, and leads to large power enhancements. The reduction of irreversibility is also an interesting aspect since irreversibility is known to limit the performance of thermodynamic tasks. The above findings might also lead to interesting applications in collective work extraction, quantum battery charging, state protection, light harvesting devices, quantum biology, but also for the study of entropy production. Moreover, some experimental realisations and observations suggest that such effects are within reach.

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arXiv2019

Heat flow reversals without reversing the arrow of time: the role of internal quantum coherences and correlations

One of the stunning consequences of quantum correlations in thermodynamics is the reversal of the arrow of time, recently shown experimentally in [K. Micadei, et al., Nat. Commun. 10:2456 (2019)], and manifesting itself by a reversal of the heat flow (from the cold system to the hot one). Here, we show that contrary to what could have been expected, heat flow reversal can happen without reversal of the arrow of time. Moreover, contrasting with previous studies, no initial correlations between system and bath is required. Instead, the heat flow reversal only relies on internal quantum coherences or correlations, which provides practical advantages over previous schemes: one does not need to have access to the bath in order to reverse the heat flow. The underlying mechanism is explained and shown to stem from the collective system-bath coupling and the impact of non-energetic coherences (coherences between degenerate energy levels) on apparent temperatures. The phenomenon is first uncovered in a broad framework valid for diverse quantum systems containing energy degeneracy. By the end of the paper, aiming at experimental realisations, more quantitative results are provided for a pair of two-level systems. Finally, as a curiosity, we mention that our scheme can be adapted as a correlations-to-energy converter, which have the particularity to be able to operate at constant entropy, similarly to ideal work sources.

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arXiv2019

Quantum effects in the brain: A review

In the mid-1990s it was proposed that quantum effects in proteins known as microtubules play a role in the nature of consciousness. The theory was largely dismissed due to the fact that quantum effects were thought unlikely to occur in biological systems, which are warm and wet and subject to decoherence. However, the development of quantum biology now suggests otherwise. Quantum effects have been implicated in photosynthesis, a process fundamental to life on earth. They are also possibly at play in other biological processes such as avian migration and olfaction. The microtubule mechanism of quantum consciousness has been joined by other theories of quantum cognition. It has been proposed that general anaesthetic, which switches off consciousness, does this through quantum means, measured by changes in electron spin. The tunnelling hypothesis developed in the context of olfaction has been applied to the action of neurotransmitters. A recent theory outlines how quantum entanglement between phosphorus nuclei might influence the firing of neurons. These, and other theories, have contributed to a growing field of research that investigates whether quantum effects might contribute to neural processing. This review aims to investigate the current state of this research and how fully the theory is supported by convincing experimental evidence. It also aims to clarify the biological sites of these proposed quantum effects and how progress made in the wider field of quantum biology might be relevant to the specific case of the brain.

q-bio.NC↗

arXiv2019

Parallel quantum trajectories via forking for sampling without redundancy

The computational cost of preparing a quantum state can be substantial depending on the structure of data to be encoded. Many quantum algorithms require repeated sampling to find the answer, mandating reconstruction of the same input state for every execution of an algorithm. Thus, the advantage of quantum computation can diminish due to redundant state initialization. We present a framework based on quantum forking that bypasses this fundamental issue and expedites a family of tasks that require sampling from independent quantum processes. Quantum forking propagates an input state to multiple quantum trajectories in superposition, and a weighted power sum of individual results from each trajectories is obtained in one measurement via quantum interference. The significance of our work is demonstrated via applications to implementing non-unitary quantum channels, studying entanglement and benchmarking quantum control. A proof-of-principle experiment is implemented on the IBM and Rigetti quantum cloud platforms.

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arXiv2019

Measure of not-completely-positive qubit maps: the general case

We show that the set of not-completely-positive (NCP) maps is unbounded, unless further assumptions are made. This is done by first proposing a reasonable definition of a valid NCP map, which is nontrivial because NCP maps may lack a full positivity domain. The definition is motivated by specific examples. We prove that for valid NCP maps, the eigenvalue spectrum of the corresponding dynamical matrix is not bounded. Based on this, we argue that in general the volume measure of qubit maps, including NCP maps, is not well defined.

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