arXiv subjects

Leonardo Novo

Publications and source records attributed to Leonardo Novo.

At least 37 records · Page 2Linked to original sources

arXiv2024

Semi-device independent characterization of multiphoton indistinguishability

Multiphoton indistinguishability is a central resource for quantum enhancement in sensing and computation. Developing and certifying large scale photonic devices requires reliable and accurate characterization of this resource, preferably using methods that are robust against experimental errors. Here, we propose a set of methods for the characterization of multiphoton indistinguishability, based on measurements of bunching and photon number variance. Our methods are robust in a semi-device independent way, in the sense of being effective even when the interferometers are incorrectly dialled. We demonstrate the effectiveness of this approach using an advanced photonic platform comprising a quantum-dot single-photon source and a universal fully-programmable integrated photonic processor. Our results show the practical usefulness of our methods, providing robust certification tools that can be scaled up to larger systems.

quant-ph↗

arXiv2024

A central limit theorem for partially distinguishable bosons

The quantum central limit theorem derived by Cushen and Hudson provides the foundations for understanding how subsystems of large bosonic systems evolving unitarily do reach equilibrium. It finds important applications in the context of quantum interferometry, for example, with photons. A practical feature of current photonic experiments, however, is that photons carry their own internal degrees of freedom pertaining to, e.g., the polarization or spatiotemporal mode they occupy, which makes them partially distinguishable. The ensuing deviation from ideal indistinguishability is well known to have observable consequences, for example in relation with boson bunching, but an understanding of its role in bosonic equilibration phenomena is still missing. Here, we generalize the Cushen-Hudson quantum central limit theorem to encompass scenarios with partial distinguishability, implying an asymptotic convergence of the subsystem's reduced state towards a multimode Gaussian state defined over the internal degrees of freedom. While these asymptotic internal states may not be directly accessible, we show that particle number distributions carry important signatures of distinguishability, which may be used to diagnose experimental imperfections in large boson sampling experiments.

quant-ph↗

arXiv2024

Unitary-invariant witnesses of quantum imaginarity

Quantum theory is traditionally formulated using complex numbers. This imaginarity of quantum theory has been quantified as a resource with applications in discrimination tasks, pseudorandomness generation, and quantum metrology. Here we propose witnesses for imaginarity that are basis-independent, relying on measurements of unitary-invariant properties of sets of states. For 3 pure states, we completely characterize the invariant values attainable by quantum theory, and give a partial characterization for 4 pure states. We show that simple pairwise overlap measurements suffice to witness imaginarity of sets of 4 states, but not for sets of 3. Our witnesses are experimentally friendly, opening up a new path for measuring and using imaginarity as a resource.

quant-ph↗

arXiv2024

Gaussian boson sampling validation via detector binning

Gaussian boson sampling (GBS), a computational problem conjectured to be hard to simulate on a classical machine, has been at the forefront of recent years' experimental and theoretical efforts to demonstrate quantum advantage. The classical intractability of the sampling task makes validating these experiments a challenging and essential undertaking. In this paper, we propose binned-detector probability distributions as a suitable quantity to statistically validate GBS experiments employing photon-number-resolving detectors. We show how to compute such distributions by leveraging their connection with their respective characteristic function. The latter may be efficiently and analytically computed for squeezed input states as well as for relevant classical hypothesis like squashed states. Our scheme encompasses other validation methods based on marginal distributions and correlation functions. Additionally, it can accommodate various sources of noise, such as losses and partial distinguishability, a feature that have received limited attention within the GBS framework so far. We also illustrate how binned-detector probability distributions behave when Haar-averaged over all possible interferometric networks, extending known results for Fock boson sampling.

quant-ph↗

arXiv2022

Boson bunching is not maximized by indistinguishable particles

Boson bunching is amongst the most remarkable features of quantum physics. A celebrated example in optics is the Hong-Ou-Mandel effect, where the bunching of two photons arises from a destructive quantum interference between the trajectories where they both either cross a beam splitter or are reflected. This effect takes its roots in the indistinguishability of identical photons. Hence, it is generally admitted -- and experimentally verified -- that bunching vanishes as soon as photons can be distinguished, e.g., when they occupy distinct time bins or have different polarizations. Here we disproof this alleged straightforward link between indistinguishability and bunching by exploiting a recent finding in the theory of matrix permanents. We exhibit a family of optical circuits where the bunching of photons into two modes can be significantly boosted by making them partially distinguishable via an appropriate polarization pattern. This boosting effect is already visible in a 7-photon interferometric process, making the observation of this phenomenon within reach of current photonic technology. This unexpected behavior questions our understanding of multiparticle interference in the grey zone between indistinguishable bosons and classical particles.

quant-ph↗

arXiv2021

Quadratic speedup for spatial search by continuous-time quantum walk

Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a quadratic advantage over classical random walks has been an outstanding problem. Thus far, this advantage is obtained only for specific graphs or when a single node of the underlying graph is marked. In this article, we provide a new continuous-time quantum walk search algorithm that completely resolves this: our algorithm can find a marked node in any graph with any number of marked nodes, in a time that is quadratically faster than classical random walks. The overall algorithm is quite simple, requiring time evolution of the quantum walk Hamiltonian followed by a projective measurement. A key component of our algorithm is a purely analog procedure to perform operations on a state of the form $e^{-tH^2}|ψ\rangle$, for a given Hamiltonian $H$: it only requires evolving $H$ for time scaling as $\sqrt{t}$. This allows us to quadratically fast-forward the dynamics of a continuous-time classical random walk. The applications of our work thus go beyond the realm of quantum walks and can lead to new analog quantum algorithms for preparing ground states of Hamiltonians or solving optimization problems.

quant-ph↗

arXiv2021

Quantum advantage from energy measurements of many-body quantum systems

The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage demonstrations can be achieved for more physically-motivated sampling problems, related to measurements of physical observables. We focus on the problem of sampling the outcomes of an energy measurement, performed on a simple-to-prepare product quantum state -- a problem we refer to as energy sampling. For different regimes of measurement resolution and measurement errors, we provide complexity theoretic arguments showing that the existence of efficient classical algorithms for energy sampling is unlikely. In particular, we describe a family of Hamiltonians with nearest-neighbour interactions on a 2D lattice that can be efficiently measured with high resolution using a quantum circuit of commuting gates (IQP circuit), whereas an efficient classical simulation of this process should be impossible. In this high resolution regime, which can only be achieved for Hamiltonians that can be exponentially fast-forwarded, it is possible to use current theoretical tools tying quantum advantage statements to a polynomial-hierarchy collapse whereas for lower resolution measurements such arguments fail. Nevertheless, we show that efficient classical algorithms for low-resolution energy sampling can still be ruled out if we assume that quantum computers are strictly more powerful than classical ones. We believe our work brings a new perspective to the problem of demonstrating quantum advantage and leads to interesting new questions in Hamiltonian complexity.

quant-ph↗

arXiv2021

Floquet engineering of continuous-time quantum walks: towards the simulation of complex and next-to-nearest neighbor couplings

The formalism of continuous-time quantum walks on graphs has been widely used in the study of quantum transport of energy and information, as well as in the development of quantum algorithms. In experimental settings, however, there is limited control over the coupling coefficients between the different nodes of the graph (which are usually considered to be real-valued), thereby restricting the types of quantum walks that can be implemented. In this work, we apply the idea of Floquet engineering in the context of continuous-time quantum walks, i.e., we define periodically-driven Hamiltonians which can be used to simulate the dynamics of certain target continuous-time quantum walks. We focus on two main applications: i) simulating quantum walks that break time-reversal symmetry due to complex coupling coefficients; ii) increasing the connectivity of the graph by simulating the presence of next-to-nearest neighbor couplings. Our work provides explicit simulation protocols that may be used for directing quantum transport, engineering the dispersion relation of one-dimensional quantum walks or investigating quantum dynamics in highly connected structures.

quant-ph↗

arXiv2020

Finding a marked node on any graph by continuous-time quantum walk

Spatial search by discrete-time quantum walk can find a marked node on any ergodic, reversible Markov chain $P$ quadratically faster than its classical counterpart, i.e.\ in a time that is in the square root of the hitting time of $P$. However, in the framework of continuous-time quantum walks, it was previously unknown whether such general speed-up is possible. In fact, in this framework, the widely used quantum algorithm by Childs and Goldstone fails to achieve such a speedup. Furthermore, it is not clear how to apply this algorithm for searching any Markov chain $P$. In this article, we aim to reconcile the apparent differences between the running times of spatial search algorithms in these two frameworks. We first present a modified version of the Childs and Goldstone algorithm which can search for a marked element for any ergodic, reversible $P$ by performing a quantum walk on its edges. Although this approach improves the algorithmic running time for several instances, it cannot provide a generic quadratic speedup for any $P$. Secondly, using the framework of interpolated Markov chains, we provide a new spatial search algorithm by continuous-time quantum walk which can find a marked node on any $P$ in the square root of the classical hitting time. In the scenario where multiple nodes are marked, the algorithmic running time scales as the square root of a quantity known as the extended hitting time. Our results establish a novel connection between discrete-time and continuous-time quantum walks and can be used to develop a number of Markov chain-based quantum algorithms.

quant-ph↗

arXiv2020

On the optimality of spatial search by continuous-time quantum walk

One of the most important algorithmic applications of quantum walks is to solve spatial search problems. A widely used quantum algorithm for this problem, introduced by Childs and Goldstone [Phys. Rev. A 70, 022314 (2004)], finds a marked node on a graph of $n$ nodes via a continuous-time quantum walk. This algorithm is said to be optimal if it can find any of the nodes in $O(\sqrt{n})$ time. However, given a graph, no general conditions for the optimality of the algorithm are known and previous works demonstrating optimal quantum search for certain graphs required an instance-specific analysis. In fact, the demonstration of necessary and sufficient conditions a graph must fulfill for quantum search to be optimal has been a long-standing open problem. In this work, we make significant progress towards solving this problem. We derive general expressions, depending on the spectral properties of the Hamiltonian driving the walk, that predict the performance of this quantum search algorithm provided certain spectral conditions are fulfilled. Our predictions are valid, for example, for (normalized) Hamiltonians whose spectral gap is considerably larger than $n^{-1/2}$. This allows us to derive necessary and sufficient conditions for optimal quantum search in this regime, as well as provide new examples of graphs where quantum search is sub-optimal. In addition, by extending this analysis, we are also able to show the optimality of quantum search for certain graphs with very small spectral gaps, such as graphs that can be efficiently partitioned into clusters. Our results imply that, to the best of our knowledge, all prior results analytically demonstrating the optimality of this algorithm for specific graphs can be recovered from our general results.

quant-ph↗

arXiv2018

Environment-assisted analog quantum search

Two main obstacles for observing quantum advantage in noisy intermediate-scale quantum computers (NISQ) are the finite precision effects due to control errors, or disorders, and decoherence effects due to thermal fluctuations. It has been shown that dissipative quantum computation is possible in presence of an idealized fully-engineered bath. However, it is not clear, in general, what performance can be achieved by NISQ when internal bath degrees of freedom are not controllable. In this work, we consider the task of quantum search of a marked node on a complete graph of $n$ nodes in the presence of both static disorder and non-zero coupling to an environment. We show that, given fixed and finite levels of disorder and thermal fluctuations, there is an optimal range of bath temperatures that can significantly improve the success probability of the algorithm. Remarkably for a fixed disorder strength $σ$, the system relaxation time decreases for higher temperatures within a robust range of parameters. In particular, we demonstrate that for strong disorder, the presence of a thermal bath increases the success probability from $1/(n σ^2)$ to at least $1/2$. While the asymptotic running time is approximately maintained, the need to repeat the algorithm many times and issues associated with unitary over-rotations can be avoided as the system relaxes to an absorbing steady state. Furthermore, we discuss for what regimes of disorder and bath parameters quantum speedup is possible and mention conditions for which similar phenomena can be observed in more general families of graphs. Our work highlights that in the presence of static disorder, even non-engineered environmental interactions can be beneficial for a quantum algorithm.

quant-ph↗

arXiv2017

Optimal quantum spatial search on random temporal networks

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of $n$ nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs $G(n,p)$, where $p$ is the probability that any two given nodes are connected: after every time interval $τ$, a new graph $G(n,p)$ replaces the previous one. We prove analytically that for any given $p$, there is always a range of values of $τ$ for which the running time of the algorithm is optimal, i.e.\ $\mathcal{O}(\sqrt{n})$, even when search on the individual static graphs constituting the temporal network is sub-optimal. On the other hand, there are regimes of $τ$ where the algorithm is sub-optimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the non-trivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.

quant-ph↗

arXiv2017

Corrected quantum walk for optimal Hamiltonian simulation

We describe a method to simulate Hamiltonian evolution on a quantum computer by repeatedly using a superposition of steps of a quantum walk, then applying a correction to the weightings for the numbers of steps of the quantum walk. This correction enables us to obtain complexity which is the same as the lower bound up to double-logarithmic factors for all parameter regimes. The scaling of the query complexity is $O\left( τ\frac{\log\logτ}{\log\log\logτ} + \log(1/ε) \right)$ where $τ:= t\|H\|_{\max}d$, for $ε$ the allowable error, $t$ the time, $\|H\|_{\max}$ the max-norm of the Hamiltonian, and $d$ the sparseness. This technique should also be useful for improving the scaling of the Taylor series approach to simulation, which is relevant to applications such as quantum chemistry.

quant-ph↗

arXiv2016

Improved Hamiltonian simulation via a truncated Taylor series and corrections

We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an operator that corrects the weightings of the Taylor series. This way, the desired accuracy is achieved with an improvement in the overall complexity of the algorithm. This quantum simulation method is applicable to a wide range of Hamiltonians of interest, including to quantum chemistry problems.

quant-ph↗

arXiv2016

Spatial search by quantum walk is optimal for almost all graphs

The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work, we prove that for Erdös-Renyi random graphs, i.e.\ graphs of $n$ vertices where each edge exists with probability $p$, search by CTQW is \textit{almost surely} optimal as long as $p\geq \log^{3/2}(n)/n$. Consequently, we show that quantum spatial search is in fact optimal for \emph{almost all} graphs, meaning that the fraction of graphs of $n$ vertices for which this optimality holds tends to one in the asymptotic limit. We obtain this result by proving that search is optimal on graphs where the ratio between the second largest and the largest eigenvalue is bounded by a constant smaller than 1. Finally, we show that we can extend our results on search to establish high fidelity quantum communication between two arbitrary nodes of a random network of interacting qubits, namely to perform quantum state transfer, as well as entanglement generation. Our work shows that quantum information tasks typically designed for structured systems retain performance in very disordered structures.

quant-ph↗

arXiv2016

Quantum walks in synthetic gauge fields with 3D integrated photonics

There is great interest in designing photonic devices capable of disorder-resistant transport and information processing. In this work we propose to exploit 3D integrated photonic circuits in order to realize 2D discrete-time quantum walks in a background synthetic gauge field. The gauge fields are generated by introducing the appropriate phase shifts between waveguides. Polarization-independent phase shifts lead to an Abelian or magnetic field, a case we describe in detail. We find that, in the disordered case, the magnetic field enhances transport due to the presence of topologically protected chiral edge states which do not localize. Polarization-dependent phase shifts lead to effective non-Abelian gauge fields, which could be adopted to realize Rashba-like quantum walks with spin-orbit coupling. Our work introduces a flexible platform for the experimental study of multi-particle quantum walks in the presence of synthetic gauge fields, which paves the way towards topologically robust transport of many-body states of photons.

quant-ph↗

arXiv2015

Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs

Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that confine the dynamics to a smaller subspace of the full Hilbert space. In this work, we use invariant subspace methods, that can be computed systematically using Lanczos algorithm, to obtain the reduced set of states that encompass the dynamics of the problem at hand without the specific knowledge of underlying symmetries. First, we apply this method to obtain new instances of graphs where the spatial quantum search algorithm is optimal: complete graphs with broken links and complete bipartite graphs, in particular, the star graph. These examples show that regularity and high-connectivity are not needed to achieve optimal spatial search. We also show that this method considerably simplifies the calculation of quantum transport efficiencies. Furthermore, we observe improved efficiencies by removing a few links from highly symmetric graphs. Finally, we show that this reduction method also allows us to obtain an upper bound for the fidelity of a single qubit transfer on an XY spin network.

quant-ph↗

arXiv2015

Disorder-assisted quantum transport in suboptimal decoherence regimes

We investigate quantum transport in binary tree structures and in hypercubes for the disordered Frenkel-exciton Hamiltonian under pure dephasing noise. We compute the energy transport efficiency as a function of disorder and dephasing rates. We demonstrate that dephasing improves transport efficiency not only in the disordered case, but also in the ordered one. The maximal transport efficiency is obtained when the dephasing timescale matches the hopping timescale, which represent new examples of the Goldilocks principle at the quantum scale. Remarkably, we find that in weak dephasing regimes, away from optimal levels of environmental fluctuations, the average effect of increasing disorder is to improve the transport efficiency until an optimal value for disorder is reached. Our results suggest that rational design of the site energies statistical distributions could lead to better performances in transport systems at nanoscale when their natural environments are far from the optimal dephasing regime.

quant-ph↗