arXiv subjects

F. Petruccione

Publications and source records attributed to F. Petruccione.

At least 19 recordsLinked to original sources

arXiv2026

Faster Quantum Simulation Of Markovian Open Quantum Systems Via Randomisation

When simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum systems, this has been achieved using first and second-order Trotter-Suzuki product formulas or probabilistic algorithms. In this work, we introduce novel non-probabilistic algorithms for simulating Markovian open quantum systems using randomisation. Our methods, including first and second-order randomised Trotter-Suzuki formulas and the QDRIFT channel, not only maintain the physicality of the system's evolution but also enhance the scalability and precision of quantum simulations. We derive error bounds and step count limits for these techniques, bypassing the need for the mixing lemma typically employed in Hamiltonian simulation proofs. Furthermore, we implement these randomised algorithms using Classical Sampling (CS), demonstrating their gate complexity advantages over deterministic TS product formulas. This work systematically extends powerful randomisation techniques from Hamiltonian simulation to the general setting of Markovian open quantum systems, highlighting their potential to enable faster and more accurate simulations.

quant-ph↗

arXiv2026

Optimising Trotter-Suzuki Simulations of Markovian Open Quantum Systems via Classical Search

Simulating an open quantum system on a digital quantum computer often involves the use of Trotter-Suzuki (TS) Product Formulas (PF) to approximate the system's time evolution. Precise estimates for the required number of Trotter steps (and hence the overall gate count) can be crucial for minimising the computational cost of these methods. Building on established theoretical guarantees, we derive analytic bounds for the First- and Second-Order Deterministic and Randomised TS-PF, directly relating the number of Trotter steps to the model parameters, evolution time and precision. These bounds enable concrete resource estimation for each method. We then present a computationally efficient classical algorithm that uses diamond norm estimates of individual Liouvillian terms and a binary search to significantly reduce the Trotter steps required for a target precision. Our numerical results on two prototypical models - an XX-Spin Chain with boundary driving and local dephasing, and a Transverse-Field Ising Model - show that the theoretical (analytic) bounds are often overly conservative, whereas the empirical (optimised) bounds yield a significantly smaller number of Trotter steps for the same precision. Among the methods investigated, the Second-Order Randomised TS-PF typically achieves the lowest resource demands, especially for larger systems. These findings emphasise the significance of empirical bounding strategies in achieving more resource-efficient simulations of Markovian open quantum systems.

quant-ph↗

arXiv2025

Tighter Error Bounds for the qDRIFT Algorithm

Randomized algorithms such as qDRIFT provide an efficient framework for quantum simulation by sampling terms from a decomposition of the system's generator. However, existing error bounds for qDRIFT scale quadratically with the norm of the generator, limiting their efficiency for large-scale closed or open quantum system simulation. In this work, we refine the qDRIFT error bound by incorporating Jensen's inequality and a careful treatment of the integral form of the error. This yields an improved scaling that significantly reduces the number of steps required to reach a fixed simulation accuracy. Our result applies to both closed and open quantum systems, and we explicitly recover the improved bound in the Hamiltonian case. To demonstrate the practical impact of this refinement, we apply it to three settings: quantum chemistry simulations, dissipative transverse field Ising models, and Hamiltonian encoding of classical data for quantum machine learning. In each case, our bound leads to a substantial reduction in gate counts, highlighting its broad utility in enhancing randomized simulation techniques.

quant-ph↗

arXiv2021

Roles of quantum coherences in thermal machines

Some of the oldest and most important applications of thermodynamics are operations of refrigeration as well as production of useful energy. Part of the efforts to understand and develop thermodynamics in the quantum regime have been focusing on harnessing quantum effects to such operations. In this review we present the recent developments regarding the role of quantum coherences in the performances of thermal machines --the devices realising the above thermodynamic operations. While this is known to be an intricate subject, in part because being largely model-dependent, the review of the recent results allow us to identify some general tendencies and to suggest some future directions.

quant-ph↗

arXiv2020

Experimental investigation of Markovian and non-Markovian channel addition

The study of memory effects in quantum channels helps in developing characterization methods for open quantum systems and strategies for quantum error correction. Two main sets of channels exist, corresponding to system dynamics with no memory (Markovian) and with memory (non-Markovian). Interestingly, these sets have a non-convex geometry, allowing one to form a channel with memory from the addition of memoryless channels and vice-versa. Here, we experimentally investigate this non-convexity in a photonic setup by subjecting a single qubit to a convex combination of Markovian and non-Markovian channels. We use both divisibility and distinguishability as criteria for the classification of memory effects, with associated measures. Our results highlight some practical considerations that may need to be taken into account when using memory criteria to study system dynamics given by the addition of Markovian and non-Markovian channels in experiments.

quant-ph↗

arXiv2019

Energetic and entropic effects of bath-induced coherences

The unavoidable interaction of a quantum system with its surrounding (bath) is not always detrimental for quantum properties. For instance, under some specific conditions (that we identify as indistinguishability), a many-body system can gain internal coherences thanks to the interaction with its bath. The most famous consequence of this phenomenon is superradiance. Beyond that, the thermodynamic effects on the system of these bath-induced coherences have been mostly unexplored. We show here, for a simple and common system (a pair of two-level systems), that the energetic and entropic impacts can indeed be dramatic and diverse, including amplification of the action of the bath but also its mitigation. Our results can be tested experimentally. They suggest that bath-induced coherences can be harnessed to enhance thermodynamic tasks, opening up interesting perspectives for thermal machines, quantum battery charging, natural or artificial energy harvesting systems, and state preparation and protection.

quant-ph↗

arXiv2019

Quantum coherence, many-body correlations, and non-thermal effects for autonomous thermal machines

One of the principal objectives of quantum thermodynamics is to explore quantum effects and their potential beneficial role in thermodynamic tasks like work extraction or refrigeration. So far, even though several papers have already shown that quantum effect could indeed bring quantum advantages, a global and deeper understanding is still lacking. Here, we extend previous models of autonomous machines to include quantum batteries made of arbitrary systems of discrete spectrum. We establish their actual efficiency, which allows us to derive an efficiency upper bound, called maximal achievable efficiency, shown to be always achievable, in contrast with previous upper bounds based only on the Second Law. Such maximal achievable efficiency can be expressed simply in term of the it apparent temperature of the quantum battery. This important result appears to be a powerful tool to understand how quantum features like coherence but also many-body correlations and non-thermal population distribution can be harnessed to increase the efficiency of thermal machines.

quant-ph↗

arXiv2018

Projection operator based expansion of the evolution operator

The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schrödinger equation allows the derivation of an alternative expression for the evolution operator, which differs from the traditional chronological exponent. An appropriate choice of projection operators results in the possibility of studying the diagonal and non-diagonal elements of the evolution operator separately. The suggested expression implies a particular form of perturbation expansion, which leads to a new formula for the short time dynamics. The new kind of perturbation expansion can be used to improve the accuracy of the usual chronological exponent significantly. The evolution operator for any arbitrary time can be efficiently recovered using the semigroup properties. The method is illustrated by two examples, namely the dynamics of a three-level system in two nonresonant laser fields and the calculation of the partition function of a finite XY-spin chain.

quant-ph↗

arXiv2018

Stochastic wave-function unravelling of the generalized Lindblad equation

We investigate generalized non-Markovian stochastic Schroeodinger equations (SSEs), driven by a multidimensional counting process and multidimensional Brownian motion introduced by A. Barchielli and C. Pellegrini [J. Math. Phys. 51, 112104 (2010)]. We show, that these SSEs can be translated in a non-linear form, which can be efficiently simulated. The simulation is illustrated by the model of a two-level system in a structured bath and the results of the simulations are compared with the exact solution of the generalized master equation.

quant-ph↗

arXiv2018

Probing decoherence in plasmonic waveguides in the quantum regime

We experimentally investigate the decoherence of single surface plasmon polaritons in metal stripe waveguides. In our study we use a Mach-Zehnder configuration previously considered for measuring decoherence in atomic, electronic and photonic systems. By placing waveguides of different length in one arm we are able to measure the amplitude damping time T_1 = 1.90 +/- 0.01 x 10^-14 s, pure phase damping time T_2^* = 11.19 +/- 4.89 x 10^-14 s and total phase damping time T_2 = 2.83 +/- 0.32 x 10^-14 s. We find that decoherence is mainly due to amplitude damping and thus loss arising from inelastic electron and photon scattering plays the most important role in the decoherence of plasmonic waveguides in the quantum regime. However, pure phase damping is not completely negligible. The results will be useful in the design of plasmonic waveguide systems for carrying out phase-sensitive quantum applications, such as quantum sensing. The probing techniques developed may also be applied to other plasmonic nanostructures, such as those used as nanoantennas, as unit cells in metamaterials and as nanotraps for cold atoms.

quant-ph↗

arXiv2017

Simulation of single-qubit open quantum systems

A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single qubit quantum channels $\{T_t\}$ specified by a generator $\mathcal{L}$. This algorithm requires only $\mathcal{O}\big((||\mathcal{L}||_{(1\rightarrow 1)} t)^{3/2}/ε^{1/2} \big)$ single qubit and CNOT gates and approximates the channel $T_t = e^{t\mathcal{L}}$ up to chosen accuracy $ε$. Inspired by developments in Hamiltonian simulation, a decomposition and recombination technique is utilised which allows for the exploitation of recently developed methods for the approximation of arbitrary single-qubit channels. In particular, as a result of these methods the algorithm requires only a single ancilla qubit, the minimal possible dilation for a non-unitary single-qubit quantum channel.

quant-ph↗

arXiv2016

Digital quantum simulation of many-body non-Markovian dynamics

We present an algorithmic method for the digital quantum simulation of many-body locally indivisible non-Markovian open quantum systems. It consists of two parts: firstly, a Suzuki-Lie-Trotter decomposition of the global system propagator into the product of subsystem propagators, which may not be quantum channels, and secondly, an algorithmic procedure for the implementation of the subsystem propagators through unitary operations and measurements on a dilated space. By providing rigorous error bounds for the relevant Suzuki-Lie-Trotter decomposition, we are able to analyze the efficiency of the method, and connect it with an appropriate measure of the local indivisibility of the system. In light of our analysis, the proposed method is expected to be experimentally achievable for a variety of interesting cases.

quant-ph↗

arXiv2015

Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices

Lattice models of fermions, bosons, and spins have long served to elucidate the essential physics of quantum phase transitions in a variety of systems. Generalizing such models to incorporate driving and dissipation has opened new vistas to investigate nonequilibrium phenomena and dissipative phase transitions in interacting many-body systems. We present a framework for the treatment of such open quantum lattices based on a resummation scheme for the Lindblad perturbation series. Employing a convenient diagrammatic representation, we utilize this method to obtain relevant observables for the open Jaynes-Cummings lattice, a model of special interest for open-system quantum simulation. We demonstrate that the resummation framework allows us to reliably predict observables for both finite and infinite Jaynes-Cummings lattices with different lattice geometries. The resummation of the Lindblad perturbation series can thus serve as a valuable tool in validating open quantum simulators, such as circuit-QED lattices, currently being investigated experimentally.

quant-ph↗

arXiv2014

An introduction to quantum machine learning

Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT industry. In the last couple of years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. Ideas range from running computationally costly algorithms or their subroutines efficiently on a quantum computer to the translation of stochastic methods into the language of quantum theory. This contribution gives a systematic overview of the emerging field of quantum machine learning. It presents the approaches as well as technical details in an accessable way, and discusses the potential of a future theory of quantum learning.

quant-ph↗

arXiv2014

The quest for a Quantum Neural Network

With the overwhelming success in the field of quantum information in the last decades, the "quest" for a Quantum Neural Network (QNN) model began in order to combine quantum computing with the striking properties of neural computing. This article presents a systematic approach to QNN research, which so far consists of a conglomeration of ideas and proposals. It outlines the challenge of combining the nonlinear, dissipative dynamics of neural computing and the linear, unitary dynamics of quantum computing. It establishes requirements for a meaningful QNN and reviews existing literature against these requirements. It is found that none of the proposals for a potential QNN model fully exploits both the advantages of quantum physics and computing in neural networks. An outlook on possible ways forward is given, emphasizing the idea of Open Quantum Neural Networks based on dissipative quantum computing.

quant-ph↗

arXiv2014

Open Quantum Random Walks

A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains. We explore the "quantum trajectory" point of view on these quantum random walks, that is, we show that measuring the position of the particle after each time- step gives rise to a classical Markov chain, on the lattice times the state space of the particle. This quantum trajectory is a simulation of the master equation of the quantum random walk. The physical pertinence of such quantum random walks and the way they can be concretely realized is discussed. Differences and connections with the already well-known quantum random walks, such as the Hadamard random walk, are established.

quant-ph↗

arXiv2014

Open Quantum Walks: a short introduction

The concept of open quantum walks (OQW), quantum walks exclusively driven by the interaction with the external environment, is reviewed. OQWs are formulated as discrete completely positive maps on graphs. The basic properties of OQWs are summarised and new examples of OQWs on $\mathbb{Z}$ and their simulation by means of quantum trajectories are presented.

quant-ph↗

arXiv2014

Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators

A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.

quant-ph↗