Research talks will be 25 minutes + 5 minutes questions.

Leonardo Ratini

**Wave Function Adapted Hamiltonians for Quantum Computing**

The use of the variational quantum eigensolver (VQE) for quantum chemistry is one of the most promising applications for noisy intermediate-scale quantum (NISQ) devices. A major limitation is represented by the need to build compact and shallow circuit ansatzes having the variational ﬂexibility to catch the complexity of the electronic structure problem. To alleviate this drawback, we introduce a modiﬁed VQE scheme in which the form of the molecular Hamiltonian is adapted to the circuit ansatz through an optimization procedure. Exploiting the invariance of the Hamiltonian by molecular orbital rotations, we can optimize it using gradients that can be calculated without signiﬁcant computational overload. The proposed method, named Wavefunction Adapted Hamiltonian Through Orbital Rotation (WAHTOR), has been applied to small molecules in numerical state vector simulations. The results demonstrate that, at variance with standard VQE, the method is less dependent on circuit topology and less prone to be trapped into high-energy local minima. It is able to recover a signiﬁcant amount of electron correlation even with only empirical ansatzes with shallow circuit depth. Noisy calculations demonstrate the robustness and feasibility of the proposed methodology and indicate the hardware requirements to eﬀectively apply the procedure using forthcoming NISQ devices.

Karen Hovhannisyan

**Long-time equilibration can determine transient thermality**

When two initially thermal many-body systems start interacting strongly, their transient states quickly become non-Gibbsian, even if the systems eventually equilibrate. To see beyond this apparent lack of structure during the transient regime, we use a refined notion of thermality, which we call *g*-local. A system is *g*-locally thermal if the states of all its small subsystems are marginals of global thermal states. We numerically demonstrate for two harmonic lattices that whenever the total system equilibrates in the long run, each lattice remains *g*-locally thermal at all times, including the transient regime. This is true even when the lattices have long-range interactions within them. In all cases, we find that the equilibrium is described by the generalized Gibbs ensemble, with 3D lattices requiring special treatment due to their extended set of conserved charges. We compare our findings with the well-known two-temperature model. While its standard form is not valid beyond weak coupling, we show that at strong coupling it can be partially salvaged by adopting the concept of a *g*-local temperature.

Claudio Sanavio

**Support Vector Machine for three-qubit entanglement classification**

Although entanglement is a basic resource for reaching quantum advantange in many computation and information protocols, we lack a universal recipe for detecting it, with analytical results obtained for low dimensional systems and few special cases of higher dimensional systems. In this work, we use a machine learning algorithm, the support vector machine with polynomial kernel, to classify separable and entangled states. We apply it to two-qubit and three-qubit systems, and we show that, after training, the support vector machine is able to recognize if a random state is entangled with an accuracy up to 96% for the two-qubit system and up to 99% for the three-qubit system. We also describe why and in what regime the support vector machine algorithm is able to implement the evaluation of an entanglement witness operator applied to many copies of the state, and we describe how we can translate this procedure into a quantum circuit.

Seongjin Ahn

**Towards exact ultrashort quantum gates**

In order to properly perform an algorithm requiring at least thousands of qubits and correspondingly many operations, e.g. factorization of a 2048-bit semiprime, it is necessary to prepare gates with sufficiently high fidelity, at least above the fault-tolerance threshold. Furthermore, achieving a fidelity even higher than this threshold is important for reducing the overhead in resources such as additional qubits and gate operations for quantum error corrections. There are basically two factors which limit the fidelity: one is a control error due to an inaccuracy of a coherent control of qubits, the other is a decoherence error. In order to reduce the decoherence error, one can use fast gates. However, due to the highly-diabatic and broadband/ultrabroadband nature of a fast control pulse, it is nontrivial to accurately control qubits in this fast-driving regime. Finding a way to perform an accurate coherent control at a sufficiently short timescale is a challenging but essential goal for entering the era of large-scale quantum computations. We apply a unitary perturbation theory [1] to find an optimal control pulse that results in a high-fidelity quantum X gate. We start at the limit of an infinitesimally short pulse, where an exact X gate can be implemented by fixing the pulse area to π. Since the pulse cannot be arbitrarily short, limited either by practical implementation issues or by a finite bandwidth set to prevent excitation outside of the subspace of qubits, the error due to a finite pulse duration arises. This error has to be understood and brought under control for its mitigation. We identify the error in the orders of the pulse duration and determine how each error term depends on the pulse shape. We then find pulse shapes which eliminate the error terms up to the first few orders and observe an order-by-order enhancement of fidelity.

[1] Moskalenko et al., Phys. Rep. 672, 1-82, (2017).

Kyrylo Simonov

**Indefinite causality in quantum mechanics and its thermodynamic applications**

The nature of causality remains one of the key puzzles in science. In quantum theory, the causal structure is not subject to quantum uncertainty and plays rather a background role. One can ask whether the background causal structure can be dropped, for example, by respecting causality only locally. Such scenarios of local validity of quantum theory while relaxing the global definite causal order of operations can be described via the machinery of process matrices. An important example of scenarios of this kind is quantum SWITCH, a process realizing a quantum superposition of causal orders of operations. Looking for the possible applications of quantum SWITCH has been the subject of growing interest in the scientific community as it could provide communication and computational resources not realizable via standard quantum theory. In the last few years, the benefits potentially offered by quantum SWITCH for thermodynamic tasks have appeared in the spotlight. This talk aims at reviewing the recent proposals of thermodynamic applications of quantum SWITCH and draw the perspectives.

Jake Xuereb

**The Impact of Imperfect Timekeeping on Quantum Control**

In order to unitarily evolve a quantum system, an agent requires knowledge of time, a parameter which no physical clock can ever perfectly characterise. In this talk, I will describe to you how limitations on acquiring knowledge of time impact controlled quantum operations in different paradigms. In particular, how the quality of timekeeping an agent has access to limits the circuit complexity they are able to achieve within circuit-based quantum computation. In this work we show this by deriving an upper bound on the average gate fidelity achievable under imperfect timekeeping for a general class of random circuits. Another area where quantum control is relevant is quantum thermodynamics. In that context, we show that cooling a qubit can be achieved using a timer of arbitrary quality for control: timekeeping error only impacts the rate of cooling and not the achievable temperature. Our analysis combines techniques from the study of autonomous quantum clocks and the theory of quantum channels to understand the effect of imperfect timekeeping on controlled quantum dynamics.

Andrey Moskalenko

**Subcycle tomography of quantum light**

Quantum properties of light play one of the central roles for emerging quantum technologies. Usually they are characterized in the frequency domain in a vicinity of a well-defined carrier frequency. In this picture the Wigner function is frequently used for a phase-space visualization of the states as well as for accessing their physical properties via the classical averaging of the corresponding quantities over the phase space. Extending this approach to a pulsed ultrabroadband quantum light would lead to a quite involved description in terms of a large set of single-frequency or shaped temporal modes, where each mode has to be characterized separately while keeping the intermode phase relation fixed, or would require an a priori knowledge about the shape of a smaller number of the localized temporal modes in which the state of the light can be expanded. An alternative approach is to consider the quantum fields directly in the time domain [1-3]. For example, we have shown that it is possible to formulate a time-domain theory of the generation and time-resolved detection of ultrabroadband pulsed squeezed vacuum states [4] and that it should be possible to get access to arbitrary rotated generalized quadratures of the field [5,6]. In this contribution, we discuss how to define and retrieve then the corresponding subcycle-resolved Wigner function.

The function reconstructed from the tomography protocol represents a joint quasi-probability distribution of the sampled instantaneous electric field and its conjugated generalized quadrature. It is capable to visualize the dynamics of the field state, providing direct access to the ultrafast evolution of its characteristic features, such as photon content, squeezing and negativity. This achievement paves the ways to further advances towards ultrafast quantum spectroscopy capable to probe femtosecond dynamics of correlations and entanglement in many-body systems, hidden to probing by methods of classical ultrafast photonics.

[1] C. Riek, D.V. Seletskiy, A.S. Moskalenko, J.F. Schmidt, P. Krauspe, S. Eckart, S. Eggert, G. Burkard, A. Leitenstorfer, Science 350, 420 (2015).

[2] A.S. Moskalenko, C. Riek, D. V. Seletskiy, G. Burkard, A. Leitenstorfer, Phys. Rev. Lett. 115, 263601 (2015).

[3] C. Riek, P. Sulzer, M. Seeger, A.S. Moskalenko, G. Burkard, D.V. Seletskiy, A. Leitenstorfer, Nature 541, 376 (2017).

[4] M. Kizmann, T.L.M. Guedes, D.V. Seletskiy, A.S. Moskalenko, A. Leitenstorfer, G. Burkard, Nat. Phys. 15, 960 (2019).

[5] M. Kizmann, A.S. Moskalenko, A. Leitenstorfer, G. Burkard, S. Mukamel, Laser Photon. Rev. 16, 2100423 (2022).

[6] S. Gündoğdu, S. Virally, M. Scaglia, D.V. Seletskiy, A.S. Moskalenko, Laser Photon. Rev., 2200706 (2023). https://doi.org/10.1002/lpor.202200706

Luca Razzoli

**Hybrid quantum thermal machines with dynamical couplings**

Quantum thermal machines can perform useful tasks, such as delivering power, cooling, or heating. In this work, we consider hybrid thermal machines, that can execute more than one task simultaneously. We characterize and find optimal working conditions for a three-terminal quantum thermal machine, where the working medium is a quantum harmonic oscillator, coupled to three heat baths, with two of the couplings driven periodically in time. We show that it is possible to operate the thermal machine efficiently, in both pure and hybrid modes, and to switch between different operational modes simply by changing the driving frequency. Moreover, the proposed setup can also be used as a high-performance transistor, in terms of output-to-input signal and differential gain. Due to its versatility and tunability, our model may be of interest for engineering thermodynamic tasks and for thermal management in quantum technologies.

Reference: arXiv:2301.09684; iScience 26, 106235 (2023) (published version)

Salvatore Marco Giampaolo

**Frustrated Quantum Batteries**

Quantum mechanics allows phenomena without classical counterparts that can be harvested to develop new technological devices. An example of this is represented by quantum batteries, i.e. quantum systems capable of storing and transferring energy in a coherent way. However, both self-discharge and decoherence processes limit their performance. In my talk, I will show how these difficulties can be overcome by exploiting the characteristics of topologically frustrated systems. In fact, topological frustration modifies both the properties of the ground state and the low-energy spectrum of systems. The result of this change is that it is possible to make high-performance quantum batteries that are much more resistant to decoherence phenomena than those currently under study.

Giacomo Guarnieri

**Quantum Thermodynamics of Precision in Driven Thermal Machines: Theory and Experiment**

Understanding and controlling microscopic quantum devices represents a major milestone. Their precision is related to the fluctuations of their measurable output, an aspect that becomes preponderant at the nano-scale. Achieving a regime where the machine operates at a given reliability/precision inevitably comes at a cost in terms of thermodynamic resources, such as dissipated heat or excess work, thus massively impacting the machines’ performances. Thermodynamic Uncertainty Relations (TURs) have represented a landmark

first step in understanding this balance, as they express a trade-off between precision, defined as the noise-to-signal ratio of a generic current, and the amount of associated entropy production. These results have deep consequences for quantum thermal machines, imposing an upper bound for their efficiency in terms of the power yield and its fluctuations. Such engines can be divided into two classes: steady-state heat engines and periodically driven heat engines.

In this talk I will present and discuss the derivation of genuinely quantum corrections to TURs in both cases, which were obtained by combining techniques from quantum information theory and thermodynamics of geometry. Finally, I will report on an experimental measurement of such quantum correction in a trapped-ion experiment.

Simone Paganelli

**Variational Quantum Eigensolver for Topological Systems**

We will give an introduction to topological systems by the discussion of a paradigmatic 1D noninteracting model, namely the Su-Schrieffer-Heeger (SSH) model. The SSH model describes the electronic properties of one-dimensional systems with alternating hoppings in a tight-binding approximation. This is the simplest model exhibiting a symmetry-protected topological phase and can be consider a prototype of topological insulator. In the SSH model, distinct bulk properties may give rise to states localized on the edges (edge states) with almost degenerate energy levels localized in the middle of the band gap. A topological phase transition from a trivial phase typically occurs via energy gap closure, then edge modes appear, consistently with the so-called bulk-boundary correspondence. The edge states of the SSH model have a very high long-distance entanglement and are almost degenerate, making them potentially more elusive to detect: even if a variational algorithm is expected to give a satisfactory estimation of the bulk’s properties, it could be inadequate for the edge states. We will try to identify this critical issues and propose a strategy to implement a suitable VQE to deal with nontrivial topological states.

Matteo Aquilina

**Entanglement Percolation in Uni-Directionally Coupled Harmonic Oscillators**

Systems of multiple harmonic oscillators coupled together through a uni-directional coupling were modelled and the manner in which entanglement was analysed. Entanglement is restricted to flow along one direction rather than the other.

Shubayan Sarkar

**Outcome-dependent quantum steering and certification of entangled bipartite composite measurements**

We first introduce the idea of outcome-dependent quantum steering in the scenario of quantum networks consisting of three parties where one of the parties is trusted, that is, the measurements performed by the trusted party are known. Then, we consider the problem of certifying composite measurements that can generate entanglement among two separable systems. For this purpose, we propose steering inequalities inspired by [Sarkar et. al, arXiv:2110.15176], which can be used to certify composite measurements composed of projectors acting on with an arbitrary amount of entanglement.

Luca Lepori

**Maximally-entangled states via driven spin molecules**

We describe a method to obtain maximally-entangled pure states, via time-driving of certain spin Hamiltonians. These schemes are currently realizable in suitable multispin molecules. The robustness against some type of noises is also discussed.

Pedro M. Q. Cruz

**Shallow unitary decompositions of Fredkin and Toffoli gates for connectivity-aware equivalent circuit averaging**

The Fredkin and Toffoli gates are at the heart of the original proposal of reversible classical computation, having found widespread use in many quantum algorithms such as the SWAP test and Grover search, to name only two. This made it imperative early on to pursue their efficient unitary decomposition in terms of the lower level gate sets and connectivity constraints native to different physical platforms. Recently, we developed a ZX-calculus-based circuit optimization technique capable of producing several CNOT-count-optimal logically equivalent circuits with different entanglement structures. In this talk, we will describe how we applied our automated method to decompose Fredkin and Toffoli gates under all-to-all and linear qubit connectivities, the latter with two different routings for control and target qubits. Besides achieving lower CNOT-counts than available in the literature for some of these configurations, we introduce several circuits and demonstrate their effectiveness at mitigating coherent errors via equivalent circuit averaging. For that, we quantify the robustness of the procedure in terms of the diamond distance to the target unitary by considering biased-CNOT gate models recently proposed to capture correlated errors in transmon-based hardware. Importantly, we also consider the case where the three qubits on which the Toffoli or Fredkin gates act are not adjacent, proposing a novel scheme to reorder the qubits that saves one CNOT for every SWAP. Our results highlight the importance of considering different entanglement structures and connectivity constraints when designing efficient quantum circuits.