arXiv subjects

Emanuel Malvetti

Publications and source records attributed to Emanuel Malvetti.

16 recordsLinked to original sources

arXiv2026

Dynamical Decoupling using Universal Optimal Tracking

Dynamical decoupling (DD) is a widely used and resource-efficient technique for error suppression, but conventional DD relies on periodically repeating a short pulse block to refocus the qubit state during idle periods. Imperfections in this block cause residual errors to accumulate, ultimately degrading state recovery over long idle times. Here, we introduce a universal optimal tracking approach that extends the original tracking concept to a fully state-independent setting for designing DD sequences. By monitoring the qubit's evolution at predefined waypoints during optimization, the method dynamically compensates residual errors while preserving regular refocusing. Experimental demonstrations on a superconducting-qubit platform confirm the suppression of error accumulation under static control imperfections, in agreement with numerical predictions. Complementary simulations further show that optimal-tracking-based sequences maintain strong performance under time-dependent noise. These results establish optimal tracking as a practical and hardware-agnostic approach to designing short, robust DD sequences suitable for noisy quantum devices.

quant-ph↗

arXiv2025

On the convergence of the variational quantum eigensolver and quantum optimal control

When does a variational quantum algorithm converge to a globally optimal solution? Despite the large literature around variational approaches to quantum computing, the answer is largely unknown. We address this open question by developing a convergence theory for the variational quantum eigensolver (VQE). By leveraging the terminology of quantum control landscapes, we prove a sufficient criterion that characterizes when convergence to a ground state of a Hamiltonian can be guaranteed for almost all initial parameter settings. More specifically, we show that if (i) a parameterized unitary transformation allows for moving in all tangent-space directions (local surjectivity) in a bounded manner and (ii) the gradient descent used for the parameter update terminates, then the VQE converges to a ground state almost surely. We develop constructions that satisfy both aspects of condition (i) and analyze two commonly employed families of quantum circuit ans\"atze. Finally, we discuss regularization techniques for guaranteeing gradient descent to terminate, as for condition (ii), and draw connections to the halting problem.

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arXiv2024

Theory and Experimental Demonstration of Wigner Tomography of Unknown Unitary Quantum Gates

We investigate the tomography of unknown unitary quantum processes within the framework of a finite-dimensional Wigner-type representation. This representation provides a rich visualization of quantum operators by depicting them as shapes assembled as a linear combination of spherical harmonics. These shapes can be experimentally tomographed using a scanning-based phase-space tomography approach. However, so far, this approach was limited to $\textit{known}$ target processes and only provided information about the controlled version of the process rather than the process itself. To overcome this limitation, we introduce a general protocol to extend Wigner tomography to $\textit{unknown}$ unitary processes. This new method enables experimental tomography by combining a set of experiments with classical post-processing algorithms introduced herein to reconstruct the unknown process. We also demonstrate the tomography approach experimentally on IBM quantum devices and present the specific calibration circuits required for quantifying undesired errors in the measurement outcomes of these demonstrations.

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arXiv2024

Optimal Control of Bipartite Quantum Systems

Closed bipartite quantum systems subject to fast local unitary control are studied using quantum optimal control theory and a method of reduced control systems based on the Schmidt decomposition. Particular focus is given to the time-optimal generation of maximally entangled states and product states, as well as to the problem of stabilizing quantum states with a certain amount of entanglement. Explicit analytical solutions are given for general systems consisting of two qubits (as well as for bosonic and fermionic analogues) and also for a class of systems consisting of two coupled qutrits which is studied using the Pontryagin Maximum Principle.

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arXiv2024

Randomized Gradient Descents on Riemannian Manifolds: Almost Sure Convergence to Global Minima in and beyond Quantum Optimization

We analyze convergence of gradient-descent methods on Riemannian manifolds. In particular, we study randomization of Riemannian gradient algorithms for minimizing smooth cost functions (of Morse-Bott type). We prove that randomized gradient descent methods, where the Riemannian gradient is replaced by a random projection of it, converge to a single local optimum almost surely despite the existence of saddle points. We consider both uniformly distributed and discrete random projections. We also discuss the time required to pass a saddle point. As a major application, we consider ground-state preparation through quantum optimization over the unitary group. In mathematical terms our randomized algorithm applied to the trace function $U \to \operatorname{tr}(AU\rho U^*)$ almost surely converges to its global minimum. The minimum corresponds to the smallest eigenvalue (ground state) of the selfadjoint operator $A$ (Hamiltonian) if $\rho$ is a rank-one projector (pure state). In this setting, one can efficiently replace the uniform random projections by implementing so-called discrete unitary 2-designs.

math.OC↗

arXiv2024

Optimal Control of a Markovian Qubit with Unitary Control

We study a single Markovian qubit governed by a Lindblad master equation and subject to fast unitary control. Using reduced control systems and optimal control theory we determine (i) controls for cooling and heating such systems in a time-optimal way as well as (ii) the set of stabilizable states in the Bloch ball. No restrictions on the Lindblad equation are assumed, and several known results, for instance for the Bloch equations, are recovered. Furthermore we introduce integral systems, for which the solutions take a particularly nice form. These integral systems include all systems with real Lindblad terms as well as all coolable systems. The method allows for intuitive visualizations and is mostly analytical, making use of only basic numerical methods.

quant-ph↗

arXiv2024

Provably Time-Optimal Cooling of Markovian Quantum Systems

We address the problem of cooling a Markovian quantum system to a pure state in the shortest amount of time possible. Here the system drift takes the form of a Lindblad master equation and we assume fast unitary control. This setting allows for a natural reduction of the control system to the eigenvalues of the state density matrix. We give a simple necessary and sufficient characterization of systems which are (asymptotically) coolable and present a powerful result which allows to considerably simplify the search for optimal cooling solutions. With these tools at our disposal we derive explicit provably time-optimal cooling protocols for rank one qubit systems, inverted $\Lambda$-systems on a qutrit, and a certain system consisting of two coupled qubits.

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arXiv2024

Entanglement in Bipartite Quantum Systems with Fast Local Unitary Control

The well-known Schmidt decomposition, or equivalently, the complex singular value decomposition, states that a pure quantum state of a bipartite system can always be brought into a "diagonal" form using local unitary transformations. In this work we consider a finite-dimensional closed bipartite system with fast local unitary control. In this setting one can define a reduced control system on the singular values of the state which is equivalent to the original control system. We explicitly describe this reduced control system and prove equivalence to the original system. Moreover, using the reduced control system, we prove that the original system is controllable and stabilizable and we deduce quantum speed limits. We also treat the fermionic and bosonic cases in parallel, which are related to the Autonne-Takagi and Hua factorization respectively.

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arXiv2023

Computing Common Eigenvectors and Simultaneous Triangulation

We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so, for computing a corresponding basis.

math.RA↗

arXiv2023

Reachability, Coolability, and Stabilizability of Open Markovian Quantum Systems with Fast Unitary Control

Open Markovian quantum systems with fast and full Hamiltonian control can be reduced to an equivalent control system on the standard simplex modelling the dynamics of the eigenvalues of the density matrix describing the quantum state. We explore this reduced control system for answering questions on reachability and stabilizability with immediate applications to the cooling of Markovian quantum systems. We show that for certain tasks of interest, the control Hamiltonian can be chosen time-independent. -- The reduction picture is an example of dissipative interconversion between equivalence classes of states, where the classes are induced by fast controls.

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arXiv2023

Reduced Control Systems on Symmetric Lie Algebras

For a symmetric Lie algebra $\mathfrak g=\mathfrak k\oplus\mathfrak p$ we consider a class of bilinear or more general control-affine systems on $\mathfrak p$ defined by a drift vector field $X$ and control vector fields $\mathrm{ad}_{k_i}$ for $k_i\in\mathfrak k$ such that one has fast and full control on the corresponding compact group $\mathbf K$. We show that under quite general assumptions on $X$ such a control system is essentially equivalent to a natural reduced system on a maximal Abelian subspace $\mathfrak a\subseteq\mathfrak p$, and likewise to related differential inclusions defined on $\mathfrak a$. We derive a number of general results for such systems and as an application we prove a simulation result with respect to the preorder induced by the Weyl group action.

math.OC↗

arXiv2023

Analytic, Differentiable and Measurable Diagonalizations in Symmetric Lie Algebras

We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix diagonalization, such as the eigenvalue decomposition of real symmetric or complex Hermitian matrices, and the real or complex singular value decomposition. Concretely, given a path of structured matrices with a certain smoothness, we study what kind of smoothness one can obtain for the corresponding diagonalization of the matrices.

math.RT↗

arXiv2023

Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources

Our aim is twofold: First, we rigorously analyse the generators of quantum-dynamical semigroups of thermodynamic processes. We characterise a wide class of GKSL-generators for quantum maps within thermal operations and argue that every infinitesimal generator of (a one-parameter semigroup of) Markovian thermal operations belongs to this class. We completely classify and visualise them and their non-Markovian counterparts for the case of a single qubit. Second, we use this description in the framework of bilinear control systems to characterise reachable sets of coherently controllable quantum systems with switchable coupling to a thermal bath. The core problem reduces to studying a hybrid control system ("toy model") on the standard simplex allowing for two types of evolution: (i) instantaneous permutations and (ii) a one-parameter semigroup of $d$-stochastic maps. We generalise upper bounds of the reachable set of this toy model invoking new results on thermomajorisation. Using tools of control theory we fully characterise these reachable sets as well as the set of stabilisable states as exemplified by exact results in qutrit systems.

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arXiv2022

The Thermomajorization Polytope and Its Degeneracies

Drawing inspiration from transportation theory, in this work we introduce the notions of "well-structured" and "stable" Gibbs states and we investigate their implications for quantum thermodynamics and its resource theory approach via thermal operations. It turns out that, in the quasi-classical realm, global cyclic state transfers are impossible if and only if the Gibbs state is stable. Moreover, using a geometric approach by studying the so-called thermomajorization polytope we prove that any subspace in equilibrium can be brought out of equilibrium via thermal operations. Interestingly, the case of some subsystem being in equilibrium can be witnessed via degenerate extreme points of the thermomajorization polytope, assuming the Gibbs state of the system is well structured. These physical considerations are complemented by simple new constructions for the polytope's extreme points as well as for an important class of extremal Gibbs-stochastic matrices.

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arXiv2021

Introduction to UniversalQCompiler

We introduce an open source software package UniversalQCompiler written in Mathematica that allows the decomposition of arbitrary quantum operations into a sequence of single-qubit rotations (with arbitrary rotation angles) and controlled-NOT (C-NOT) gates. Together with the existing package QI, this allows quantum information protocols to be analysed and then compiled to quantum circuits. Our decompositions are based on Phys. Rev. A 93, 032318 (2016), and hence, for generic operations, they are near optimal in terms of the number of gates required. UniversalQCompiler allows the compilation of any isometry (in particular, it can be used for unitaries and state preparation), quantum channel, positive-operator valued measure (POVM) or quantum instrument, although the run time becomes prohibitive for large numbers of qubits. The resulting circuits can be displayed graphically within Mathematica or exported to LaTeX. We also provide functionality to translate the circuits to OpenQASM, the quantum assembly language used, for instance, by the IBM Q Experience.

quant-ph↗

arXiv2021

Quantum Circuits for Sparse Isometries

We consider the task of breaking down a quantum computation given as an isometry into C-NOTs and single-qubit gates, while keeping the number of C-NOT gates small. Although several decompositions are known for general isometries, here we focus on a method based on Householder reflections that adapts well in the case of sparse isometries. We show how to use this method to decompose an arbitrary isometry before illustrating that the method can lead to significant improvements in the case of sparse isometries. We also discuss the classical complexity of this method and illustrate its effectiveness in the case of sparse state preparation by applying it to randomly chosen sparse states.

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