arXiv subjects

Niklas Hörnedal

Publications and source records attributed to Niklas Hörnedal.

11 recordsLinked to original sources

arXiv2026

Measurement and Control of the Complex Berry Phase in a Quantum System

The Berry phase is a geometric phase acquired during adiabatic evolution over a closed loop in parameter space. It plays an essential role in geometric quantum gates and other phase-based protocols. In non-Hermitian systems, the Berry phase is complex, introducing fundamentally new geometric effects, including state amplification. In this work, we report experimental measurement of both the real and imaginary components of a Berry phase in a fully quantum system using a superconducting transmon circuit with engineered dissipation. We also demonstrate the path-dependent effects of the imaginary part on the dissipation and its utility in the implementation of non-unitary quantum control. These findings establish a clear geometric distinction between the real and imaginary components of the Berry phase and experimentally confirm the unique adiabatic behavior of non-Hermitian quantum systems.

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arXiv2025

Exploring the topology of a non-Hermitian superconducting qubit using shortcuts to adiabaticity

Open quantum systems described by a non-Hermitian Hamiltonian exhibit rich dynamics due to the topology of their complex energy spectrum. By encircling an exceptional point degeneracy, this topology allows for topological state transport, chiral geometric phases, and eigenvalue braiding. To access these topological features, it is desirable to drive the system adiabatically. However, adiabatic transport in a system with complex spectrum is conventionally only possible for the eigenstate whose eigenenergy has the lowest loss. Previous experiments have demonstrated such adiabatic evolution for the quantum state with relative gain, yet observed a breakdown in adiabaticity for quantum states with relative loss. In this work, we harness a shortcut to adiabaticity -- counterdiabatic driving -- to avoid the effects of loss while maintaining trajectories that follow the instantaneous eigenstates in significantly shorter timescales. We experimentally investigate the robustness of this control method using a superconducting transmon circuit with engineered dissipation. We observe that counterdiabatic driving stabilizes quasistatic transport and preserves the complex energy spectrum's topology.

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arXiv2025

A geometrical description of non-Hermitian dynamics: speed limits in finite rank density operators

Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. Using this insight, we develop a geometric framework to describe its time evolution. In particular, we identify mutually orthogonal coherent and incoherent directions and provide their physical interpretation. This understanding enables us to optimize the success rate of non-Hermitian driving along prescribed trajectories, with direct relevance to shortcuts to adiabaticity. Next, we explore the geometric interpretation of a speed limit for non-Hermitian Hamiltonians and analyze its tightness. We derive the explicit expression that saturates this bound and illustrate our results with a minimal example of a dissipative qubit.

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arXiv2023

Tight lower bounds on the time it takes to generate a geometric phase

Geometric phase is a concept of central importance in virtually every branch of physics. In this paper, we show that the evolution time of a cyclically evolving quantum system is restricted by the system's energy resources and the geometric phase acquired by the state. Specifically, we derive and examine three tight lower bounds on the time required to generate any prescribed Aharonov-Anandan geometric phase. The derivations are based on recent results on the geometric character of the Mandelstam-Tamm and Margolus-Levitin quantum speed limits.

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arXiv2023

Closed systems refuting quantum-speed-limit hypotheses

Many quantum speed limits for isolated systems can be generalized to also apply to closed systems. This is, for example, the case with the well-known Mandelstam-Tamm quantum speed limit. Margolus and Levitin derived an equally well-known and ostensibly related quantum speed limit, and it seems to be widely believed that the Margolus-Levitin quantum speed limit can be similarly generalized to closed systems. However, a recent geometrical examination of this limit reveals that it differs significantly from most known quantum speed limits. In this paper, we show that, contrary to the common belief, the Margolus-Levitin quantum speed limit does not extend to closed systems in an obvious way. More precisely, we show that for every hypothetical bound of Margolus-Levitin type, there are closed systems that evolve with a conserved normalized expected energy between states with any given fidelity in a time shorter than the bound. We also show that for isolated systems, the Mandelstam-Tamm quantum speed limit and a slightly weakened version of this limit that we call the Bhatia-Davies quantum speed limit always saturate simultaneously. Both of these evolution time estimates extend straightforwardly to closed systems. We demonstrate that there are closed systems that saturate the Mandelstam-Tamm but not the Bhatia-Davies quantum speed limit.

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arXiv2023

Margolus-Levitin quantum speed limit for an arbitrary fidelity

The Mandelstam-Tamm and Margolus-Levitin quantum speed limits are two well-known evolution time estimates for isolated quantum systems. These bounds are usually formulated for fully distinguishable initial and final states, but both have tight extensions to systems that evolve between states with an arbitrary fidelity. However, the foundations of these extensions differ in some essential respects. The extended Mandelstam-Tamm quantum speed limit has been proven analytically and has a clear geometric interpretation. Furthermore, which systems saturate the limit is known. The derivation of the extended Margolus-Levitin quantum speed limit, on the other hand, is based on numerical estimates. Moreover, the limit lacks a geometric interpretation, and no complete characterization of the systems reaching it exists. In this paper, we derive the extended Margolus-Levitin quantum speed limit analytically and describe the systems that saturate the limit in detail. We also provide the limit with a symplectic-geometric interpretation, which indicates that it is of a different character than most existing quantum speed limits. At the end of the paper, we analyze the maximum of the extended Mandelstam-Tamm and Margolus-Levitin quantum speed limits and derive a dual version of the extended Margolus-Levitin quantum speed limit. The maximum limit is tight regardless of the fidelity of the initial and final states. However, the conditions under which the maximum limit is saturated differ depending on whether or not the initial state and the final state are fully distinguishable. The dual limit is also tight and follows from a time reversal argument. We describe the systems that saturate the dual quantum speed limit.

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arXiv2023

Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth

Quantum speed limits (QSLs) provide lower bounds on the minimum time required for a process to unfold by using a distance between quantum states and identifying the speed of evolution or an upper bound to it. We introduce a generalization of QSL to characterize the evolution of a general operator when conjugated by a unitary. The resulting operator QSL (OQSL) admits a geometric interpretation, is shown to be tight, and holds for operator flows induced by arbitrary unitaries, i.e., with time- or parameter-dependent generators. The derived OQSL is applied to the Wegner flow equations in Hamiltonian renormalization group theory and the operator growth quantified by the Krylov complexity.

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arXiv2023

Ultimate Speed Limits to the Growth of Operator Complexity

In an isolated system, the time evolution of a given observable in the Heisenberg picture can be efficiently represented in Krylov space. In this representation, an initial operator becomes increasingly complex as time goes by, a feature that can be quantified by the Krylov complexity. We introduce a fundamental and universal limit to the growth of the Krylov complexity by formulating a Robertson uncertainty relation, involving the Krylov complexity operator and the Liouvillian, as generator of time evolution. We further show the conditions for this bound to be saturated and illustrate its validity in paradigmatic models of quantum chaos.

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arXiv2022

Quantum speed limits on operator flows and correlation functions

Quantum speed limits (QSLs) identify fundamental time scales of physical processes by providing lower bounds on the rate of change of a quantum state or the expectation value of an observable. We introduce a generalization of QSL for unitary operator flows, which are ubiquitous in physics and relevant for applications in both the quantum and classical domains. We derive two types of QSLs and assess the existence of a crossover between them, that we illustrate with a qubit and a random matrix Hamiltonian, as canonical examples. We further apply our results to the time evolution of autocorrelation functions, obtaining computable constraints on the linear dynamical response of quantum systems out of equilibrium and the quantum Fisher information governing the precision in quantum parameter estimation.

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arXiv2022

Extensions of the Mandelstam-Tamm quantum speed limit to systems in mixed states

The Mandelstam-Tamm quantum speed limit puts a bound on how fast a closed system in a pure state can evolve. In this paper, we derive several extensions of this quantum speed limit to closed systems in mixed states. We also compare the strengths of these extensions and examine their tightness. The most widely used extension of the Mandelstam-Tamm quantum speed limit originates in Uhlmann's energy dispersion estimate. We carefully analyze the underlying geometry of this estimate, an analysis that makes apparent that the Bures metric, or equivalently the quantum Fisher information, will rarely give rise to tight extensions. This observation leads us to address whether there is a tightest general extension of the Mandelstam-Tamm quantum speed limit. Using a geometric construction similar to that developed by Uhlmann, we prove that this is indeed the case. In addition, we show that tight evolutions of mixed states are typically generated by time-varying Hamiltonians, which contrasts with the case for systems in pure states.

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arXiv2021

Time-optimal quantum transformations with bounded bandwidth

In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is initially in an incoherent state relative to the observable and that the state evolves according to a von Neumann equation with a Hamiltonian whose bandwidth is uniformly bounded. The transformation time depends intricately on the observable's and the initial state's eigenvalue spectrum and the relative constellation of the associated eigenspaces. The problem of finding quantum speed limits consequently divides into different cases requiring different strategies. We derive quantum speed limits in a large number of cases, and we simultaneously develop a method to break down complex cases into manageable ones. The derivations involve both combinatorial and differential geometric techniques. We also study multipartite systems and show that allowing correlations between the parts can speed up the transformation time. In a final section, we use the quantum speed limits to obtain upper bounds on the power with which energy can be extracted from quantum batteries.

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