arXiv subjects

Emma C. King

Publications and source records attributed to Emma C. King.

7 recordsLinked to original sources

arXiv2026

Shortcuts to adiabaticity with a quantum control field

Quantum adiabatic dynamics is the crucial element of adiabatic quantum computing and quantum annealing. Shortcuts to adiabaticity enable acceleration of the computational time by suppressing unwanted non-adiabatic processes with designed classical fields. Here, we consider quantum state transfer in the Landau-Zener model, which exemplifies the key elements of quantum adiabatic dynamics. We argue that non-adiabatic transitions can be suppressed by autonomous quantum dynamics, which involves coupling the Landau-Zener qubit to a second quantum system. By tuning the coupling strength, the composite quantum dynamics can reduce the probability of unwanted processes by more than two orders of magnitude. This is a prime example of control where the quantum properties of the control fields are key for implementing shortcuts to adiabaticity.

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arXiv2026

Time complexity of a monitored quantum search with resetting

Searching a database is a central task in computer science and is paradigmatic of transport and optimization problems in physics. For an unstructured search, Grover's algorithm predicts a quadratic speedup, with the search time $τ(N)=Θ(\sqrt{N})$ and $N$ the database size. Numerical studies suggest that the time complexity can change in the presence of feedback, injecting information during the search. Here, we determine the time complexity of the quantum analog of a randomized algorithm, which implements feedback in a simple form. The search is a continuous-time quantum walk on a complete graph, where the target is continuously monitored by a detector. Additionally, the quantum state is reset if the detector does not click within a specified time interval. This yields a non-unitary, non-Markovian dynamics. We optimize the search time as a function of the hopping amplitude, detection rate, and resetting rate, and identify the conditions under which time complexity could outperform Grover's scaling. The overall search time does not violate Grover's optimality bound when including the time budget of the physical implementation of the measurement. For databases of finite sizes monitoring can warrant rapid convergence and provides a promising avenue for fault-tolerant quantum searches.

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arXiv2026

Nonlinear quantum Kibble-Zurek ramps in open systems at finite temperature

We analyze quantum systems under a broad class of protocols in which the temperature and a Hamiltonian control parameter are ramped simultaneously and, in general, in a nonlinear fashion toward a quantum critical point. Using an open-system version of a Kitaev quantum wire as an example, we show that, unlike finite-temperature protocols at fixed temperature, these protocols allow us to probe, in an out-of-equilibrium situation and at finite temperature, the universality class (characterized by the critical exponents $ν$ and $z$) of an equilibrium quantum phase transition at zero temperature. Key to this is the identification of ramps in which both coherent and incoherent parts of the open-system dynamics affect the excitation density in a non-negligible way. We also identify the specific ramps for which subleading corrections to the asymptotic scaling laws are suppressed, which serves as a guide to dynamically probing quantum critical exponents in experimentally realistic finite-temperature situations.

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arXiv2025

Optimal spatial searches with long-range tunneling

A quantum walk on a lattice is a paradigm of a quantum search in a database. The database qubit strings are the lattice sites, qubit rotations are tunneling events, and the target site is tagged by an energy shift. For quantum walks on a continuous time, the walker diffuses across the lattice and the search ends when it localizes at the target site. The search time $T$ can exhibit Grover's optimal scaling with the lattice size $N$, namely, $T\sim \sqrt{N}$, on an all-connected, complete lattice. For finite-range tunneling between sites, instead, Grover's optimal scaling is warranted when the lattice is a hypercube of $d>4$ dimensions. Here, we show that Grover's optimum can be reached in lower dimensions on lattices of long-range interacting particles, when the interaction strength scales algebraically with the distance $r$ as $1/r^α$ and $0<α<3d/2$. For $α 4$. Our work identifies an exact relation between criticality of long-range and short-range systems, it provides a quantitative demonstration of the resources that long-range interactions provide for quantum technologies, and indicates when existing experimental platforms can implement efficient analog quantum search algorithms.

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arXiv2024

Adiabatic quantum trajectories in engineered reservoirs

We analyze the efficiency of protocols for adiabatic quantum state transfer assisted by an engineered reservoir. The target dynamics is a quantum trajectory in the Hilbert space and is a fixed point of a time-dependent master equation in the limit of adiabatic dynamics. We specialize to quantum state transfer in a qubit and determine the optimal schedule for a class of time-dependent Lindblad equations. The speed limit on state transfer is extracted from a physical model of a qubit coupled to a reservoir, from which the Lindblad equation is derived in the Born-Markov limit. Our analysis shows that the resulting efficiency is comparable to the efficiency of the optimal unitary dynamics. Numerical studies indicate that reservoir-engineered protocols could outperform unitary protocols outside the regime of the Born-Markov master equation, namely, when correlations between the qubit and reservoir become relevant. Our study contributes to the theory of shortcuts to adiabaticity for open quantum systems and to the toolbox of protocols of the NISQ era.

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arXiv2023

Universal cooling dynamics toward a quantum critical point

We investigate the loss of adiabaticity when cooling a many-body quantum system from an initial thermal state toward a quantum critical point. The excitation density, which quantifies the degree of adiabaticity of the dynamics, is found to obey scaling laws in the cooling velocity as well as in the initial and final temperatures of the cooling protocol. The scaling laws are universal, governed by the critical exponents of the quantum phase transition. The validity of these statements is shown analytically for a Kitaev quantum wire coupled to Markovian baths and argued to be valid under rather general conditions. Our results establish that quantum critical properties can be probed dynamically at finite temperature, without even varying the control parameter of the quantum phase transition.

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arXiv2022

Long-range Kitaev chain in a thermal bath: Analytic techniques for time-dependent systems and environments

We construct and solve a "minimal model" with which nonequilibrium phenomena in many-body open quantum systems can be studied analytically under time-dependent parameter changes in the system and/or the bath. Coupling a suitable configuration of baths to a Kitaev chain, we self-consistently derive a Lindblad master equation which, at least in the absence of explicit time dependencies, leads to thermalization. Using the method of Third Quantization we derive time-evolution equations for the correlation matrix, which we relate to the occupation of the system's quasiparticle modes. These results permit analytic and efficient numeric descriptions of the nonequilibrium dynamics of open Kitaev chains under a wide range of driving protocols, which in turn facilitate the investigation of the interplay between bath-induced dissipation and the generation of coherent excitations by nonadiabatic driving. We advertise this minimal model of maximum simplicity for the study of finite-temperature generalizations of Kibble-Zurek ramps, Floquet physics, and many other nonequilibrium protocols of quantum many-body systems driven by time-varying parameters and/or temperatures.

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