Related papers: Bounds on the recurrence probability in periodical…

We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm [Liu et al., PNAS 118, 2021] answering one of…

We study the time it takes for all states of a finite quantum system to return simultaneously to their original configuration. In particular, we define the recurrence time for a quantum system to be the time at which all time-evolved states…

In the dynamics of open quantum systems, the interaction with the external environment usually leads to a contraction of the set of reachable states for the system as time increases, eventually shrinking to a single stationary point. In…

Quantum computers have long been anticipated to excel in simulating quantum many-body physics. While most previous work has focused on Hermitian physics, we demonstrate the power of variational quantum circuits for resource-efficient…

From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…

We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…

Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which…

Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can…

The rise of programmable quantum devices has motivated the exploration of circuit models which could realize novel physics. A promising candidate is a class of hybrid circuits, where entangling unitary dynamics compete with disentangling…

Quantum dynamics that explore an unexpectedly small fraction of Hilbert space is inherently interesting. Integrable systems, quantum scars, MBL, hidden tensor structures, and systems with gauge symmetries are examples. Beyond dimension and…

We explore set-stabilizability by constrained controls, and both controllability and stabilizability can be regarded as the special case of set-stabilizability. We not only clarify how to define an equilibrium point of Schr$\ddot{o}$dinger…

Quantum computers have the potential to solve certain interesting problems significantly faster than classical computers. To exploit the power of a quantum computation it is necessary to perform inter-qubit operations and generate entangled…

As quantum control approaches hardware-imposed performance limits, weak effects omitted by reduced models become consequential. Assumptions required for analytic tractability then cease to guide control design and instead constrain further…

Quantum algorithms are built enabling to find Poincar\'e recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of…

The quantum form of the Poincar\'e recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly…

We show how to implement quantum computation on a system with an intrinsic Hamiltonian by controlling a limited subset of spins. Our primary result is an efficient control sequence on a nearest-neighbor XY spin chain through control of a…

Efficient methods for the simulation of quantum circuits on classic computers are crucial for their analysis due to the exponential growth of the problem size with the number of qubits. Here we study lumping methods based on bisimulation,…

Control protocol to drive finite dimensional quantum systems to an arbitrary target state using square pulses is proposed explicitly. It is a multi-cycle control process and in each cycle we apply square pulses to cause single or a few…

This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to…

Quantum phase transitions play an important role in many-body systems and have been a research focus in conventional condensed matter physics over the past few decades. Artificial atoms, such as superconducting qubits that can be…