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Quantum language models have shown competitive performance on sequential tasks, yet whether trained quantum circuits exploit genuinely quantum resources -- or merely embed classical computation in quantum hardware -- remains unknown. Prior…
Quantum computers promise dramatic advantages over their classical counterparts, but the answer to the most basic question "What is the source of the power in quantum computing?" has remained elusive. Here we prove a remarkable equivalence…
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 computation has made considerable progress in the last decade with multiple emerging technologies providing proof-of-principle experimental demonstrations of such calculations. However, these experimental demonstrations of quantum…
We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…
We introduce a volumetric benchmark for near-term quantum platforms based on the generation and verification of genuine entanglement across n-qubits using graph states and direct stabilizer measurements. Our benchmark evaluates the…
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
We present a general protocol for stabilizer measurements and pumping in a system of N superconducting qubits. We assume always-on, equal dispersive couplings to a single mode of a high-Q microwave resonator in the ultra-strong dispersive…
Contextuality, the impossibility of assigning a single random variable to represent the outcomes of the same measurement procedure under different experimental conditions, is a central aspect of quantum mechanics. Thus defined, it appears…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Recent experiments have shown that nature violates noncontextual inequalities regardless of the state of the physical system. So far, all these inequalities involve measurements of dichotomic observables. We show that state-independent…
Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…
Quantum instruments describe both the classical output and the updated quantum state in a measurement process. To do this in a non-trivial way, instruments must have the capability to interact coherently with the state that they measure.…
While there is strong evidence for advantages of quantum over classical computation, the repertoire of computational primitives with proven or conjectured quantum advantage remains limited. A big challenge of quantum algorithmic design is a…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
As a phenomenon encompassing measurement incompatibility and Bell nonlocality, quantum contextuality is not only central to our understanding of quantum mechanics, but also an essential resource in many quantum information processing tasks.…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…