Related papers: A mathematical framework for quantum Hamiltonian s…
Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath.…
Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…
Quantum theory can be formulated with certain non-Hermitian Hamiltonians. An anti-linear involution, denoted by PT, is a symmetry of such Hamiltonians. In the PT-symmetric regime the non-Hermitian Hamiltonian is related to a Hermitian one…
Hamiltonian learning is a cornerstone for advancing accurate many-body simulations, improving quantum device performance, and enabling quantum-enhanced sensing. Existing readily deployable quantum metrology techniques primarily focus on…
The prospect of AGI instantiated on quantum substrates motivates the development of mathematical frameworks that enable direct comparison of their operation in classical and quantum environments. To this end, we introduce a Hamiltonian…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
The entanglement Hamiltonian (EH) provides the most comprehensive characterization of bipartite entanglement in many-body quantum systems. Ground states of local Hamiltonians inherit this locality, resulting in EHs that are dominated by…
There is an extensive philosophical literature on the interrelated issues of identity, individuality, and distinguishability in quantum systems. A key consideration is whether quantum systems are subject to a strong form of individuality…
Quantum entanglement is considered, by and large, to be a very delicate and non-robust phenomenon that is very hard to maintain in the presence of noise, or non-zero temperatures. In recent years however, and motivated, in part, by a quest…
The concept of parity-time (PT) symmetry originates from the framework of quantum mechanics, where if the Hamiltonian operator satisfies the commutation relation with the parity and time operators, it shows all real eigen-energy spectrum.…
We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…
Recent work has characterised rigorously what it means for one quantum system to simulate another, and demonstrated the existence of universal Hamiltonians -- simple spin lattice Hamiltonians that can replicate the entire physics of any…
A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of duality: a dual model with inverse Planck constant exists such that the…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
This paper builds on our earlier proposal for construction of a positive inner product for pseudo-Hermitian Hamiltonians and we give several examples to clarify our method. We show through the example of the harmonic oscillator how our…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
Since quantum feedback is based on classically accessible measurement results, it can provide fundamental insights into the dynamics of quantum systems by making available classical information on the evolution of system properties and on…
In a predicative framework from basic logic, defined for a model of quantum parallelism by sequents, we characterize a class of first order domains, termed {\em virtual singletons}, which allows a generalization of the notion of duality,…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
Simulating quantum many-body systems is crucial for advancing physics but poses substantial challenges for classical computers. Quantum simulations overcome these limitations, with analog simulators offering unique advantages over digital…