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Model Hamiltonians are regularly derived from first-principles data to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model…
The existence of inequivalent representations in quantum field theory with {\it finitely} many degrees of freedom is shown. Their properties are exemplified and analysed for concrete and simple models. In particular the relations to…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating…
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired…
Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…
A new formulation of the Hamiltonian dynamics of the gravitational field interacting with(non-dissipative) thermo-elastic matter is discussed. It is based on a gauge condition which allows us to encode the six degrees of freedom of the…
Analog quantum simulations---simulations of one Hamiltonian by another---is one of the major goals in the noisy intermediate-scale quantum computation (NISQ) era, and has many applications in quantum complexity. We initiate the rigorous…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
Given an initial quantum state |psi_I> and a final quantum state |psi_F> in a Hilbert space, there exist Hamiltonians H under which |psi_I> evolves into |psi_F>. Consider the following quantum brachistochrone problem: Subject to the…
Measurement in quantum simulations provides a means for extracting meaningful information from a complex quantum state, and for quantum computing reducing the complexity of measurement will be vital for near-term applications. For most…
We present a self-contained formulation of spin-free nonrelativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories,…
Quantum backflow is the classically-forbidden effect pertaining to the fact that a particle with a positive momentum may exhibit a negative probability current at some space-time point. We investigate how this peculiar phenomenon extends to…
In an ideal quantum measurement, the wave function of a quantum system collapses to an eigenstate of the measured observable, and the corresponding eigenvalue determines the measurement outcome. If the observable commutes with the system…
Precise measurement or perfect cloning of unknown quantum states is forbidden by the laws of quantum mechanics. Yet, quantum teleportation in principle allows for a faithful and disembodied transmission of unknown quantum states between…
Quantum computing relies on processing information within a quantum system with many continuous degrees of freedom. The practical implementation of this idea requires complete control over all of the 2^n independent amplitudes of a…
We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…
The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a…
Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…