Related papers: A Simple Method of Calculating Commutators in Hami…
In this work, the commutator of any two reasonable functions of several pairs of canonical conjugate operators is obtained as a sum of terms of partial derivatives of those functions (equations 9, 10 or 11). When applied to quantum…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
We consider the quantum mechanics of Calogero models in an oscillator or Coulomb potential on the N-dimensional sphere. Their Hamiltonians are obtained by an appropriate Dunkl deformation of the oscillator/Coulomb system on the sphere and…
We construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a…
In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schr\"odinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of…
Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…
Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent…
In computer simulations, quantum delocalization of atomic nuclei can be modeled making use of the Path Integral (PI) formulation of quantum statistical mechanics. This approach, however, comes with a large computational cost. By restricting…
We have proved new estimates for the coherent control errors of quantum circuits used in quantum computing. These estimates essentially take into account the commutator properties of the Hamiltonians and are based on the formulas of the…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
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…
The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with…
With our recently proposed effective Hamiltonian via Monte Carlo, we are able to compute low energy physics of quantum systems. The advantage is that we can obtain not only the spectrum of ground and excited states, but also wave functions.…
We demonstrate the feasibility of quantum computing for large-scale, realistic chemical systems through the development of a new interface using a quantum circuit simulator and CP2K, a highly efficient first-principles calculation software.…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
We introduce \textsc{qcmath}, a user-friendly quantum chemistry software tailored for electronic structure calculations, implemented using the Wolfram Mathematica language and available at \url{https://github.com/LCPQ/qcmath}. This…