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Unitary transformations play a fundamental role in many-body physics, and except for special cases, they are not expressible in closed form. We present closed-form expressions for unitary transformations generated by a single fermionic…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Unimodular gravity is based on a modification of the usual Einstein-Hilbert action that allows one to recover general relativity with a dynamical cosmological constant. It also has the interesting property of providing, as the momentum…
Discrete circular convolution over $\mathbb{Z}/N\mathbb{Z}$ is a linear operator and can be implemented on quantum hardware within the linear-combination-of-unitaries (LCU) framework. In this work, we make this connection explicit through…
Recent advances in quantum technologies have enabled quantum simulation of gauge theories -- some of the most fundamental frameworks of nature -- in regimes far from equilibrium, where classical computation is severely limited. These…
Conservation of symmetries plays a crucial role in both classical and quantum simulations of many-body systems, enabling the tracking of states with specific symmetry properties and leading to substantial reductions in the number of…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation…
A non-relativistic system such as an ultracold trapped ion may perform a quantum simulation of a Dirac equation dynamics under specific conditions. The resulting Hamiltonian and dynamics are highly controllable, but the coupling between…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
The finite parts of a large, locally interacting many-body system prepared out-of-equilibrium eventually equilibrate. Characterising the underlying mechanisms of this process and its timescales, however, is particularly hard as it requires…
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
We establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum physics. As established by Wigner, all quantum symmetries must be represented by either unitary or…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
Many physical and chemical processes in the condensed phase environment exhibit non-Markovian quantum dynamics. As such simulations are challenging on classical computers, we developed a variational quantum algorithm that is capable of…
Spacetime inversion symmetries such as parity and time reversal play a central role in physics, but they are usually treated as global symmetries. In quantum gravity there are no global symmetries, so any spacetime inversion symmetries must…
We propose a method of simulating efficiently many-body interacting fermion lattice models in trapped ions, including highly nonlinear interactions in arbitrary spatial dimensions and for arbitrarily distant couplings. We map products of…
In light of recent exciting progress in building up quantum computing facilities based on both optical and cold-atom techniques, the algorithms for quantum simulations of particle-physics systems are in rapid progress. In this paper, we…
The control of quantum systems is of fundamental scientific interest and promises powerful applications and technologies. Impressive progress has been achieved in isolating the systems from the environment and coherently controlling their…