Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantum Circuits assisted by LOCC: Transformations and Phases of Matter
154
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We introduce deterministic state-transformation protocols between many-body quantum states which can be implemented by low-depth Quantum Circuits (QC) followed by Local Operations and Classical Communication (LOCC). We show that this gives rise to a classification of phases in which topologically-ordered states or other paradigmatic entangled states become trivial. We also investigate how the set of unitary operations is enhanced by LOCC in this scenario, allowing one to perform certain large-depth QC in terms of low-depth ones.
rate research
Read More
The entanglement spectrum (ES) provides a barometer of quantum entanglement and encodes physical information beyond that contained in the entanglement entropy. In this paper, we explore the ES of stabilizer codes, which furnish exactly solvable models for a plethora of gapped quantum phases of matter. Studying the ES for stabilizer Hamiltonians in the presence of arbitrary weak local perturbations thus allows us to develop a general framework within which the entanglement features of gapped topological phases can be computed and contrasted. In particular, we study models harboring fracton order, both type-I and type-II, and compare the resulting ES with that of both conventional topological order and of (strong) subsystem symmetry protected topological (SSPT) states. We find that non-local surface stabilizers (NLSS), a set of symmetries of the Hamiltonian which form on the boundary of the entanglement cut, act as purveyors of universal non-local features appearing in the entanglement spectrum. While in conventional topological orders and fracton orders, the NLSS retain a form of topological invariance with respect to the entanglement cut, subsystem symmetric systems---fracton and SSPT phases---additionally show a non-trivial geometric dependence on the entanglement cut, corresponding to the subsystem symmetry. This sheds further light on the interplay between geometric and topological effects in fracton phases of matter and demonstrates that strong SSPT phases harbour a measure of quasi-local entanglement beyond that encountered in conventional SPT phases. We further show that a version of the edge-entanglement correspondence, established earlier for gapped two-dimensional topological phases, also holds for gapped three-dimensional fracton models.
Simulation of a quantum many-body system at finite temperatures is crucially important but quite challenging. Here we present an experimentally feasible quantum algorithm assisted with continuous-variable for simulating quantum systems at finite temperatures. Our algorithm has a time complexity scaling polynomially with the inverse temperature and the desired accuracy. We demonstrate the quantum algorithm by simulating finite temperature phase diagram of the Kitaev model. It is found that the important crossover phase diagram of the Kitaev ring can be accurately simulated by a quantum computer with only a few qubits and thus the algorithm may be readily implemented on current quantum processors. We further propose a protocol implementable with superconducting or trapped ion quantum computers.
An open quantum system, whose time evolution is governed by a master equation, can be driven into a given pure quantum state by an appropriate design of the system-reservoir coupling. This points out a route towards preparing many body states and non-equilibrium quantum phases by quantum reservoir engineering. Here we discuss in detail the example of a emph{driven dissipative Bose Einstein Condensate} of bosons and of paired fermions, where atoms in an optical lattice are coupled to a bath of Bogoliubov excitations via the atomic current representing emph{local dissipation}. In the absence of interactions the lattice gas is driven into a pure state with long range order. Weak interactions lead to a weakly mixed state, which in 3D can be understood as a depletion of the condensate, and in 1D and 2D exhibits properties reminiscent of a Luttinger liquid or a Kosterlitz-Thouless critical phase at finite temperature, with the role of the ``finite temperature played by the interactions.
Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical order parameter explicitly. Here, we exploit quantum kernels instead. They are naturally related to the fidelity and thus it is possible to interpret the learning process with the help of quantum information tools. In particular, we use a support vector machine (with a quantum kernel) to predict and characterize quantum phase transitions. The general theory is tested in the Ising chain in transverse field. We show that for small-sized systems, the algorithm gives accurate results, even when trained away from criticality. Besides, for larger sizes we confirm the success of the technique by extracting the correct critical exponent $ u$. The characterization is completed by computing the kernel alignment between the quantum and ideal kernels. Finally, we argue that our algorithm can be implemented on a circuit based on a varational quantum eigensolver.
We study the growth of genuine multipartite entanglement in random quantum circuit models, which include random unitary circuit models and the random Clifford circuit. We find that for the random Clifford circuit, the growth of multipartite entanglement remains slower in comparison to the random unitary case. However, the final saturation value of multipartite entanglement is almost the same in both cases. The behavior is then compared to the genuine multipartite entanglement obtained in random matrix product states with a moderately high bond dimension. We then relate the behavior of multipartite entanglement to other global properties of the system, viz. the delocalization of the many-body wavefunctions in Hilbert space. Along with this, we analyze the robustness of such highly entangled quantum states obtained through random unitary dynamics under weak measurements.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
