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Register a new userAlgorithmic simulation of far-from-equilibrium dynamics using quantum computer
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We point out that superconducting quantum computers are prospective for the simulation of the dynamics of spin models far from equilibrium, including nonadiabatic phenomena and quenches. The important advantage of these machines is that they are programmable, so that different spin models can be simulated in the same chip, as well as various initial states can be encoded into it in a controllable way. This opens an opportunity to use superconducting quantum computers in studies of fundamental problems of statistical physics such as the absence or presence of thermalization in the free evolution of a closed quantum system depending on the choice of the initial state as well as on the integrability of the model. In the present paper, we performed proof-of-principle digital simulations of two spin models, which are the central spin model and the transverse-field Ising model, using 5- and 16-qubit superconducting quantum computers of the IBM Quantum Experience. We found that these devices are able to reproduce some important consequences of the symmetry of the initial state for the systems subsequent dynamics, such as the excitation blockade. However, lengths of algorithms are currently limited due to quantum gate errors. We also discuss some heuristic methods which can be used to extract valuable information from the imperfect experimental data.
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We propose a fully operational framework to study the non-equilibrium thermodynamics of a quantum system $S$ that is coupled to a detector $D$ whose state is continuously monitored, allowing to single out individual quantum trajectories of $S$. We focus on detailed fluctuation theorems and characterize the entropy production of the system. We establish fundamental differences with respect to the thermodynamic of unmonitored, unitarily evolved systems. We consider the paradigmatic example of circuit-QED, where superconducting qubits can be coupled to a continuously monitored resonator and show numerical simulations using state of the art experimental parameters.
We implement several quantum algorithms in real five-qubit superconducting quantum processor IBMqx4 to perform quantum computation of the dynamics of spin-1/2 particles interacting directly and indirectly through the boson field. Particularly, we focus on effects arising due to the presence of entanglement in the initial state of the system. The dynamics is implemented in a digital way using Trotter expansion of evolution operator. Our results demonstrate that dynamics in our modeling based on real device is governed by quantum interference effects being highly sensitive to phase parameters of the initial state. We also discuss limitations of our approach due to the device imperfection as well as possible scaling towards larger systems.
Methods of processing quantum data become more important as quantum computing devices improve their quality towards fault tolerant universal quantum computers. These methods include discrimination and filtering of quantum states given as an input to the device that may find numerous applications in quantum information technologies. In the present paper, we address a scheme of a classification of input states, which is nondestructive and deterministic for certain inputs, while probabilistic, in general case. This can be achieved by incorporating phase estimation algorithm into the hybrid quantum-classical computation scheme, where quantum block is trained classically. We perform proof-of-principle implementation of this idea using superconducting quantum processor of IBM Quantum Experience. Another aspect we are interested in is a mitigation of errors occurring due to the quantum device imperfections. We apply a series of heuristic tricks at the stage of classical postprocessing in order to improve raw experimental data and to recognize patterns in them. These ideas may find applications in other realization of hybrid quantum-classical computations with noisy quantum machines.
The quantum dynamics of interacting many-body systems has become a unique venue for the realization of novel states of matter. Here we unveil a new class of nonequilibrium states that are eigenstates of an emergent local Hamiltonian. The latter is explicitly time dependent and, even though it does not commute with the physical Hamiltonian, it behaves as a conserved quantity of the time-evolving system. We discuss two examples in which the emergent eigenstate solution can be applied for an extensive (in system size) time: transport in one-dimensional lattices with initial particle (or spin) imbalance, and sudden expansion of quantum gases in optical lattices. We focus on noninteracting spinless fermions, hard-core bosons, and the Heisenberg model. We show that current-carrying states can be ground states of emergent local Hamiltonians, and that they can exhibit a quasimomentum distribution function that is peaked at nonzero (and tunable) quasimomentum. We also show that time-evolving states can be highly-excited eigenstates of emergent local Hamiltonians, with an entanglement entropy that does not exhibit volume-law scaling.
We present exact results on a novel kind of emergent random matrix universality that quantum many-body systems at infinite temperature can exhibit. Specifically, we consider an ensemble of pure states supported on a small subsystem, generated from projective measurements of the remainder of the system in a local basis. We rigorously show that the ensemble, derived for a class of quantum chaotic systems undergoing quench dynamics, approaches a universal form completely independent of system details: it becomes uniformly distributed in Hilbert space. This goes beyond the standard paradigm of quantum thermalization, which dictates that the subsystem relaxes to an ensemble of quantum states that reproduces the expectation values of local observables in a thermal mixed state. Our results imply more generally that the distribution of quantum states themselves becomes indistinguishable from those of uniformly random ones, i.e. the ensemble forms a quantum state-design in the parlance of quantum information theory. Our work establishes bridges between quantum many-body physics, quantum information and random matrix theory, by showing that pseudo-random states can arise from isolated quantum dynamics, opening up new ways to design applications for quantum state tomography and benchmarking.
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