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Register a new userPairwise tomography networks for many-body quantum systems
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We introduce the concept of pairwise tomography networks to characterise quantum properties in many-body systems and demonstrate an efficient protocol to measure them experimentally. Pairwise tomography networks are generators of multiplex networks where each layer represents the graph of a relevant quantifier such as, e.g., concurrence, quantum discord, purity, quantum mutual information, or classical correlations. We propose a measurement scheme to perform two-qubit tomography of all pairs showing exponential improvement in the number of qubits $N$ with respect to previously existing methods. We illustrate the usefulness of our approach by means of several examples revealing its potential impact to quantum computation, communication and simulation. We perform a proof-of-principle experiment demonstrating pairwise tomography networks of $W$ states on IBM Q devices.
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Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes impractical as the effort required grows exponentially in the number of constituents. Developing more efficient techniques is particularly pressing as precisely-controllable quantum systems that are well beyond the reach of QST are emerging in laboratories. Motivated by this, there is a considerable ongoing effort to develop new characterisation tools for quantum many-body systems. Here we demonstrate Matrix Product State (MPS) tomography, which is theoretically proven to allow the states of a broad class of quantum systems to be accurately estimated with an effort that increases efficiently with constituent number. We first prove that this broad class includes the out-of-equilbrium states produced by 1D systems with finite-range interactions, up to any fixed point in time. We then use the technique to reconstruct the dynamical state of a trapped-ion quantum simulator comprising up to 14 entangled spins (qubits): a size far beyond the reach of QST. Our results reveal the dynamical growth of entanglement and description complexity as correlations spread out during a quench: a necessary condition for future beyond-classical performance. MPS tomography should find widespread use to study large quantum many-body systems and to benchmark and verify quantum simulators and computers.
Coupling a quantum many-body system to an external environment dramatically changes its dynamics and offers novel possibilities not found in closed systems. Of special interest are the properties of the steady state of such open quantum many-body systems, as well as the relaxation dynamics towards the steady state. However, new computational tools are required to simulate open quantum many-body systems, as methods developed for closed systems cannot be readily applied. We review several approaches to simulate open many-body systems and point out the advances made in recent years towards the simulation of large system sizes.
A hierarchy of equations for equilibrium reduced density matrices obtained earlier is used to consider systems of spinless bosons bound by forces of gravity alone. The systems are assumed to be at absolute zero of temperature under conditions of Bose condensation. In this case, a peculiar interplay of quantum effects and of very weak gravitational interaction between microparticles occurs. As a result, there can form spatially-bounded equilibrium structures macroscopic in size, both immobile and rotating. The size of a structure is inversely related to the number of particles in the structure. When the number of particles is relatively small the size can be enormous, whereas if this numbder equals Avogadros number the radius of the structure is about 30 cm in the case that the structure consists of hydrogen atoms. The rotating objects have the form of rings and exhibit superfluidity. An atmosphere that can be captured by tiny celestial bodies from the ambient medium is considered too. The thickness of the atmosphere decreases as its mass increases. If short-range intermolecular forces are taken into account, the results obtained hold for excited states whose lifetime can however be very long. The results of the paper can be utilized for explaining the first stage of formation of celestial bodies from interstellar and even intergalactic gases.
Controllable systems relying on quantum behavior to simulate distinctly quantum models so far rely on increasingly challenging classical computing to verify their results. We develop a general protocol for confirming that an arbitrary many-body system, such as a quantum simulator, can entangle distant objects. The protocol verifies that distant qubits interacting separately with the system can become mutually entangled, and therefore serves as a local test that excitations of the system can create non-local quantum correlations. We derive an inequality analogous to Bells inequality which can only be violated through entanglement between distant sites of the many-body system. Although our protocol is applicable to general many-body systems, it requires finding system-dependent local operations to violate the inequality. A specific example in quantum magnetism is presented.
Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions in instances of quantum simulations. This article provides an overview on the progress in understanding dynamical equilibration and thermalisation of closed quantum many-body systems out of equilibrium due to quenches, ramps and periodic driving. It also addresses topics such as the eigenstate thermalisation hypothesis, typicality, transport, many-body localisation, universality near phase transitions, and prospects for quantum simulations.
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