arXiv subjects

J. Ignacio Cirac

Publications and source records attributed to J. Ignacio Cirac.

At least 289 records · Page 16Linked to original sources

arXiv2008

Matter--wave emission in optical lattices: Single particle and collective effects

We introduce a simple set--up corresponding to the matter-wave analogue of impurity atoms embedded in an infinite photonic crystal and interacting with the radiation field. Atoms in a given internal level are trapped in an optical lattice, and play the role of the impurities. Atoms in an untrapped level play the role of the radiation field. The interaction is mediated by means of lasers that couple those levels. By tuning the lasers parameters, it is possible to drive the system through different regimes, and observe phenomena like matter wave superradiance, non-Markovian atom emission, and the appearance of bound atomic states.

quant-ph↗

arXiv2008

Quantum circuits for strongly correlated quantum systems

In recent years, we have witnessed an explosion of experimental tools by which quantum systems can be manipulated in a controlled and coherent way. One of the most important goals now is to build quantum simulators, which would open up the possibility of exciting experiments probing various theories in regimes that are not achievable under normal lab circumstances. Here we present a novel approach to gain detailed control on the quantum simulation of strongly correlated quantum many-body systems by constructing the explicit quantum circuits that diagonalize their dynamics. We show that the exact quantum circuits underlying some of the most relevant many-body Hamiltonians only need a finite amount of local gates. As a particularly simple instance, the full dynamics of a one-dimensional Quantum Ising model in a transverse field with four spins is shown to be reproduced using a quantum circuit of only six local gates. This opens up the possibility of experimentally producing strongly correlated states, their time evolution at zero time and even thermal superpositions at zero temperature. Our method also allows to uncover the exact circuits corresponding to models that exhibit topological order and to stabilizer states.

quant-ph↗

arXiv2008

On entropy growth and the hardness of simulating time evolution

The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix Product States (MPS), their time evolution can encode quantum computations, so that simulating the latter should be hard classically. However, one might believe that for systems with high enough symmetry, and thus insufficient parameters to encode a quantum computation, efficient classical simulation is possible. We discuss supporting evidence to the contrary: We provide a rigorous proof of the observation that a time independent local Hamiltonian can yield a linear increase of the entropy when acting on a product state in a translational invariant framework. This criterion has to be met by any classical simulation method, which in particular implies that every global approximation of the evolution requires exponential resources for any MPS based method.

quant-ph↗

arXiv2008

Strings, Projected Entangled Pair States, and variational Monte Carlo methods

We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in Quantum Information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational abgorithm which extends DMRG to higher dimensional and irregular systems. Numerical results demonstrate the applicability of these states to the simulation of many-body sytems.

quant-ph↗

arXiv2008

Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation

We investigate the computational power of creating steady-states of quantum dissipative systems whose evolution is governed by time-independent and local couplings to a memoryless environment. We show that such a model allows for efficient universal quantum computation with the result of the computation encoded in the steady state. Due to the purely dissipative nature of the process, this way of doing quantum computation exhibits some inherent robustness and defies some of the DiVincenzo criteria for quantum computation. We show that there is a natural class of problems that can be solved with such a model - the preparation of ground states of frustration free quantum Hamiltonians. This allows for robust and efficient creation of exotic states that exhibit features like topological quantum order and the creation of PEPS and it proves the existence of novel dissipative phase transitions. In particular the latter can in principle be verified experimentally with present day technology such as with optical lattices.

quant-ph↗

arXiv2008

Dividing Quantum Channels

We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible' channels which can not be written as non-trivial products of other channels and study the set of 'infinitesimal divisible' channels which are elements of continuous completely positive evolutions. For qubit channels we obtain a complete characterization of the sets of indivisible and infinitesimal divisible channels. Moreover, we identify those channels which are solutions of time-dependent master equations for both positive and completely positive evolutions. For arbitrary finite dimension we prove a representation theorem for elements of continuous completely positive evolutions based on new results on determinants of quantum channels and Markovian approximations.

math-ph↗

arXiv2008

Sequentially generated states for the study of two dimensional systems

Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product States, expectation values of few body observables can be efficiently evaluated and, for the case of translationally invariant systems, the correlation functions decay exponentially with the distance. We show that such states are a subclass of Projected Entangled Pair States and investigate their suitability for approximating the ground states of local Hamiltonians.

quant-ph↗

arXiv2008

Quantum Phases of Trapped Ions in an Optical Lattice

We propose loading trapped ions into microtraps formed by an optical lattice. For harmonic microtraps, the Coulomb coupling of the spatial motions of neighboring ions can be used to construct a broad class of effective short-range Hamiltonians acting on an internal degree of freedom of the ions. For large anharmonicities, on the other hand, the spatial motion of the ions itself represents a spin-1/2 model with frustrated dipolar XY interactions. We illustrate the latter setup with three systems: the linear chain, the zig-zag ladder, and the triangular lattice. In the frustrated zig-zag ladder with dipolar interactions we find chiral ordering beyond what was predicted previously for a next-nearest-neighbor model. In the frustrated anisotropic triangular lattice with nearest-neighbor interactions we find that the transition from the one-dimensional gapless spin-liquid phase to the two-dimensional spiraling ordered phase passes through a gapped spin-liquid phase, similar to what has been predicted for the same model with Heisenberg interactions. Further, a second gapped spin-liquid phase marks the transition to the two-dimensional Neel-ordered phase.

cond-mat.str-el↗

arXiv2008

Entropy scaling and simulability by Matrix Product States

We investigate the relation between the scaling of block entropies and the efficient simulability by Matrix Product States (MPS), and clarify the connection both for von Neumann and Renyi entropies (see Table I). Most notably, even states obeying a strict area law for the von Neumann entropy are not necessarily approximable by MPS. We apply these results to illustrate that quantum computers might outperform classical computers in simulating the time evolution of quantum systems, even for completely translational invariant systems subject to a time independent Hamiltonian.

quant-ph↗

arXiv2007

Detection of Spin Correlations in Optical Lattices by Light Scattering

We show that spin correlations of atoms in an optical lattice can be reconstructed by coupling the system to the light, and by measuring correlations between the emitted photons. This principle is the basis for a method to characterize states in quantum computation and simulation with optical lattices. As examples, we study the detection of spin correlations in a quantum magnetic phase, and the characterization of cluster states.

quant-ph↗

arXiv2007

PEPS as unique ground states of local Hamiltonians

In this paper we consider projected entangled pair states (PEPS) on arbitrary lattices. We construct local parent Hamiltonians for each PEPS and isolate a condition under which the state is the unique ground state of the Hamiltonian. This condition, verified by generic PEPS and examples like the AKLT model, is an injective relation between the boundary and the bulk of any local region. While it implies the existence of an energy gap in the 1D case we will show that in certain cases (e.g., on a 2D hexagonal lattice) the parent Hamiltonian can be gapless with a critical ground state. To show this we invoke a mapping between classical and quantum models and prove that in these cases the injectivity relation between boundary and bulk solely depends on the lattice geometry.

quant-ph↗

arXiv2007

Entanglement in fermionic systems

The anticommuting properties of fermionic operators, together with the presence of parity conservation, affect the concept of entanglement in a composite fermionic system. Hence different points of view can give rise to different reasonable definitions of separable and entangled states. Here we analyze these possibilities and the relationship between the different classes of separable states. We illustrate the differences by providing a complete characterization of all the sets defined for systems of two fermionic modes. The results are applied to Gibbs states of infinite chains of fermions whose interaction corresponds to a XY-Hamiltonian with transverse magnetic field.

quant-ph↗

arXiv2007

The computational complexity of PEPS

We determine the computational power of preparing Projected Entangled Pair States (PEPS), as well as the complexity of classically simulating them, and generally the complexity of contracting tensor networks. While creating PEPS allows to solve PP problems, the latter two tasks are both proven to be #P-complete. We further show how PEPS can be used to approximate ground states of gapped Hamiltonians, and that creating them is easier than creating arbitrary PEPS. The main tool for our proofs is a duality between PEPS and postselection which allows to use existing results from quantum compexity.

quant-ph↗

arXiv2007

A measurement-based measure of the size of macroscopic quantum superpositions

Recent experiments claiming formation of quantum superposition states in near macroscopic sys- tems raise the question of how the sizes of general quantum superposition states in an interacting system are to be quantified. We propose here a measure of size for such superposition states that is based on what measurements can be performed to probe and distinguish the different branches of the state. The measure allows comparison of the effective size for superposition states in very different physical systems. It can be applied to a very general class of superposition states and reproduces known results for near-ideal cases. Comparison with a prior measure based on analy- sis of coherence between branches indicates that significantly smaller effective superposition sizes result from our measurement-based measure. Application to a system of interacting bosons in a double-well trapping potential shows that the effective superposition size is strongly dependent on the relative magnitude of the barrier height and interparticle interaction.

quant-ph↗

arXiv2007

Quantum processing photonic states in optical lattices

The mapping of photonic states to collective excitations of atomic ensembles is a powerful tool which finds a useful application in the realization of quantum memories and quantum repeaters. In this work we show that cold atoms in optical lattices can be used to perform an entangling unitary operation on the transferred atomic excitations. After the release of the quantum atomic state, our protocol results in a deterministic two qubit gate for photons. The proposed scheme is feasible with current experimental techniques and robust against the dominant sources of noise.

quant-ph↗

arXiv2006

Entanglement Percolation in Quantum Networks

Quantum networks are composed of nodes which can send and receive quantum states by exchanging photons. Their goal is to facilitate quantum communication between any nodes, something which can be used to send secret messages in a secure way, and to communicate more efficiently than in classical networks. These goals can be achieved, for instance, via teleportation. Here we show that the design of efficient quantum communication protocols in quantum networks involves intriguing quantum phenomena, depending both on the way the nodes are displayed, and the entanglement between them. These phenomena can be employed to design protocols which overcome the exponential decrease of signals with the number of nodes. We relate the problem of establishing maximally entangled states between nodes to classical percolation in statistical mechanics, and demonstrate that quantum phase transitions can be used to optimize the operation of quantum networks.

quant-ph↗

arXiv2006

Quantum simulations under translational symmetry

We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those that can not be simulated. Whereas for general spin systems no finite universal set of generating interactions is shown to exist, universality turns out to be generic for quadratic bosonic and fermionic nearest-neighbor interactions when supplemented by all translationally invariant on-site Hamiltonians.

quant-ph↗

arXiv2006

Quantum emulsion: a glassy phase of bosonic mixtures in optical lattices

We numerically investigate mixtures of two interacting bosonic species with unequal parameters in one-dimensional optical lattices. In large parameter regions full phase segregation is seen to minimize the energy of the system, but the true ground state is masked by an exponentially large number of metastable states characterized by microscopic phase separation. The ensemble of these quantum emulsion states, reminiscent of emulsions of immiscible fluids, has macroscopic properties analogous to those of a Bose glass, namely a finite compressibility in absence of superfluidity. Their metastability is probed by extensive quantum Monte Carlo simulations generating a rich correlated stochastic dynamics. The tuning of the repulsion of one of the two species via a Feshbach resonance drives the system through a quantum phase transition to the superfluid state.

cond-mat.str-el↗