arXiv subjects

J. Ignacio Cirac

Publications and source records attributed to J. Ignacio Cirac.

At least 91 records · Page 5Linked to original sources

arXiv2022

Adiabatic Spectroscopy and a Variational Quantum Adiabatic Algorithm

Preparing the ground state of a Hamiltonian is a problem of great significance in physics with deep implications in the field of combinatorial optimization. The adiabatic algorithm is known to return the ground state for sufficiently long preparation times which depend on the a priori unknown spectral gap. Our work relates in a twofold way. First, we propose a method to obtain information about the spectral profile of the adiabatic evolution. Second, we present the concept of a variational quantum adiabatic algorithm (VQAA) for optimized adiabatic paths. We aim at combining the strengths of the adiabatic and the variational approaches for fast and high-fidelity ground state preparation while keeping the number of measurements as low as possible. Our algorithms build upon ancilla protocols which we present that allow to directly evaluate the ground state overlap. We benchmark for a non-integrable spin-1/2 transverse and longitudinal Ising chain with $N=53$ sites using tensor network techniques. Using a black box, gradient-based approach, we report a reduction in the total evolution time for a given desired ground state fidelity by a factor of ten, which makes our method suitable for the limited decoherence time of noisy-intermediate scale quantum devices.

quant-ph↗

arXiv2022

Gaussian matrix product states cannot efficiently describe critical systems

Gaussian fermionic matrix product states (GfMPS) form a class of ansatz quantum states for 1d systems of noninteracting fermions. We show, for a simple critical model of free hopping fermions, that: (i) any GfMPS approximation to its ground state must have bond dimension scaling superpolynomially with the system size, whereas (ii) there exists a non-Gaussian fermionic MPS approximation to this state with polynomial bond dimension. This proves that, in general, imposing Gaussianity at the level of the tensor network may significantly alter its capability to efficiently approximate critical Gaussian states. We also provide numerical evidence that the required bond dimension is subexponential, and thus can still be simulated with moderate resources.

quant-ph↗

arXiv2022

Spin-Holstein models in trapped-ion systems

In this work, we highlight how trapped-ion quantum systems can be used to study generalized Holstein models, and benchmark expensive numerical calculations. We study a particular spin-Holstein model that can be implemented with arrays of ions confined by individual microtraps, and that is closely related to the Holstein model of condensed matter physics, used to describe electron-phonon interactions. In contrast to earlier proposals, we focus on simulating many-electron systems and inspect the competition between charge-density wave order, fermion pairing and phase separation. In our numerical study, we employ a combination of complementary approaches, based on non-Gaussian variational ansatz states and matrix product states, respectively. We demonstrate that this hybrid approach outperforms standard density-matrix renormalization group calculations.

quant-ph↗

arXiv2022

Locality optimization for parent Hamiltonians of Tensor Networks

Tensor Network states form a powerful framework for both the analytical and numerical study of strongly correlated phases. Vital to their analytical utility is that they appear as the exact ground states of associated parent Hamiltonians, where canonical proof techniques guarantee a controlled ground space structure. Yet, while those Hamiltonians are local by construction, the known techniques often yield complex Hamiltonians which act on a rather large number of spins. In this paper, we present an algorithm to systematically simplify parent Hamiltonians, breaking them down into any given basis of elementary interaction terms. The underlying optimization problem is a semidefinite program, and thus the optimal solution can be found efficiently. Our method exploits a degree of freedom in the construction of parent Hamiltonians -- the excitation spectrum of the local terms -- over which it optimizes such as to obtain the best possible approximation. We benchmark our method on the AKLT model and the Toric Code model, where we show that the canonical parent Hamiltonians (acting on 3 or 4 and 12 sites, respectively) can be broken down to the known optimal 2-body and 4-body terms. We then apply our method to the paradigmatic Resonating Valence Bond (RVB) model on the kagome lattice. Here, the simplest previously known parent Hamiltonian acts on all the 12 spins on one kagome star. With our optimization algorithm, we obtain a vastly simpler Hamiltonian: We find that the RVB model is the exact ground state of a parent Hamiltonian whose terms are all products of at most four Heisenberg interactions, and whose range can be further constrained, providing a major improvement over the previously known 12-body Hamiltonian.

cond-mat.str-el↗

arXiv2022

Generation of photonic tensor network states with Circuit QED

We propose a circuit QED platform and protocol to generate microwave photonic tensor network states deterministically. We first show that using a microwave cavity as ancilla and a transmon qubit as emitter is a good platform to produce photonic matrix product states. The ancilla cavity combines a large controllable Hilbert space with a long coherence time, which we predict translates into a high number of entangled photons and states with a high bond dimension. Going beyond this paradigm, we then consider a natural generalization of this platform, in which several cavity-qubit pairs are coupled to form a chain. The photonic states thus produced feature a two-dimensional entanglement structure and can be interpreted as $\textit{radial plaquette}$ projected entangled pair states [Wei, Malz, and Cirac, Phys. Rev. Lett. 128, 010607 (2022)], which include many paradigmatic states, such as the broad class of isometric tensor network states, graph states, and string-net states.

quant-ph↗

arXiv2022

Long-range electron-electron interactions in quantum dot systems and applications in quantum chemistry

Long-range interactions play a key role in several phenomena of quantum physics and chemistry. To study these phenomena, analog quantum simulators provide an appealing alternative to classical numerical methods. Gate-defined quantum dots have been established as a platform for quantum simulation, but for those experiments the effect of long-range interactions between the electrons did not play a crucial role. Here we present the first detailed experimental characterization of long-range electron-electron interactions in an array of gate-defined semiconductor quantum dots. We demonstrate significant interaction strength among electrons that are separated by up to four sites, and show that our theoretical prediction of the screening effects matches well the experimental results. Based on these findings, we investigate how long-range interactions in quantum-dot arrays may be utilized for analog simulations of artificial quantum matter. We numerically show that about ten quantum dots are sufficient to observe binding for a one-dimensional $H_2$-like molecule. These combined experimental and theoretical results pave the way for future quantum simulations with quantum dot arrays and benchmarks of numerical methods in quantum chemistry.

quant-ph↗

arXiv2022

Sequential generation of projected entangled-pair states

We introduce plaquette projected entangled-pair states, a class of states in a lattice that can be generated by applying sequential unitaries acting on plaquettes of overlapping regions. They satisfy area-law entanglement, possess long-range correlations, and naturally generalize other relevant classes of tensor network states. We identify a subclass that can be more efficiently prepared in a radial fashion and that contains the family of isometric tensor network states [M. P. Zaletel and F. Pollmann, Phys. Rev. Lett. 124, 037201 (2020)]. We also show how this subclass can be efficiently prepared using an array of photon sources.

quant-ph↗

arXiv2021

Locally accurate tensor networks for thermal states and time evolution

Tensor network methods are routinely used in approximating various equilibrium and non-equilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a rigorous mathematical justification, since existing approximations to thermal states and time evolution demand a bond dimension growing with system size. To address this problem, we construct PEPOs that approximate, for all local observables, $i)$ their thermal expectation values and $ii)$ their Heisenberg time evolution. The bond dimension required does not depend on system size, but only on the temperature or time. We also show how these can be used to approximate thermal correlation functions and expectation values in quantum quenches.

quant-ph↗

arXiv2021

Convergence guarantees for discrete mode approximations to non-Markovian quantum baths

Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. The non-Markovian environment is often approximated by discrete bosonic modes, thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been previously proposed, the resulting approximation lacks rigorous and general convergence guarantees. In this letter, we show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that this approximation error typically falls off polynomially with the number of modes. Our results lend rigor to classical and quantum algorithms for approximating non-Markovian dynamics.

quant-ph↗

arXiv2021

Quantum Circuits assisted by LOCC: Transformations and Phases of Matter

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.

quant-ph↗

arXiv2021

Symmetries and local transformations of translationally invariant Matrix Product States

We determine the local symmetries and local transformation properties of translationally invariant matrix product states (MPS). We focus on physical dimension $d=2$ and bond dimension $D=3$ and use the procedure introduced in D. Sauerwein et al., Phys. Rev. Lett. 123, 170504 (2019) to determine all (including non--global) symmetries of those states. We identify and classify the stochastic local transformations (SLOCC) that are allowed among MPS. We scrutinize two very distinct sets of MPS and show the big diversity (also compared to the case $D=2$) occurring in both, their symmetries and the possible SLOCC transformations. These results reflect the variety of local properties of MPS, even if restricted to translationally invariant states with low bond dimension. Finally, we show that states with non-trivial local symmetries are of measure zero for $d = 2$ and $D > 3$.

quant-ph↗

arXiv2021

Computable Rényi mutual information: Area laws and correlations

The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on Rényi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.

quant-ph↗

arXiv2021

From Efimov Physics to the Bose Polaron using Gaussian States

Since the Efimov effect was introduced in 1970, a detailed theoretical understanding of Efimov physics has been developed in the few-body context. However, it has proven to be challenging to describe the role Efimov-type correlations play in many-body systems such as quenched or collapsing Bose-Einstein condensates (BECs). To study the impact the Efimov effect can have in such scenarios, we consider a light impurity immersed in a weakly interacting BEC, forming a Bose polaron. In this case, the higher-order correlations are localized around the impurity, making it more feasible to develop a theoretical description. Specifically, we employ a Gaussian state variational Ansatz in the reference frame of the impurity, capable of both capturing the Efimov effect and the formation of the polaron cloud. We find that the Efimov effect leads to a cooperative binding of bosons to the impurity and the formation of a many-body bound state. As a result, the polaron is not the ground state, but rendered a metastable excited state which can decay into these Efimov clusters. While this decay is slow for small interaction strengths, it becomes more prominent as the attractive scattering length increases, up to the point where the polaron becomes completely unstable. This critical scattering length can be interpreted as a many-body shifted Efimov resonance, where the scattering of two excitations of the bath with the polaron can lead to bound state formation. Compared to the few-body case, the resonance is shifted to smaller attractive scattering lengths due to the participation of the polaron cloud in the cooperative binding process. This corresponds to an intriguing scenario of polaron-assisted chemistry, where many-body effects lead to enhanced signal of the chemical recombination process, which can be directly probed in state-of-the-art experiments.

cond-mat.quant-gas↗

arXiv2021

Chemistry of a light impurity in a Bose-Einstein condensate

In ultracold atomic gases, a unique interplay arises between phenomena known from condensed matter physics, few-body physics and chemistry. Similar to an electron in a solid, an impurity in an ultracold gas can get dressed by excitations from the medium, forming a quasiparticle called the polaron. We study how dressing of an impurity leads to a modification of its chemical reactivity. Using a Gaussian state variational method in the frame of the impurity, we demonstrate that three-body correlations lead to an instability of the polaron. This instability is connected to an Efimov resonance, but shifted to smaller interactions by many-body effects, showing that polaron formation stimulates Efimov physics and the associated chemistry.

cond-mat.quant-gas↗

arXiv2021

Atomic waveguide QED with atomic dimers

Quantum emitters coupled to a waveguide is a paradigm of quantum optics, whose essential properties are described by waveguide quantum electrodynamics (QED). We study the possibility of observing the typical features of the conventional waveguide QED scenario in a system where the role of the waveguide is played by a one-dimensional subwavelength atomic array. For the role of emitters, we propose to use anti-symmetric states of atomic dimers - a pair of closely spaced atoms - as effective two-level systems, which significantly reduces the effect of free-space spontaneous emission. We solve the dynamics of the system both when the dimer frequency lies inside and when it lies outside the band of modes of the array. Along with well-known phenomena of collective emission into the guided modes and waveguide mediated long-range dimer-dimer interactions, we uncover significant non-Markovian corrections which arise from both the finiteness of the array and through retardation effects.

quant-ph↗

arXiv2021

Rényi free energy and variational approximations to thermal states

We propose the construction of thermodynamic ensembles that minimize the Rényi free energy, as an alternative to Gibbs states. For large systems, the local properties of these Rényi ensembles coincide with those of thermal equilibrium, and they can be used as approximations to thermal states. We provide algorithms to find tensor network approximations to the 2-Rényi ensemble. In particular, a matrix-product-state representation can be found by using gradient-based optimization on Riemannian manifolds, or via a non-linear evolution which yields the desired state as a fixed point. We analyze the performance of the algorithms and the properties of the ensembles on one-dimensional spin chains.

quant-ph↗

arXiv2021

Generalization of group-theoretic coherent states for variational calculations

We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan subalgebra elements and by applying these unitaries to regular group-theoretic coherent states. This enables us to generate entanglement not found in the coherent states themselves, while retaining many of their desirable properties. Most importantly, we explain how the expectation values of physical observables can be evaluated efficiently. Examples include generalized spin-coherent states and generalized Gaussian states, but our construction can be applied to any Lie group represented on the Hilbert space of a quantum system. We comment on their applicability as variational families in condensed matter physics and quantum information.

quant-ph↗

arXiv2021

Algorithms for quantum simulation at finite energies

We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a finite energy interval around its mean energy. This algorithm is based on a filtering operator, similar to quantum phase estimation, which projects out energies outside the desired energy interval. However, instead of performing this operation on a physical state, it recovers the physical values by performing interferometric measurements without the need to prepare the filtered state. We show that the computational time scales polynomially with the number of qubits, the inverse of the prescribed variance, and the inverse error. In practice, the algorithm does not require the evolution for long times, but instead a significant number of measurements in order to obtain sensible results. Our second algorithm is a quantum-assisted Monte Carlo sampling method to compute other quantities which approach the expectation values for the microcanonical and canonical ensembles. Using classical Monte Carlo techniques and the quantum computer as a resource, this method circumvents the sign problem that is plaguing classical Quantum Monte Carlo simulations, as long as one can prepare states with suitable energies. All algorithms can be used with small quantum computers and analog quantum simulators, as long as they can perform the interferometric measurements. We also show that this last task can be greatly simplified at the expense of performing more measurements.

quant-ph↗