arXiv subjects

Ivan Rungger

Publications and source records attributed to Ivan Rungger.

At least 37 records · Page 2Linked to original sources

arXiv2022

Quantum subspace expansion algorithm for Green's functions

We present an algorithm to compute Green's functions on quantum computers for interacting electron systems, which is a challenging task on conventional computers. It uses a continued fraction representation based on the Lanczos method, where the wave functions are expanded as linear combination of basis states within a quantum subspace. While on conventional computers the cost of the computation grows exponentially with system size, limiting the method to small systems, by representing the basis states on a quantum computer one may overcome this exponential scaling barrier. We propose a two-level multigrid Trotter time evolution for an efficient preparation of the basis states in a quantum circuit, which takes advantage of the robustness of the subspace expansion against Trotter errors. Using a quantum emulator we demonstrate the algorithm for the Hubbard model on a Bethe lattice with infinite coordination, which we map to a 16 qubit Anderson impurity model within the dynamical mean field theory. Our algorithm computes the Green's function accurately for both the metallic and Mott insulating regimes, with a circuit depth several orders of magnitude below what has been proposed using time evolution. The two-level multigrid time evolution reduces the number of Trotter steps required to compute the Green's function to about four to six. We therefore expect that the method can be used on near term quantum computers for moderate system sizes, while allowing for scalability to larger circuit depths and qubit numbers on future fault tolerant quantum computers.

quant-ph↗

arXiv2022

Spectral analysis for noise diagnostics and filter-based digital error mitigation

We investigate the effects of noise on parameterised quantum circuits using spectral analysis and classical signal processing tools. For different noise models, we quantify the additional, higher frequency modes in the output signal caused by device errors. We show that filtering these noise-induced modes effectively mitigates device errors. When combined with existing methods, this yields an improved reconstruction of the noiseless variational landscape. Moreover, we describe the classical and quantum resource requirements for these techniques and test their effectiveness for application motivated circuits on quantum hardware.

quant-ph↗

arXiv2022

Non-trivial symmetries in quantum landscapes and their resilience to quantum noise

Very little is known about the cost landscape for parametrized Quantum Circuits (PQCs). Nevertheless, PQCs are employed in Quantum Neural Networks and Variational Quantum Algorithms, which may allow for near-term quantum advantage. Such applications require good optimizers to train PQCs. Recent works have focused on quantum-aware optimizers specifically tailored for PQCs. However, ignorance of the cost landscape could hinder progress towards such optimizers. In this work, we analytically prove two results for PQCs: (1) We find an exponentially large symmetry in PQCs, yielding an exponentially large degeneracy of the minima in the cost landscape. Alternatively, this can be cast as an exponential reduction in the volume of relevant hyperparameter space. (2) We study the resilience of the symmetries under noise, and show that while it is conserved under unital noise, non-unital channels can break these symmetries and lift the degeneracy of minima, leading to multiple new local minima. Based on these results, we introduce an optimization method called Symmetry-based Minima Hopping (SYMH), which exploits the underlying symmetries in PQCs. Our numerical simulations show that SYMH improves the overall optimizer performance in the presence of non-unital noise at a level comparable to current hardware. Overall, this work derives large-scale circuit symmetries from local gate transformations, and uses them to construct a noise-aware optimization method.

quant-ph↗

arXiv2022

The Variational Quantum Eigensolver: a review of methods and best practices

The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are constrained in their accuracy due to the computational limits. The VQE may be used to model complex wavefunctions in polynomial time, making it one of the most promising near-term applications for quantum computing. Finding a path to navigate the relevant literature has rapidly become an overwhelming task, with many methods promising to improve different parts of the algorithm. Despite strong theoretical underpinnings suggesting excellent scaling of individual VQE components, studies have pointed out that their various pre-factors could be too large to reach a quantum computing advantage over conventional methods. This review aims to provide an overview of the progress that has been made on the different parts of the algorithm. All the different components of the algorithm are reviewed in detail including representation of Hamiltonians and wavefunctions on a quantum computer, the optimization process, the post-processing mitigation of errors, and best practices are suggested. We identify four main areas of future research:(1) optimal measurement schemes for reduction of circuit repetitions; (2) large scale parallelization across many quantum computers;(3) ways to overcome the potential appearance of vanishing gradients in the optimization process, and how the number of iterations required for the optimization scales with system size; (4) the extent to which VQE suffers for quantum noise, and whether this noise can be mitigated. The answers to these open research questions will determine the routes for the VQE to achieve quantum advantage as the quantum computing hardware scales up and as the noise levels are reduced.

quant-ph↗

arXiv2022

Efficient recovery of variational quantum algorithms landscapes using classical signal processing

We employ spectral analysis and compressed sensing to identify settings where a variational algorithm's cost function can be recovered purely classically or with minimal quantum computer access. We present theoretical and numerical evidence supporting the viability of sparse recovery techniques. To demonstrate this approach, we use basis pursuit denoising to efficiently recover simulated Quantum Approximate Optimization Algorithm (QAOA) instances of large system size from very few samples. Our results indicate that sparse recovery can enable a more efficient use and distribution of quantum resources in the optimisation of variational algorithms.

quant-ph↗

arXiv2022

Dynamical Mean-Field Theory for spin-dependent electron transport in spin-valve devices

We present the combination of Density Functional Theory (DFT) and Dynamical Mean Field Theory (DMFT) for computing the electron transmission through two-terminals nanoscale devices. The method is then applied to metallic junctions presenting alternating Cu and Co layers, which exhibit spin-dependent charge transport and giant magnetoresistance (GMR) effect. The calculations show that the coherent transmission through the $3d$ states is greatly suppressed by electron correlations. This is mainly due to the finite lifetime induced by the electron-electron interaction and is directly related to the imaginary part of the computed many-body DMFT self-energy. At the Fermi energy, where in accordance with the Fermi-liquid behavior the imaginary part of the self-energy vanishes, the suppression of the transmission is entirely due to the shifts of the energy spectrum induced by electron correlations. Based our results, we finally suggest that the GMR measured in Cu/Co heterostructures for electrons with energies about 1 eV above the Fermi energy is a clear manifestation of dynamical correlation effects.

cond-mat.str-el↗

arXiv2022

The DFT+$Σ_2$ method for electron correlation effects at transition metal surfaces

We present a computational approach for electronically correlated metallic surfaces and interfaces, which combines Density Functional and Dynamical Mean Field Theory using a multi-orbital perturbative solver for the many-body problem. Our implementation is designed to describe ferromagnetic metallic thin films on a substrate. The performances are assessed in detail for a Fe monolayer on a W(110) substrate, a prototypical nanoscale magnetic system. Comparing our results to photoemission data, we find qualitative and quantitative improvements in the calculated spectral function with respect to the results of Density Functional Theory within the local spin density approximation. In particular, the spin-splitting of the $d$ states is drastically reduced and, at the same time, their spectral width becomes narrower. The method is therefore able to account for the main correlation effects in the system.

cond-mat.str-el↗

arXiv2022

Spin-orbit induced equilibrium spin currents in materials

The existence of spin-currents in absence of any driving external fields is commonly considered an exotic phenomenon appearing only in quantum materials, such as topological insulators. We demonstrate instead that equilibrium spin currents are a rather general property of materials with non negligible spin-orbit coupling (SOC). Equilibrium spin currents can be present at the surfaces of a slab. Yet, we also propose the existence of global equilibrium spin currents, which are net bulk spin-currents along specific crystallographic directions of materials. Equilibrium spin currents are allowed by symmetry in a very broad class of systems having gyrotropic point groups. The physics behind equilibrium spin currents is uncovered by making an analogy between electronic systems with SOC and non-Abelian gauge theories. The electron spin can be seen as the analogous of the color degree of freedom and equilibrium spin currents can then be identified with diamagnetic color currents appearing as the response to an effective non-Abelian magnetic field generated by SOC. Equilibrium spin currents are not associated with spin transport and accumulation, but they should nonetheless be carefully taken into account when computing transport spin currents. We provide quantitative estimates of equilibrium spin currents for several systems, specifically metallic surfaces presenting Rashba-like surface states, nitride semiconducting nanostructures and bulk materials, such as the prototypical gyrotropic medium tellurium. In doing so, we also point out the limitations of model approaches showing that first-principles calculations are needed to obtain reliable predictions. We therefore use Density Functional Theory computing the so-called bond currents, which represent a powerful tool to understand the relation between equilibrium currents, electronic structure and crystal point group.

cond-mat.mes-hall↗

arXiv2021

Data-Driven Dynamical Mean-Field Theory: an error-correction approach to solve the quantum many-body problem using machine learning

Machine learning opens new avenues for modelling correlated materials. Quantum embedding approaches, such as the dynamical mean-field theory (DMFT), provide corrections to first-principles calculations for strongly correlated materials, which are poorly described at lower levels of theory. Such embedding approaches are computationally demanding on classical computing architectures, and hence remain restricted to small systems, which limits the scope of applicability without exceptional computational resources. Here we outline a data-driven machine learning process for solving the Anderson Impurity Model (AIM) - the central component of DMFT calculations. The key advance is the use of an ensemble error-correction approach to generate fast and accurate solutions of AIM. An example calculation of the Mott transition using DMFT in the single band Hubbard model is given as an example of the technique, and is validated against the most accurate available method. This new approach is called data-driven dynamical mean-field theory (\textbf{d$^{3}$MFT}).

physics.comp-ph↗

arXiv2021

Krylov variational quantum algorithm for first principles materials simulations

We propose an algorithm to obtain Green's functions as a continued fraction on quantum computers, which is based on the construction of the Krylov basis using variational quantum algorithms, and included in a Lanczos iterative scheme. This allows the integration of quantum algorithms with first principles material science simulations, as we demonstrate within the dynamical mean-field theory (DMFT) framework. DMFT enables quantitative predictions for strongly correlated materials, and relies on the calculation of Green's functions. On conventional computers the exponential growth of the Hilbert space with the number of orbitals limits DMFT to small systems. Quantum computers open new avenues and can lead to a significant speedup in the computation of expectation values required to obtain the Green's function. We apply our Krylov variational quantum algorithm combined with DMFT to the charge transfer insulator La$_{2}$CuO$_4$ using a quantum computing emulator, and show that with 8 qubits it predicts the correct insulating material properties for the paramagnetic phase. We therefore expect that the method is ideally suited to perform simulations for real materials on near term quantum hardware.

quant-ph↗

arXiv2021

Pressure induced electronic transitions in Samarium monochalcogenides

Pressure induced isostructural insulator to metal transition for SmS is characterised by the presence of an intermediate valence state at higher pressure which cannot be captured by the density functional theory. As a direct outcome of including the charge and spin fluctuations incorporated in dynamical mean field theory, we see the emergence of insulating and metallic phases with increasing pressure as a function of changing valence. This is accompanied by significantly improved predictions of the equilibrium lattice constants and bulk moduli for all Sm-monochalcogenides verifying experiments. Nudged Elastic Band analysis reveals the insulating states to have a finite quasiparticle weight, decreasing as the gap closes rendering the transition to be not Mott-like, and classifies these materials as correlated band insulators. The difference between the discontinuous and continuous natures of these transitions can be attributed to the closeness of the sharply resonant Sm-4f peaks to the fermi level in the predicted metallic states in SmS as compared to SmSe and SmTe.

cond-mat.str-el↗

arXiv2021

Reduced Density Matrix Sampling: Self-consistent Embedding and Multiscale Electronic Structure on Current Generation Quantum Computers

We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum chemistry and condensed matter physics. In both of these contexts, a strongly correlated quantum region of the extended system is isolated and self-consistently coupled to its environment via the sampling of reduced density matrices. We analyze the viability of current generation quantum devices to provide the required fidelity of these objects for a robust and efficient optimization of this subspace. We show that with a simple error mitigation strategy and optimization of compact tensor product bases to minimize the number of terms to sample, these self-consistent algorithms are indeed highly robust, even in the presence of significant noises on quantum hardware. Furthermore, we demonstrate the use of these density matrices for the sampling of non-energetic properties, including dipole moments and Fermi liquid parameters in condensed phase systems, achieving a reliable accuracy with sparse sampling. It appears that uncertainties derived from the iterative optimization of these subspaces is smaller than variances in the energy for a single subspace optimization with current quantum hardware. This boosts the prospect for routine self-consistency to improve the choice of correlated subspaces in hybrid quantum-classical approaches to electronic structure for large systems in this multiscale fashion.

quant-ph↗

arXiv2021

Maximally Localized Dynamical Quantum Embedding for Solving Many-Body Correlated Systems

We present a quantum embedding methodology to resolve the Anderson impurity model in the context of dynamical mean-field theory, based on an extended exact diagonalization method. Our method provides a maximally localized quantum impurity model, where the non-local components of the correlation potential remain minimal. This method comes at a large benefit, as the environment used in the quantum embedding approach is described by propagating correlated electrons and hence offers a polynomial increase $O(N^4)$ of the number of degrees of freedom for the embedding mapping without adding bath sites. We report that quantum impurity models with as few as 3 bath sites can reproduce both the Mott transition and the Kondo physics, thus opening a more accessible route to the description of time-dependent phenomena. Finally, we obtain excellent agreement for dynamical magnetic susceptibilities, poising this approach as a candidate to describe 2-particle excitations such as excitons in correlated systems. We expect that our approach will be highly beneficial for the implementation of embedding algorithms on quantum computers, as it allows for a fine description of the correlation in materials with a reduced number of required qubits.

cond-mat.str-el↗

arXiv2020

Evaluating the noise resilience of variational quantum algorithms

We simulate the effects of different types of noise in state preparation circuits of variational quantum algorithms. We first use a variational quantum eigensolver to find the ground state of a Hamiltonian in presence of noise, and adopt two quality measures in addition to the energy, namely fidelity and concurrence. We then extend the task to the one of constructing, with a layered quantum circuit ansatz, a set of general random target states. We determine the optimal circuit depth for different types and levels of noise, and observe that the variational algorithms mitigate the effects of noise by adapting the optimised parameters. We find that the inclusion of redundant parameterised gates makes the quantum circuits more resilient to noise. For such overparameterised circuits different sets of parameters can result in the same final state in the noiseless case, which we denote as parameter degeneracy. Numerically, we show that this degeneracy can be lifted in the presence of noise, with some states being significantly more resilient to noise than others. We also show that the average deviation from the target state is linear in the noise level, as long as this is small compared to a circuit-dependent threshold. In this region the deviation is well described by a stochastic model. Above the threshold, the optimisation can converge to states with largely different physical properties from the true target state, so that for practical applications it is critical to ensure that noise levels are below this threshold.

quant-ph↗

arXiv2020

Quantum State Discrimination Using Noisy Quantum Neural Networks

Near-term quantum computers are noisy, and therefore must run algorithms with a low circuit depth and qubit count. Here we investigate how noise affects a quantum neural network (QNN) for state discrimination, applicable on near-term quantum devices as it fulfils the above criteria. We find that when simulating gradient calculation on a noisy device, a large number of parameters is disadvantageous. By introducing a new smaller circuit ansatz we overcome this limitation, and find that the QNN performs well at noise levels of current quantum hardware. We also show that networks trained at higher noise levels can still converge to useful parameters. Our findings show that noisy quantum computers can be used in applications for state discrimination and for classifiers of the output of quantum generative adversarial networks.

quant-ph↗

arXiv2019

Existence of Shapiro Steps in the Dissipative Regime in Superconducting Weak Links

We present measurements of microwave-induced Shapiro steps in a superconducting nanobridge weak link in the dissipative branch of a hysteretic current-voltage characteristic. We demonstrate that Shapiro steps can be used to infer a reduced critical current and associated effective local temperature. Our observation of Shapiro steps in the dissipative branch hows that a finite Josephson coupling exists in the dissipative state and thus can be used to put an upper limit on the effective temperature and on the size of the region that can be heated above the critical temperature. This work provides evidence that Josephson behaviour can still exist in thermally-hysteretic weak link devices and will allow extension of the temperature ranges that nanobridge based single flux quantum circuits, nanoSQUIDs and Josephson voltage standards can be used.

cond-mat.supr-con↗

arXiv2018

Robust organic radical molecular junctions using acetylene terminated groups for C-Au bond formation

Organic paramagnetic and electroactive molecules are attracting interest as core components of molecular electronic and spintronic devices. Currently, further progress is hindered by the modest stability and reproducibility of the molecule/electrode contact. We report the synthesis of a persistent organic radical bearing one and two terminal alkyne groups to form Au-C σ bonds. The formation and stability of self-assembled monolayers and the electron transport through single-molecule junctions at room temperature have been studied. The combined analysis of both systems demonstrates that this linker forms a robust covalent bond with gold and a better-defined contact when compared to traditional sulfur-based linkers. Density functional theory and quantum transport calculations support the experimental observation highlighting a reduced variability of conductance values for the C-Au based junction. Our findings advance the quest for robustness and reproducibility of devices based on electroactive molecules.

cond-mat.mes-hall↗

arXiv2018

Search for alternative magnetic tunnel junctions based on all-Heusler stacks

By imposing the constraints of structural compatibility, stability and a large tunneling magneto-resistance, we have identified the Fe$_3$Al/BiF$_3$/Fe$_3$Al stack as a possible alternative to the well-established FeCoB/MgO/FeCoB in the search for a novel materials platform for high-performance magnetic tunnel junctions. Various geometries of the Fe$_3$Al/BiF$_3$/Fe$_3$Al structure have been analyzed, demonstrating that a barrier of less than 2~nm yields a tunneling magneto-resistance in excess of 25,000~\% at low bias, without the need for the electrodes to be half-metallic. Importantly, the presence of a significant spin gap in Fe$_3$Al for states with $Δ_1$ symmetry along the stack direction makes the TMR very resilient to high voltages.

cond-mat.mtrl-sci↗