Exact Quantum Research Articles

Robust three-qubit search algorithm in Rydberg atoms via geometric control

Rydberg atoms possess long coherence time and inherent scalability, which makes it promising to implement quantum algorithms. An exact and robust quantum search algorithm (SA) is essential to some practical applications. Here we propose a multisolution three-qubit SA by employing quantum circuit and geometric operations, in which the target states can be successfully searched with the fidelity of at least 99.8$%$ and the geometric operators guarantee robustness against systematic errors. In particular, the geometric three-qubit gate operators employed reduce the implementation time and help to resist against the detrimental influence of decoherence. Moreover, our scheme can be straightforwardly extended to multiqubit cases. We have carried out numerical simulations based on the master equation to illustrate the superiority of our scheme. We consider that our study provides an alternative method for executing quantum SAs with high success probability.

Simulation of exact quantum Ising models with a Mott insulator of paired atoms

Quantum simulation of the XXZ model with a two-component Bose or Fermi Hubbard model based on a Mott insulator background has been widely used in the investigations of quantum magnetism with ultracold neutral atoms. In most cases, the diagonal spin-spin interaction is always accompanied by a large spin-exchange interaction which hinders the formation of long-range magnetic order at low temperature. Here we show that the spin-exchange interaction can be strongly reduced in a Mott insulator of paired atoms, while the diagonal spin-spin interaction remains unaffected. Thus, the effective magnetic model is quite close to an exact classical Ising model in the textbook. And we analysed an experimentally achievable three-component Fermi-Hubbard model of $\mathrm{{}^{6}Li}$ with two hyperfine levels of atoms paired in the lattice. We find the long-range antiferromagnetic order of such a three-component Fermi-Hubbard model can be much stronger than that of a typical two-component Fermi-Hubbard model at low temperature. And we discussed the possiblity of simulating an exact two-dimensional ferromagnetic Ising model in a Mott insulator of paired bosonic atoms. Our results may be useful for experimental investigation of the long-range Ising-like magnetism with ultracold neutral atoms under thermal equilibrium.

Nonadiabatic Couplings Can Speed Up Quantum Tunneling Transition Path Times.

Quantum tunneling is known to play an important role in the dynamics of systems with nonadiabatic couplings. However, until recently, the time-domain properties of nonadiabatic scattering have been severely under-explored. Using numerically exact quantum methods, we study the impact that nonadiabatic couplings have on the time it takes to tunnel through a barrier. We find that the Wigner phase time is the appropriate measure to use when determining the tunneling flight time also when considering nonadiabatic systems. The central result of the present study is that in an avoided crossing system in one dimension, the nonadiabatic couplings speed up the tunneling event, relative to the adiabatic case in which all nonadiabatic coupling is ignored. This has implications for both the study of quantum tunneling times and for the field of nonadiabatic scattering and chemistry.

A linear algorithm for the restricted subtraction games

The subtraction game is a well-known problem in the field of game theory, which is often called a one-heap Nim game. There are two players, a heap of tokens, and a strategy matrix, in this game. It is called a restricted subtraction game if some constraints are imposed on the strategy matrix. The subtraction game could be solved by a classical algorithm with a query complexity no less than O(N2) and computed by an O(N32logN) quantum query algorithm with an error probability ϵ≤1N. The restricted subtraction game proposed by Huang et al. can be computed by an exact quantum algorithm with O(N32) queries. They also proved that the classical exact query complexity is Θ(N2). In this study, we use an array and an adjacency list to replace the strategy matrix and propose another more general subtraction game than the one introduced by Huang et al. Based on dynamic programming and the replaced game strategy, two linear classical query algorithms are designed to solve the restricted subtraction game proposed by Huang and this study, respectively.

Bypassing backmapping: Coarse-grained electronic property distributions using heteroscedastic Gaussian processes.

We employ deep kernel learning electronic coarse-graining (DKL-ECG) with approximate Gaussian processes as a flexible and scalable framework for learning heteroscedastic electronic property distributions as a smooth function of coarse-grained (CG) configuration. The appropriateness of the Gaussian prior on predictive CG property distributions is justified as a function of CG model resolution by examining the statistics of target distributions. The certainties of predictive CG distributions are shown to be limited by CG model resolution with DKL-ECG predictive noise converging to the intrinsic physical noise induced by the CG mapping operator for multiple chemistries. Further analysis of the resolution dependence of learned CG property distributions allows for the identification of CG mapping operators that capture CG degrees of freedom with strong electron-phonon coupling. We further demonstrate the ability to construct the exact quantum chemical valence electronic density of states (EDOS), including behavior in the tails of the EDOS, from an entirely CG model by combining iterative Boltzmann inversion and DKL-ECG. DKL-ECG provides a means of learning CG distributions of all-atom properties that are traditionally "lost" in CG model development, introducing a promising methodological alternative to backmapping algorithms commonly employed to recover all-atom property distributions from CG simulations.

Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale

The numerical simulation of quantum circuits is an indispensable tool for development, verification, and validation of hybrid quantum-classical algorithms intended for near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. We present a modernized version of the Tensor Network Quantum Virtual Machine (TNQVM) that serves as the quantum circuit simulation backend in the eXtreme-scale ACCelerator (XACC) framework. The new version is based on the scalable tensor network processing library ExaTN (Exascale Tensor Networks). It provides multiple configurable quantum circuit simulators that perform either an exact quantum circuit simulation via the full tensor network contraction or an approximate simulation via a suitably chosen tensor factorization scheme. Upon necessity, stochastic noise modeling from real quantum processors is incorporated into the simulations by modeling quantum channels with Kraus tensors. By combining the portable XACC quantum programming frontend and the scalable ExaTN numerical processing backend, we introduce an end-to-end virtual quantum development environment that can scale from laptops to future exascale platforms. We report initial benchmarks of our framework, which include a demonstration of the distributed execution, incorporation of quantum decoherence models, and simulation of the random quantum circuits used for the certification of quantum supremacy on Google’s Sycamore superconducting architecture.

Quantum Clones inside Black Holes

A systematic procedure is proposed for better understanding the evolution laws of black holes in terms of pure quantum states. We start with the two opposed regions I and II in the Penrose diagram, and study the evolution of matter in these regions, using the algebra derived earlier from the Shapiro effect in quantum particles. Since this spacetime has two distinct asymptotic regions, one must assume that there is a mechanism that reduces the number of states. In earlier work we proposed that region II describes the angular antipodes of region I, the ‘antipodal identification’, but this eventually leads to contradictions. Our much simpler proposal is now that all states defined in region II are exact quantum clones of those in region I. This indicates more precisely how to restore unitarity by making all quantum states observable, and in addition suggests that generalisations towards other black hole structures will be possible. An apparent complication is that the wave function must evolve with a purely antisymmetric, imaginary-valued Hamiltonian, but this complication can be well-understood in a realistic interpretation of quantum mechanics.

Localization and delocalization in networks with varied connectivity

We study the phenomenon of localization and delocalization in a circuit-QED network with connectivity varying from finite-range coupling to all-to-all coupling. We find a fascinating interplay between interactions and connectivity. In particular, we consider (i) harmonic, (ii) Jaynes-Cummings, and (iii) Bose-Hubbard networks. We start with the initial condition where one of the nodes in the network is populated and then let it evolve in time. The time dynamics and steady state characterize the features of localization (self-trapping) in these large-scale networks. For the case of harmonic networks, exact analytical results are obtained, and we demonstrate that all-to-all connection shows self-trapping whereas the finite-ranged connectivity shows delocalization. The interacting cases (Jaynes-Cummings and Bose-Hubbard networks) are investigated both via exact quantum dynamics and via a semiclassical approach. We obtain an interesting phase diagram when one varies the range of connectivity and the strength of the interaction. We investigate the consequence of imperfections in the cavity or qubit and the role of inevitable disorder. Our results are relevant especially given recent experimental progress in engineering systems with long-range connectivity.

Assigning quantum labels and improving accuracy for the ro-vibrational eigenstates of H3+ calculated using ScalIT

In a recent article [AIP Adv. 11, 045033 (2021)], we carried out exact quantum dynamical calculations and computed ro-vibrational energy levels and wave functions for the H3+ molecular ion up to the dissociation threshold (at J = 46) using a recently developed potential energy surface (PES) [Mol. Phys. 117, 1663 (2019)]—arguably, the most accurate to date —together with the ScalIT suite of parallel codes. In this work, we further improved the convergence accuracy and range of our ScalIT calculations for all J values up to J = 20 to a few 10–5 cm−1 (or better). In addition, we performed an ab initio assignment of the ro-vibrational energy levels, providing vibrational ‘v1, v2, |l|’ and rotational ‘J, G, U, K’ quantum labels for more than 2,200 ro-vibrational states, including every single 0 ≤ J ≤ 20 state up to and above the barrier to linearity at 10,000 cm−1. The main underlying motivation of our work is to provide a list of reliably labeled, spectroscopically accurate energy levels in a format that can be used in spectroscopic line lists, which are based on both experimental and theoretical levels. Such line lists are of huge importance in various astrochemical and astrophysical contexts.

Numerical Interchain Mean-Field Theory for the Specific Heat of the Bimetallic Ferromagnetically Coupled Chain Compound MnNi(NO2)4(en)2 (en = Ethylenediamine).

We present a detailed study of the field-dependent specific heat of the bimetallic ferromagnetically coupled chain compound MnNi(NO)(en), en = ethylenediamine. For this material, which in zero field orders antiferromagnetically below K, small fields suppress magnetic order. Instead, in such fields, a double-peak-like structure in the temperature dependence of the specific heat is observed. We attribute this behavior to the existence of an acoustic and an optical mode in the spin-wave dispersion as a result of the existence of two different spins per unit cell. We compare our experimental data to numerical results for the specific heat obtained by exact diagonalization and Quantum Monte Carlo simulations for the alternating spin-chain model, using parameters that have been derived from the high-temperature behavior of the magnetic susceptibility. The interchain coupling is included in the numerical treatment at the mean-field level. We observe remarkable agreement between experiment and theory, including the ordering transition, using previously determined parameters. Furthermore, the observed strong effect of an applied magnetic field on the ordered state of MnNi(NO)(en) promises interesting magnetocaloric properties.

Radiative properties of an artificial atom coupled to a Josephson-junction array

We study the radiative properties -- the Lamb shift, Purcell decay rate and the spontaneous emission dynamics -- of an artificial atom coupled to a long, multimode cavity formed by an array of Josephson junctions. Introducing a tunable coupling element between the atom and the array, we demonstrate that such a system can exhibit a crossover from a perturbative to non-perturbative regime of light-matter interaction as one strengthens the coupling between the atom and the Josephson junction array (JJA). As a consequence, the concept of spontaneous emission as the occupation of the local atomic site being governed by a single complex-valued exponent breaks down. This breakdown, we show, can be interpreted in terms of formation of hybrid atom-resonator modes with radiative losses that are non-trivially related to the effective coupling between individual modes. We develop a singular function expansion approach for the description of the open quantum system dynamics in such a multimode non-perturbative regime. This modal framework generalizes the normal mode description of quantum fields in a finite volume, incorporating exact radiative losses and incident quantum noise at the delimiting surface. Our results are pertinent to recent experiments with Josephson atoms coupled to high impedance Josephson junction arrays.

Importance-sampling FCIQMC: Solving weak sign-problem systems.

We investigate the exact full configuration interaction quantum Monte Carlo algorithm (without the initiator approximation) applied to weak sign-problem fermionic systems, namely, systems in which the energy gap to the corresponding sign-free or "stoquastized" state is small. We show that the minimum number of walkers required to exactly overcome the signproblem can be significantly reduced via an importance-sampling similarity transformation even though the similarity-transformed Hamiltonian has the same stoquastic gap as the untransformed one. Furthermore, we show that in the off-half-filling Hubbard model at U/t = 8, the real-space (site) representation has a much weaker signproblem compared to the momentum space representation. By applying importance sampling using a Gutzwiller-like guiding wavefunction, we are able to substantially reduce the minimum number of walkers in the case of 2 × ℓ Hubbard ladders, enabling us to get exact energies for sizable ladders. With these results, we calculate the fundamental charge gap ΔEfund = E(N + 1) + E(N - 1) - 2E(N) for the ladder systems compared to strictly one-dimensional Hubbard chains and show that the ladder systems have a reduced fundamental gap compared to the 1D chains.

Nonlocality as the source of purely quantum dynamics of BCS superconductors

We show that the classical (mean-field) description of far from equilibrium superconductivity is exact in the thermodynamic limit for local observables but breaks down for global quantities, such as the entanglement entropy or Loschmidt echo. We do this by solving for and comparing exact quantum and exact classical long-time dynamics of a BCS superconductor with interaction strength inversely proportional to time and evaluating local observables explicitly. Mean field is exact for both normal and anomalous averages (superconducting order) in the thermodynamic limit. However, for anomalous expectation values, this limit does not commute with adiabatic and strong coupling limits and, as a consequence, their quantum fluctuations can be unusually strong. The long-time steady state of the system is a gapless superconductor whose superfluid properties are only accessible through energy resolved measurements. This state is nonthermal but conforms to an emergent generalized Gibbs ensemble. Our study clarifies the nature of symmetry-broken many-body states in and out of equilibrium and fills a crucial gap in the theory of time-dependent quantum integrability.

2D spectroscopies from condensed phase dynamics: Accessing third-order response properties from equilibrium multi-time correlation functions

The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two-dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopic techniques provide access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established, it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, centroid molecular dynamics, and Ring Polymer Molecular Dynamics (RPMD), naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.

New quantum physics, solving puzzles of Wheeler’s delayed choice and a particle’s passing N slits simultaneously and quantum oscillator in experiments

This paper discovers new quantum physics, and gives solutions to puzzles of Wheeler’s delayed choice and a particle’s passing many slits simultaneously by exact quantum physics expressions. We further show new quantum control, new quantum oscillation, new quantum control experiments and new quantum oscillator being able to be installed in quantum communication network etc. We discover that the ability of a photon to hit electrons out in photoelectric effect is complementarily equivalent to the ability of wave of a photon to simultaneously pass through many slits in wave-particle duality. Objective criterion for distinguishing classical and quantum particles is found, and this paper gives applicable realm of quantum theories and new quantum physics expressions of wave-particle duality. All these studies above should be classified as classical and quantum particles, then classical particle and quantum particle wave cannot and can pass many slits, respectively. This paper discovers wave-particle duality’s origin of displaying both wave property from plane wave part of the general Fourier expansion and particle property from the general Fourier expansion coefficients with the particle’s global property and spins etc. We give the superposition state representation of wave-particle duality, further find the collapse of the duality superposition state to wave or particle state. The collapsed wave or particle state is related to the measure of wave or particle property. Then, we explain why sometimes it's a wave or a particle. Our achieved results are truly tested, and we discover new measured attractive state and quantum wave collapse velocity expression.

Non-adiabatic mapping dynamics in the phase space of the SU(N) Lie group.

We present the rigorous theoretical framework of the generalized spin mapping representation for non-adiabatic dynamics. Our work is based upon a new mapping formalism recently introduced by Runeson and Richardson [J. Chem. Phys. 152, 084110 (2020)], which uses the generators of the su(N) Lie algebra to represent N discrete electronic states, thus preserving the size of the original Hilbert space. Following this interesting idea, the Stratonovich-Weyl transform is used to map an operator in the Hilbert space to a continuous function on the SU(N) Lie group, i.e., a smooth manifold which is a phase space of continuous variables. We further use the Wigner representation to describe the nuclear degrees of freedom and derive an exact expression of the time-correlation function as well as the exact quantum Liouvillian for the non-adiabatic system. Making the linearization approximation, this exact Liouvillian is reduced to the Liouvillian of several recently proposed methods, and the performance of this linearized method is tested using non-adiabatic models. We envision that the theoretical work presented here provides a rigorous and unified framework to formally derive non-adiabatic quantum dynamics approaches with continuous variables and connects the previous methods in a clear and concise manner.

Bootstrapping Calabi–Yau quantum mechanics

Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems was proposed. We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi–Yau geometries, where the exact quantization conditions have been conjecturally related to topological string theory. We find that the bootstrap method provides a promising alternative for the precision numerical calculations of the energy eigenvalues. An improvement in our approach is to use a larger set of two-dimensional operators instead of one-dimensional ones. We also apply our improved bootstrap methods to some non-relativistic models in the recent literature and demonstrate better numerical accuracies.

Mechanism of superconductivity in the Hubbard model at intermediate interaction strength

We study the fluctuations responsible for pairing in the d-wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum- and frequency-dependent fluctuations generate the d-wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity in both the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin fluctuation theory.

Modeling Spin-Dependent Nonadiabatic Dynamics with Electronic Degeneracy: A Phase-Space Surface-Hopping Method.

Nuclear Berry curvature effects emerge from electronic spin degeneracy and can lead to nontrivial spin-dependent (nonadiabatic) nuclear dynamics. However, such effects are not captured fully by any current mixed quantum-classical method such as fewest-switches surface hopping. In this work, we present a phase-space surface-hopping (PSSH) approach to simulate singlet-triplet intersystem crossing dynamics. We show that with a simple pseudodiabatic ansatz, a PSSH algorithm can capture the relevant Berry curvature effects and make predictions in agreement with exact quantum dynamics for a simple singlet-triplet model Hamiltonian. Thus, this approach represents an important step toward simulating photochemical and spin processes concomitantly, as relevant to intersystem crossing and spin-lattice relaxation dynamics.

A Exact Quantum Learning Algorithm for the 2-Junta Problem in Constant Time

A Exact Quantum Learning Algorithm for the 2-Junta Problem in Constant Time