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We propose introducing an extended Hubbard Hamiltonian derived via the ab initio downfolding method, which was originally formulated for periodic materials, toward efficient quantum computing of molecular electronic structure calculations. By utilizing this method, the first-principles Hamiltonian of chemical systems can be coarse-grained by eliminating the electronic degrees of freedom in higher energy space and reducing the number of terms of electron repulsion integral from O ( N 4 ) to O ( N 2 ). Our approach is validated numerically on the vertical excitation energies and excitation characters of ethylene, butadiene, and hexatriene. The dynamical electron correlation is incorporated within the framework of the constrained random phase approximation in advance of quantum computations, and the constructed models capture the trend of experimental and high-level quantum chemical calculation results. As expected, the L1-norm of the fermion-to-qubit mapped model Hamiltonians is significantly lower than that of conventional ab initio Hamiltonians, suggesting improved scalability of quantum computing. Those numerical outcomes and the results of the simulation of excited-state sampling demonstrate that the ab initio extended Hubbard Hamiltonian may hold significant potential for quantum chemical calculations using quantum computers. [ABSTRACT FROM AUTHOR]

We propose a scheme for achieving basic quantum gates using ultracold polar molecules in pendular states. The qubits are encoded in the YbF molecules trapped in an electric field with a certain gradient and coupled by the dipole–dipole interaction. The time-dependent control sequences consisting of multiple pulses are considered to interact with the pendular qubits. To achieve high-fidelity quantum gates, we map the control problem for the coupled molecular system into a Markov decision process and deal with it using the techniques of deep reinforcement learning (DRL). By training the agents over multiple episodes, the optimal control pulse sequences for the two-qubit gates of NOT, controlled NOT, and Hadamard are discovered with high fidelities. Moreover, the population dynamics of YbF molecules driven by the discovered gate sequences are analyzed in detail. Furthermore, by combining the optimal gate sequences, we successfully simulate the quantum circuit for entanglement. Our findings could offer new insights into efficiently controlling molecular systems for practical molecule-based quantum computing using DRL. [ABSTRACT FROM AUTHOR]

Quantum computers hold immense potential in the field of chemistry, ushering new frontiers to solve complex many-body problems that are beyond the reach of classical computers. However, noise in the current quantum hardware limits their applicability to large chemical systems. This work encompasses the development of a projective formalism that aims to compute ground-state energies of molecular systems accurately using noisy intermediate scale quantum (NISQ) hardware in a resource-efficient manner. Our approach is reliant upon the formulation of a bipartitely decoupled parameterized ansatz within the disentangled unitary coupled cluster framework based on the principles of nonlinear dynamics and synergetics. Such decoupling emulates total parameter optimization in a lower dimensional manifold, while a mutual synergistic relationship among the parameters is exploited to ensure characteristic accuracy via a non-iterative energy correction. Without any pre-circuit measurements, our method leads to a highly compact fixed-depth ansatz with shallower circuits and fewer expectation value evaluations. Through analytical and numerical demonstrations, we establish the method's superior performance under noise while concurrently ensuring requisite accuracy in future fault-tolerant systems. This approach enables rapid exploration of emerging chemical spaces by the efficient utilization of near-term quantum hardware resources. [ABSTRACT FROM AUTHOR]

With the development of quantum computers, traditional communication security based on classical computers can no longer guarantee unconditional security. At the same time, a series of encrypted communication solutions that rely on quantum mechanical properties have been spawned. This article focuses on the field of quantum signatures, based on the entangled Greenberger–Horne–Zeilinger state, combining group signatures (any member of the group can sign on behalf of the group) and blind signatures (the signer cannot know the accuracy of the signature content) proposed a new quantum group blind signature scheme that utilizes quantum key distribution to achieve unconditional security. By splitting the original message, the scheme strengthens the relevance of the signature participants and makes the signature to have stronger binding. Then, the security of the scheme against internal and external attacks is analyzed. In this scheme, a pleasing efficiency has been achieved, and the non-repudiation of signatures has been enhanced. At the same time, disputed signatures can be traced back to the signer. [ABSTRACT FROM AUTHOR]

Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. In the variational quantum eigensolver, a decomposition of the target Hamiltonian into exactly solvable fragments can be used for the evaluation of the energies via repeated quantum measurements. In this work, we apply more general classes of exactly solvable qubit Hamiltonians than previously considered to address the Hamiltonian measurement problem. The most general exactly solvable Hamiltonians we use are defined by the condition that within each simultaneous eigenspace of a set of Pauli symmetries, the Hamiltonian acts effectively as an element of a direct sum of so(N) Lie algebras and can, therefore, be measured using a combination of unitaries in the associated Lie group, Clifford unitaries, and mid-circuit measurements. The application of such Hamiltonians to decomposing molecular electronic Hamiltonians via graph partitioning techniques shows a reduction in the total number of measurements required to estimate the expectation value compared to previously used exactly solvable qubit Hamiltonians. [ABSTRACT FROM AUTHOR]

Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research. [ABSTRACT FROM AUTHOR]

Quantum chemistry is one of the most promising applications for which quantum computing is expected to have a significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remains a relatively unexplored field. In this work, we develop a vibrational Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction, which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT-VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators that may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior. [ABSTRACT FROM AUTHOR]

Trapped ions are among the leading candidates for quantum computing technologies. Interfacing ion qubits in separate traps and interfacing ion qubits with superconducting qubits are two of the many challenges to scale up quantum computers. One approach to overcome both problems is to use a conducting wire to mediate the Coulomb interaction between ions in different traps or between ions and superconducting qubits. To this end, a trapped charged particle inducing charge on a conductor has long been modeled as a system of equivalent lumped element electronic components. Our careful consideration reveals two assumptions in the derivation of this model, which are generally unjustified. We explain how these assumptions undermine the model's validity, and then introduce an improved way to use linear relationships to describe the interaction of trapped ions with nearby conductors. The new method reproduces results equivalent to those of other works that are not based on the circuit element model. This method is targeted for trouble-shooting experimental designs and allows experiments to test and compare the accuracy of different theoretical models. [ABSTRACT FROM AUTHOR]

The electronic energies of molecules have been successfully evaluated on quantum computers. However, more attention is paid to the dynamics simulation of molecules in practical applications. Based on the variational quantum eigensolver (VQE) algorithm, Fedorov et al. proposed a correlated sampling (CS) method and demonstrated the vibrational dynamics of H2 molecules [J. Chem. Phys. 154, 164103 (2021)]. In this study, we have developed a quantum approach by extending the CS method based on the VQE algorithm (labeled eCS-VQE) for simulating chemical reaction dynamics. First, the CS method is extended to the three-dimensional cases for calculation of first-order energy gradients, and then, it is further generalized to calculate the second-order gradients of energies. By calculating atomic forces and vibrational frequencies for H2, LiH, H+ + H2, and Cl− + CH3Cl systems, we have seen that the approach has achieved the CCSD level of accuracy. Thus, we have simulated dynamics processes for two typical chemical reactions, hydrogen exchange and chlorine substitution, and obtained high-precision reaction dynamics trajectories consistent with the classical methods. Our eCS-VQE approach, as measurement expectations and ground-state wave functions can be reused, is less demanding in quantum computing resources and is, therefore, a feasible means for the dynamics simulation of chemical reactions on the current noisy intermediate-scale quantum-era quantum devices. [ABSTRACT FROM AUTHOR]

The operations of current quantum computers are still significantly affected by decoherence caused by interaction with the environment. In this work, we employ the non-perturbative hierarchical equations of motion (HEOM) method to simulate the operation of model quantum computers and reveal the effects of dissipation on the entangled quantum states and on the performance of well-known quantum algorithms. Multi-qubit entangled states in Shor's factorizing algorithm are first generated and propagated using the HEOM. It is found that the failure of factorization is accompanied by a loss of fidelity and mutual information. An important challenge in using the HEOM to simulate quantum computers in a dissipative environment is how to efficiently treat systems with many qubits. We propose a two-dimensional tensor network scheme for this problem and demonstrate its capability by simulating a one-dimensional random circuit model with 21 qubits. [ABSTRACT FROM AUTHOR]

First-order derivatives of energies with respect to atomic coordinates are widely computed and used in quantum chemistry simulations. The rapidly emerging technology of quantum computing offers a new paradigm for solving relevant quantum chemistry equations. In this work, we have achieved analytical calculations of atomic forces based on the Hellmann–Feynman theorem within the framework of the variational quantum eigensolver. The accuracy of the approach is demonstrated by calculating the atomic forces of H2, LiH, H2O, and NH3 molecules, which are in excellent agreement with values obtained from full configuration interaction calculations. In particular, for systems with degenerate molecular orbitals, the analytical approach has a significant accuracy advantage over finite-difference-based methods and will not involve additional computational effort on a quantum computer. The calculated forces are further used to optimize the geometries of NH3 and CH4 molecules and to perform ab initio molecular dynamics simulations for the umbrella inversion of NH3, demonstrating the feasibility of the approach in practical quantum chemistry simulations. [ABSTRACT FROM AUTHOR]

The recently developed Projective Quantum Eigensolver (PQE) offers an elegant procedure to evaluate the ground state energies of molecular systems in quantum computers. However, the noise in available quantum hardware can result in significant errors in computed outcomes, limiting the realization of quantum advantage. Although PQE comes equipped with some degree of inherent noise resilience, any practical implementation with apposite accuracy would require additional routines to eliminate or mitigate the errors further. In this work, we propose a way to enhance the efficiency of PQE by developing an optimal framework for introducing Zero Noise Extrapolation (ZNE) in the nonlinear iterative procedure that outlines the PQE, leading to the formulation of ZNE-PQE. Moreover, we perform a detailed analysis of how various components involved in it affect the accuracy and efficiency of the reciprocated energy convergence trajectory. Additionally, we investigate the underlying mechanism that leads to the improvements observed in ZNE-PQE over conventional PQE by performing a comparative analysis of their residue norm landscape. This approach is expected to facilitate practical applications of quantum computing in fields related to molecular sciences, where it is essential to determine molecular energies accurately. [ABSTRACT FROM AUTHOR]

In this work, we test a recently developed method to enhance classical auxiliary-field quantum Monte Carlo (AFQMC) calculations with quantum computers against examples from chemistry and material science, representative of classes of industry-relevant systems. As molecular test cases, we calculate the energy curve of H4 and the relative energies of ozone and singlet molecular oxygen with respect to triplet molecular oxygen, which is industrially relevant in organic oxidation reactions. We find that trial wave functions beyond single Slater determinants improve the performance of AFQMC and allow it to generate energies close to chemical accuracy compared to full configuration interaction or experimental results. In the field of material science, we study the electronic structure properties of cuprates through the quasi-1D Fermi–Hubbard model derived from CuBr2, where we find that trial wave functions with both significantly larger fidelities and lower energies over a mean-field solution do not necessarily lead to AFQMC results closer to the exact ground state energy. [ABSTRACT FROM AUTHOR]

A major roadblock to scalable quantum computing is phase decoherence and energy relaxation caused by qubits interacting with defect-related two-level systems (TLSs). Native oxides present on the surfaces of superconducting metals used in quantum devices are acknowledged to be a source of TLS that decrease qubit coherence times. Reducing microwave loss by "surface engineering" (i.e., replacing the uncontrolled native oxide of superconducting metals with a thin, stable surface with predictable characteristics) can be a key enabler for pushing performance forward with devices of higher intrinsic quality factor. In this work, we present a novel approach to replace the native oxide of niobium (typically formed in an uncontrolled fashion when its pristine surface is exposed to air) with an engineered oxide, using a room-temperature process that leverages accelerated neutral atom beam (ANAB) technology at 300 mm wafer scale. This ANAB is composed of a mixture of argon and oxygen, with tunable energy per atom, which is rastered across the wafer surface. The ANAB-engineered Nb-oxide thickness was found to vary from 2 to 6 nm depending on ANAB process parameters. The modeling of variable-energy x-ray photoelectron spectroscopy data confirms the thickness and compositional control of Nb surface oxide by the ANAB process. These results correlate well with those from transmission electron microscopy and x-ray reflectometry. Since ANAB is broadly applicable to material surfaces, the present study indicates its promise for modification of the surfaces of superconducting quantum circuits to achieve longer coherence times. [ABSTRACT FROM AUTHOR]

A challenge in building large-scale superconducting quantum processors is the precise control and manipulation of the qubit state. However, the crosstalk between the microwave control lines impedes the parallel execution of high-fidelity digital and analog quantum operations. Here, we propose and demonstrate a universal compensation protocol for calibrating the microwave signal crosstalk. We also introduce amplified error sequences to optimize accuracy. Furthermore, we show a definitive improvement in parallel gate operations with crosstalk cancellation, demonstrating the technique's effectiveness. This work paves the way for superconducting hardware that features the automated calibration of microwave crosstalk, leading to enhanced fidelities in multiqubit circuits. [ABSTRACT FROM AUTHOR]

Ultra-sensitive sensors based on the resonant properties of whispering gallery modes (WGMs) can detect fractional changes in nanoscale environments down to the length and time scales of single molecules. However, it is challenging to isolate single-molecule signals from competing noise sources in experiments, such as thermal and mechanical sources of noise, and—at the most fundamental level—the shot noise limit of classical light. Additionally, in contrast to traditional bulk refractive index measurements, analyzing single-molecule signals is complicated by the localized nature of their interactions with nanoscale field gradients. This perspective discusses multifaceted solutions to these challenges, including the use of quantum light sources to boost the signal-to-noise ratio in experiments and leveraging the power of supercomputers to predict the electronic response of molecules to WGM optoplasmonic fields. We further discuss the role of machine learning in WGM sensing, including several advanced models that can predict molecular polarizability and solvent effects. These advancements in WGM spectroscopy and computational modeling can help to decipher the molecular mechanics of enzymes, enable studies of catalysis on the nanoscale, and probe the quantum nature of molecules. [ABSTRACT FROM AUTHOR]

We are investigating a novel enrichment process that could allow the use of industrial complementary metal–oxide–semiconductor implanters to manufacture "quantum grade" 28Si layers for use in quantum computers. Our implanted layer exchange enrichment process leverages conventional deposition-based layer exchange approaches but replaces a step of depositing a Si layer above an Al layer with a 28Si implant into the top of an Al layer. A subsequent anneal dissolves Si into Al beneath the implanted region where Si diffuses and either epitaxially grows onto the substrate or forms poly-crystals in the Al [Schneider and England, ACS Appl. Mater. Interfaces 15, 21609 (2023)]. We have developed a qualitative model using simple assumptions and boundary conditions to estimate characteristic times and rates of epitaxy or poly-crystallization for this novel layer exchange process. We have used the model to explain crystallization outcomes reported in this paper and previously. We find that the absence of an oxide boundary layer separating Si and Al allows Si diffusion to become established within the first second of all the anneals studied and that crystallization actually completes during the temperature ramp of most of the anneals. The rapid evolution of Si supersaturation in Al beneath the implanted layer explains the ratios of epitaxial growth to poly-crystallization observed after these anneals. We use this understanding to propose the implant layer exchange conditions that could produce the highest quality mono-crystalline quantum grade Si. [ABSTRACT FROM AUTHOR]

Using quantum computers for computational chemistry and materials science will enable us to tackle problems that are intractable on classical computers. In this paper, we show how the relative energy of defective graphene structures can be calculated by using a quantum annealer. This simple system is used to guide the reader through the steps needed to translate a chemical structure (a set of atoms) and energy model to a representation that can be implemented on quantum annealers (a set of qubits). We discuss in detail how different energy contributions can be included in the model and what their effect is on the final result. The code used to run the simulation on D-Wave quantum annealers is made available as a Jupyter Notebook. This Tutorial was designed to be a quick-start guide for the computational chemists interested in running their first quantum annealing simulations. The methodology outlined in this paper represents the foundation for simulating more complex systems, such as solid solutions and disordered systems. [ABSTRACT FROM AUTHOR]

Nuclear quantum phenomena beyond the Born–Oppenheimer approximation are known to play an important role in a growing number of chemical and biological processes. While there exists no unique consensus on a rigorous and efficient implementation of coupled electron–nuclear quantum dynamics, it is recognized that these problems scale exponentially with system size on classical processors and, therefore, may benefit from quantum computing implementations. Here, we introduce a methodology for the efficient quantum treatment of the electron–nuclear problem on near-term quantum computers, based upon the Nuclear–Electronic Orbital (NEO) approach. We generalize the electronic two-qubit tapering scheme to include nuclei by exploiting symmetries inherent in the NEO framework, thereby reducing the Hamiltonian dimension, number of qubits, gates, and measurements needed for calculations. We also develop parameter transfer and initialization techniques, which improve convergence behavior relative to conventional initialization. These techniques are applied to H2 and malonaldehyde for which results agree with NEO full configuration interaction and NEO complete active space configuration interaction benchmarks for ground state energy to within 10−6 hartree and entanglement entropy to within 10−4. These implementations therefore significantly reduce resource requirements for full quantum simulations of molecules on near-term quantum devices while maintaining high accuracy. [ABSTRACT FROM AUTHOR]

Circuit depth reduction is of critical importance for quantum chemistry simulations on current and near term quantum computers. This issue is tackled by introducing a chemically aware strategy for the unitary coupled cluster ansatz. The objective is to use the chemical description of a system to aid in the synthesis of a quantum circuit. We combine this approach with two flavors of symmetry verification for the reduction of experimental noise. These methods enable the use of Quantinuum's System Model H1 ion trap quantum computer for a 6-qubit quantum subspace expansion calculation. We present (i) calculations to obtain methane's optical spectra; (ii) an atmospheric gas reaction simulation involving [ C H 3 ⋅ —H—OH]‡. Using our chemically aware unitary coupled cluster state-preparation strategy in tandem with state of the art symmetry verification methods, we improve device yield for CH4 at 6 qubits. This is demonstrated by a 90% improvement in two-qubit gate count and a reduction in relative error to 0.2% for electronic energy calculated on System Model H1. [ABSTRACT FROM AUTHOR]

Sparse connectivity of a superconducting quantum computer results in large experimental overheads of SWAP gates. In this study, we consider employing a virtual two-qubit gate (VTQG) as an error suppression technique. The VTQG enables a non-local operation between a pair of distant qubits using only single qubit gates and projective measurements. Here, we apply the VTQG to the digital quantum simulation of the transverse-field Ising model on an IBM quantum computer to suppress the errors due to the noisy two-qubit operations. We present an effective use of VTQG, where the reduction in multiple SWAP gates results in increasing the fidelity of output states. The obtained results indicate that the VTQG can be useful for suppressing the errors due to additional SWAP gates. In our experiments, we have observed one order of magnitude improvement in accuracy for the quantum simulation of the transverse-field Ising model with 8 qubits. Finally, we have demonstrated an efficient implementation of the VTQG by utilizing dynamic circuits. This scheme reduces experimental overheads for implementing m VTQGs from O (10 m) to O (6 m). [ABSTRACT FROM AUTHOR]

Three-dimensional magneto-optical traps (3D-MOTs) are an integral component of atomic clocks, quantum computers, and other cold-atom science applications. Due to the dependence on bulk optics and lasers, conventional 3D-MOTs occupy a large volume, limiting their portability. Efforts to build 3D-MOTs using integrated photonics promise to reduce the size and weight of these systems allowing applications beyond the lab. However, the need for counterpropagating beams to facilitate 4- and 6-beam geometries necessitates free-space mirrors and quarter wave plates (QWPs) that limit integration. Replacing these mirrors and QWPs with planar retroreflecting metasurfaces provides a route to achieving a complete 3D-MOT within an integrated package. Here, we report on the design and demonstration of a retroreflecting metasurface for 3D-MOTs that operates at large angles and preserves circular polarization. Specifically, we utilize Bayesian optimization to design an amorphous silicon (a-Si) on gold metasurface for high efficiency polarization-insensitive retroreflection of 780 nm circularly polarized light at 54.7°. Numerical simulations demonstrate maintenance of circular polarization after highly efficient retroreflection ( ϵ − 1 = 1.10 , R − 1 = 0.86). Experimentally, we demonstrate similarly excellent performance at 736 nm at 50.3 ° ( ϵ − 1 = 1.04 , R − 1 = 0.73) and show that deviation from the target design is due to oxidation of the a-Si metaelements. We conclude by discussing mitigation strategies for future devices and propose a corrective optic for the currently fabricated device. This work represents a step toward the miniaturization of 3D-MOTs and expansion of cold-atom science beyond the laboratory. [ABSTRACT FROM AUTHOR]

Accurate on-chip temperature sensing is critical for the optimal performance of modern complementary metal-oxide-semiconductor (CMOS) integrated circuits (ICs), to understand and monitor localized heating around the chip during operation. The development of quantum computers has stimulated much interest in ICs operating at deep cryogenic temperatures (typically 0.01–4 K), in which the reduced thermal conductivity of silicon and silicon oxide and the limited cooling power budgets make local on-chip temperature sensing even more important. Here, we report four different methods for on-chip temperature measurements native to CMOS industrial fabrication processes. These include secondary and primary thermometry methods and cover conventional thermometry structures used at room temperature as well as methods exploiting phenomena that emerge at cryogenic temperatures, such as superconductivity and Coulomb blockade. We benchmark the sensitivity of the methods as a function of temperature and use them to measure local excess temperature produced by on-chip heating elements. Our results demonstrate thermometry methods that may be readily integrated in CMOS chips with operation from the millikelvin range to room temperature. [ABSTRACT FROM AUTHOR]

Time evolution of the populations of spin states coupled with bosons, which can be a model of photosynthetic excitation energy transfer of dye molecules surrounded by proteins, is simulated using the projected-variational quantum dynamics algorithm. By a transformation of the Hamiltonian describing the spin-boson model into the one-dimensional nearest-neighbor form, it is shown that the spin-boson model can be simulated using the sequential ansatz even if a quantum computer has limited connectivity. The optimization of the parametrized quantum circuits is performed by the gradient descent method on a classical computer using the automatic differentiation, and the population of the spins is simulated on a noisy intermediate-scale quantum computer. The error originating from the quantum computing is mitigated by the Clifford data regression, in which the noise channel is estimated using the data obtained from all the time steps. [ABSTRACT FROM AUTHOR]

Majorana bound states are quasiparticle excitations localized at the boundaries of a topologically nontrivial superconductor. They are zero-energy, charge-neutral, particle–hole symmetric, and spatially-separated end modes which are topologically protected by the particle–hole symmetry of the superconducting state. Due to their topological nature, they are robust against local perturbations and, in an ideal environment, free from decoherence. Furthermore, unlike ordinary fermions and bosons, the adiabatic exchange of Majorana modes is noncommutative, i.e., the outcome of exchanging two or more Majorana modes depends on the order in which exchanges are performed. These properties make them ideal candidates for the realization of topological quantum computers. In this tutorial, I will present a pedagogical review of 1D topological superconductors and Majorana modes in quantum nanowires. I will give an overview of the Kitaev model and the more realistic Oreg–Lutchyn model, discuss the experimental signatures of Majorana modes, and highlight their relevance in the field of topological quantum computation. This tutorial may serve as a pedagogical and relatively self-contained introduction for graduate students and researchers new to the field, as well as an overview of the current state-of-the-art of the field and a reference guide to specialists. [ABSTRACT FROM AUTHOR]

In this paper, we have developed a unitary variant of a double exponential coupled cluster theory, which is capable of handling molecular strong correlation with arbitrary electronic complexity. With the Hartree–Fock determinant taken as the reference, we introduce a sequential product of parameterized unitary Ansätze. While the first unitary, containing the excitation operators, acts directly on the reference determinant, the second unitary, containing a set of rank-two, vacuum-annihilating scattering operators, has nontrivial action only on certain entangled states. We demonstrate the theoretical bottleneck of such an implementation in a classical computer, whereas the same is implemented in the hybrid quantum–classical variational quantum eigensolver framework with a reasonably shallow quantum circuit without any additional approximation. We have further introduced a number of variants of the proposed Ansatz with different degrees of sophistication by judiciously approximating the scattering operators. With a number of applications on strongly correlated molecules, we have shown that all our schemes can perform uniformly well throughout the molecular potential energy surface without significant additional implementation cost over the conventional unitary coupled cluster approach with single and double excitations. [ABSTRACT FROM AUTHOR]

Quantum simulation of chemical Hamiltonians enables the efficient calculation of chemical properties. Mapping is one of the essential steps in simulating fermionic systems on quantum computers. In this work, a unified framework of transformations mapping fermionic systems to qubit systems is presented and many existing transformations—such as Jordan–Wigner, Bravyi–Kitaev, and parity transformations—are included in this framework. Based on this framework, the Multilayer Segmented Parity (MSP) transformation is proposed. The MSP transformation is a general mapping with an adjustable parameter vector, which can be viewed as a generalization of the above-mentioned mappings. Furthermore, the MSP transformation can adjust flexibly when dealing with different systems. Applying these mappings to the electronic structure Hamiltonians of various molecules, the MSP transformation is found to perform better on a number of Pauli operators and gates needed in the circuit of Hamiltonian simulation. The MSP transformation will reduce the qubit gate requirement for Hamiltonian simulation on noisy intermediate-scale quantum devices, and it will provide a much wider choice of mappings for researchers. [ABSTRACT FROM AUTHOR]

Photonic interconnects between quantum systems will play a central role in both scalable quantum computing and quantum networking. Entanglement of remote qubits via photons has been demonstrated in many platforms; however, improving the rate of entanglement generation will be instrumental for integrating photonic links into modular quantum computers. We present an ion trap system that has the highest reported free-space photon collection efficiency for quantum networking. We use a pair of in-vacuum aspheric lenses, each with a numerical aperture of 0.8, to couple 10(1)% of the 493 nm photons emitted from a 138Ba+ ion into single-mode fibers. We also demonstrate that proximal effects of the lenses on the ion position and motion can be mitigated. [ABSTRACT FROM AUTHOR]

There has been debate around applicability of exceptional points (EPs) for quantum sensing. To resolve this, we first explore how to experimentally implement the non-Hermitian non-diagonalizable Hamiltonians, which exhibit EPs, in quantum computers that run on unitary gates. We propose to use an ancilla-based method in this regard. Next, we show how such Hamiltonians can be used for parameter estimation using quantum computers and analyze its performance in terms of the quantum Fisher information (QFI) at EPs, both without noise and in the presence of noise. It is well known that QFI of a parameter to be estimated is inversely related to the variance of the parameter by the quantum Cramer–Rao bound. Therefore, the divergence of the QFI at EPs promises sensing advantages. We experimentally demonstrate in a cloud quantum architecture and theoretically show, using Puiseux series, that the QFI indeed diverges in such EP systems that were earlier considered to be non-divergent. [ABSTRACT FROM AUTHOR]

With its rich dynamics, the quantum harmonic oscillator is an innate platform for understanding real-world quantum systems and could even excel as the heart of a quantum computer. A particularly promising and rapidly advancing platform that harnesses quantum harmonic oscillators for information processing is the bosonic circuit quantum electrodynamics (cQED) system. In this article, we provide perspectives on the progress, challenges, and future directions in building a bosonic cQED quantum computer. We describe the main hardware building blocks and how they facilitate quantum error correction, metrology, and simulation. We conclude with our views of the key challenges that lie on the horizon, as well as scientific and cultural strategies for overcoming them and building a practical quantum computer with bosonic cQED hardware. [ABSTRACT FROM AUTHOR]

With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained with a fixed ansatz implementable on current quantum computers can be used for accurate regression models of global potential energy surfaces (PESs) for polyatomic molecules. To obtain accurate regression models, we apply Bayesian optimization to maximize marginal likelihood by varying the parameters of the quantum gates. This yields Gaussian process models with quantum kernels. We illustrate the effect of qubit entanglement in the quantum kernels and explore the generalization performance of quantum Gaussian processes by extrapolating global six-dimensional PESs in the energy domain. [ABSTRACT FROM AUTHOR]

In order to demonstrate an applicability of quantum computing to fundamental electronic structure problems of molecules, we describe the Hückel Hamiltonian matrix in terms of quantum gates and obtain the orbital energies of fundamental π-electron molecules (C2H4, C3H4, C4H4, C4H6, and C6H6) using a superconducting-qubit-type quantum computer (ibm_kawasaki) with a post-selection error mitigation method. We show that the orbital energies are obtained with sufficiently high accuracy and small uncertainties and that characteristic features of the electronic structure of the π-electron molecules can be extracted by quantum computing in a straightforward manner. [ABSTRACT FROM AUTHOR]

Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in the condensed phase. To facilitate effective development, code sharing, and uptake of newly developed dynamics methods, it is important that software implementations can be easily accessed and built upon. Using the Julia programming language, we have developed the NQCDynamics.jl package, which provides a framework for established and emerging methods for performing semiclassical and mixed quantum–classical dynamics in the condensed phase. The code provides several interfaces to existing atomistic simulation frameworks, electronic structure codes, and machine learning representations. In addition to the existing methods, the package provides infrastructure for developing and deploying new dynamics methods, which we hope will benefit reproducibility and code sharing in the field of condensed phase quantum dynamics. Herein, we present our code design choices and the specific Julia programming features from which they benefit. We further demonstrate the capabilities of the package on two examples of chemical dynamics in the condensed phase: the population dynamics of the spin-boson model as described by a wide variety of semiclassical and mixed quantum–classical nonadiabatic methods and the reactive scattering of H2 on Ag(111) using the molecular dynamics with electronic friction method. Together, they exemplify the broad scope of the package to study effective model Hamiltonians and realistic atomistic systems. [ABSTRACT FROM AUTHOR]

In recent years, the performance of different entanglement indicators obtained directly from tomograms has been assessed in continuous-variable and hybrid quantum systems. In this paper, we carry out this task in the case of spin systems. We compute the entanglement indicators from actual experimental data obtained from three liquid-state nuclear magnetic resonance (NMR) experiments and compare them with standard entanglement measures calculated from the corresponding density matrices, both experimentally reconstructed and numerically computed. The gross features of entanglement dynamics and spin squeezing properties are found to be reproduced by these entanglement indicators. However, the extent to which these indicators and spin squeezing track the entanglement during time evolution of the multipartite systems in the NMR experiments is very sensitive to the precise nature and strength of interactions as well as the manner in which the full system is partitioned into subsystems. We also use the IBM quantum computer to implement equivalent circuits that capture the dynamics of the multipartite system in one of the NMR experiments and carry out a similar comparative assessment of the performance of tomographic indicators. This exercise shows that these indicators can estimate the degree of entanglement without necessitating detailed state reconstruction procedures, establishing the advantage of the tomographic approach. [ABSTRACT FROM AUTHOR]

Prime factorization is a procedure of determining the prime factors of a given number N that requires super-polynomial time for conventional digital computers. Peter Shor developed a polynomial-time algorithm for quantum computers. Period finding is the key part of the algorithm, which is accomplished with the help of quantum superposition of states and quantum entanglement. The period finding can be also accomplished using classical wave superposition. In this study, we present experimental data obtained on a multi-port spin wave interferometer made of Y3Fe2(FeO4)3. Number 817 was factorized by a sequence of phase measurements. We also present the results of numerical modeling on the prime factorization of larger numbers 334 597 , 1 172 693 , 3 377 663 , and 9 363 239. The results of numerical modeling reveal significant shortcomings of the period-based approach. The major problems are associated with an inability to predict the period of the modular function, significant overhead over classical digital computers in some cases, and phase accuracy requirements. We argue that the same problems are inherent in classical analog and quantum computers. [ABSTRACT FROM AUTHOR]

These findings suggest that the CT-F12 approach might be a good candidate for reducing the basis set error of the high-order CC methods, perhaps better than the traditional high-order CC-F12 approaches.[21] Further investigation along these lines will be reported shortly elsewhere. 6 fThe CBS CCSD energy from Ref. [20] corrected for the difference between CCSDT-F12 and CCSD-F12 energies evaluated with the aug-cc-pV6Z basis from Ref. [21]. The same method nomenclature as in Ref. [1] is used here, i.e., F12 I X i refers to method I X i using the CT-F12 Hamiltonian. [Extracted from the article]

The factorized form of the unitary coupled cluster Ansatz is a popular state preparation Ansatz for electronic structure calculations of molecules on quantum computers. It is often viewed as an approximation (based on the Trotter product formula) for the conventional unitary coupled cluster operator. In this work, we show that the factorized form is quite flexible, allowing one to range from a conventional configuration interaction, to conventional unitary coupled cluster, to efficient approximations that lie in between these two. The variational minimization of the energy often allows simpler factorized unitary coupled cluster approximations to achieve high accuracy, even if they do not accurately approximate the Trotter product formula. This is similar to how quantum approximate optimization algorithms can achieve high accuracy with a small number of levels. [ABSTRACT FROM AUTHOR]

Quantum physics has some unique properties, such as quantum entanglement and quantum superposition. Encryption algorithms designed based on quantum physical properties usually have higher security than classical computing. Applying quantum cryptography to data retrieval can realize cloud database encryption of quantum information. We propose a cloud ciphertext retrieval scheme, which combines quantum encryption and quantum search algorithm to ensure the privacy of data while the server completes information retrieval. In this scheme, the data are stored in the form of qubits string and placed in the quantum superposition state. We establish the mapping relationship between classical information and quantum states. Our scheme solves the problem of a large amount of computing and lack of sufficient computing resources at the client, assigns computing tasks to servers with sufficient resources, and ensures the security of information. [ABSTRACT FROM AUTHOR]