Basis States Research Articles

High sensitivity absorption spectroscopy of acetylene near 770 nm

The Cavity Ring-Down Spectra (CRDS) of acetylene were recorded in the 12933–13087 cm−1 region with sensitivity of 2 × 10−11 cm−1. Six bands of 12C2H2 and one band of 12C13CH2 were assigned in these spectra. The 3ν1+ν3 band is the strongest one lying in this region. The line positions and intensities were recovered from the recorded spectra. The line intensities in this region are reported for the first time. The line positions were modeled using the traditional power series expression in terms of the angular momentum quantum number for an isolated band. The line intensities were modeled using the vibrational transition dipole moment squared and the Herman-Wallis parameters. The recommended line list of acetylene was prepared for the 12887–13084 cm−1 region. It is based on the calculated line parameters. But in the case of the perturbations, the calculated line parameters are substituted by the observed ones. The harmonic basis state compositions of the upper states of the two bands at 12991.08 and 12988.75 cm−1 were considered in detail.

Interference of nuclear wavepackets in a pair of proton transfer reactions

Quantum mechanics revolutionized chemists' understanding of molecular structure. In contrast, the kinetics of molecular reactions in solution are well described by classical, statistical theories. To reveal how the dynamics of chemical systems transition from quantum to classical, we study femtosecond proton transfer in a symmetric molecule with two identical reactant sites that are spatially apart. With the reaction launched from a superposition of two local basis states, we hypothesize that the ensuing motions of the electrons and nuclei will proceed, conceptually, in lockstep as a superposition of probability amplitudes until decoherence collapses the system to a product. Using ultrafast spectroscopy, we observe that the initial superposition state affects the reaction kinetics by an interference mechanism. With the aid of a quantum dynamics model, we propose how the evolution of nuclear wavepackets manifests the unusual intersite quantum correlations during the reaction.

Semiclassical and VSCF/VCI Calculations of the Vibrational Energies of trans- and gauche-Ethanol Using a CCSD(T) Potential Energy Surface.

A recent full-dimensional Δ-Machine learning potential energy surface (PES) for ethanol is employed in semiclassical and vibrational self-consistent field (VSCF) and virtual-state configuration interaction (VCI) calculations, using MULTIMODE, to determine the anharmonic vibrational frequencies of vibration for both the trans and gauche conformers of ethanol. Both semiclassical and VSCF/VCI energies agree well with the experimental data. We find significant mixing between the VSCF basis states due to Fermi resonances between bending and stretching modes. The same effects are also accurately described by the full-dimensional semiclassical calculations. These are the first high-level anharmonic calculations using a PES, in particular a "gold-standard" CCSD(T) one.

SWAP test for an arbitrary number of quantum states

We develop a recursive algorithm to generalize the quantum SWAP test for an arbitrary number m of quantum states requiring O(m) controlled-swap (CSWAP) gates and $$O(\log m)$$ ancillary qubits. We construct a quantum circuit able to simultaneously measure overlaps $$|\langle \phi _i, \phi _j\rangle |^2$$ of m arbitrary pure states $${|{\phi _1\ldots \phi _m}\rangle }$$ . Our construction relies on a pairing unitary that generates a superposition state where every pair of input states is labeled by a basis state formed by the ancillaries. By implementing a simple genetic algorithm, we give numerical evidence indicating that our method of labeling each pair of inputs using CSWAP gates is optimal up to $$m=8$$ . Potential applications of the new circuits in the context of quantum machine learning are discussed.

Analytic Solution of an Active Brownian Particle in a Harmonic Well.

We provide an analytical solution for the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle trapped in an isotropic harmonic potential. Using the passive Brownian particle as basis states we show that the Fokker-Planck operator becomes lower diagonal, implying that the eigenvalues are unaffected by the activity. The propagator is then expressed as a combination of the equilibrium eigenstates with weights obeying exact iterative relations. We show that for the low-order correlation functions, such as the positional autocorrelation function, the recursion terminates at finite order in the Péclet number, allowing us to generate exact compact expressions and derive the velocity autocorrelation function and the time-dependent diffusion coefficient. The nonmonotonic behavior of latter quantities serves as a fingerprint of the nonequilibrium dynamics.

Decoherence of a Hadamard basis state in three-spin system: The case of tunnel-couplings to semi-infinite graphene electrodes with armchair edges

We study the model of three-spin system consisting of a spin-1/2 quantum dot and two spin-1 particles. The three-spin system has two quantum states under the condition of isotropic exchange interaction, in which each of the states is corresponding to Bloch vector's pole and the control of these ones by the coherent manipulation yields another Hadamard basis state on the Bloch sphere. The purpose of this work is to clarify decoherence of a Hadamard basis state in the case that the system is tunnel-coupled to semi-infinite graphene electrodes with armchair edges. The results show that decay rate of a Hadamard basis state due to interaction with graphene electrodes is much smaller than that of metallic electrodes, and depends weakly on bias voltage. In addition, with the decrease of hybridization width, decoherence shows the transition from exponential decay to non-exponential one. Contrary to these features, decoherence of a Hadamard basis state undergoes the short-time dynamics for tunnel-couplings to zigzag edges.

Quantum variational learning for quantum error-correcting codes

Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum computation. In the past two decades, various constructions of quantum error-correcting codes (QECCs) have been developed, leading to many good code families. However, the majority of these codes are not suitable for near-term quantum devices. Here we present VarQEC, a noise-resilient variational quantum algorithm to search for quantum codes with a hardware-efficient encoding circuit. The cost functions are inspired by the most general and fundamental requirements of a QECC, the Knill-Laflamme conditions. Given the target noise channel (or the target code parameters) and the hardware connectivity graph, we optimize a shallow variational quantum circuit to prepare the basis states of an eligible code. In principle, VarQEC can find quantum codes for any error model, whether additive or non-additive, degenerate or non-degenerate, pure or impure. We have verified its effectiveness by (re)discovering some symmetric and asymmetric codes, e.g., ((n,2n−6,3))2 for n from 7 to 14. We also found new ((6,2,3))2 and ((7,2,3))2 codes that are not equivalent to any stabilizer code, and extensive numerical evidence with VarQEC suggests that a ((7,3,3))2 code does not exist. Furthermore, we found many new channel-adaptive codes for error models involving nearest-neighbor correlated errors. Our work sheds new light on the understanding of QECC in general, which may also help to enhance near-term device performance with channel-adaptive error-correcting codes.

Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms

Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of the QSD algorithms have focused on solving the eigenpair problem for ground, excited-state, and thermal observable estimation, there has been a lot less work in considering QSD algorithms for the problem of quantum dynamical simulation. In this work, we propose several quantum Krylov fast-forwarding (QKFF) algorithms capable of predicting long-time dynamics well beyond the coherence time of current quantum hardware. Our algorithms use real-time evolved Krylov basis states prepared on the quantum computer and a multi-reference subspace method to ensure convergence towards high-fidelity, long-time dynamics. In particular, we show that the proposed multi-reference methodology provides a systematic way of trading off circuit depth with classical post-processing complexity. We also demonstrate the efficacy of our approach through numerical implementations for several quantum chemistry problems including the calculation of the auto-correlation and dipole moment correlation functions

An exact tunneling model and its application to transmission and reflection delay times

Electron emission into a nanogap is not instantaneous, which presents a difficulty in simulating ultra-fast behavior using particle models. A method of approximating the transmission and reflection delay (TARD) times of a wave packet interacting with barriers described by a delta function, a metal–insulator–metal (MIM, rectangular) barrier, and a Fowler Nordheim (FN, triangular) barrier is given and has application to simulation. It is based on the superposition of a finite number of exact basis states obtained from Schrödinger’s equation, analogous to how quantum carpets are simulated. As a result, it can exactly and uniquely follow exponentially small tunneling currents. A Bohm-like trajectory is obtained from the time evolution of the density: it shows delay in both the transmitted and reflected packets that can be simply evaluated. The relations to prior studies of the analytic [Formula: see text]-function barrier and the Wigner distribution function (WDF) methods are described. A comparison of the TARD times is contrasted to alternate times in the Büttiker–Landauer (BL) and McColl–Hartman (MH) times; the MH approach is further reformulated explicitly in terms of Gamow factors to consider how the McColl–Hartman effect is to be related, particularly in the case of the FN barrier of field emission.

Initial-State Dependent Optimization of Controlled Gate Operations with Quantum Computer

There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivity, and coherence times, a quantum circuit optimization is essential to make the best use of near-term quantum devices. We introduce a new circuit optimizer called AQCEL, which aims to remove redundant controlled operations from controlled gates, depending on initial states of the circuit. Especially, the AQCEL can remove unnecessary qubit controls from multi-controlled gates in polynomial computational resources, even when all the relevant qubits are entangled, by identifying zero-amplitude computational basis states using a quantum computer. As a benchmark, the AQCEL is deployed on a quantum algorithm designed to model final state radiation in high energy physics. For this benchmark, we have demonstrated that the AQCEL-optimized circuit can produce equivalent final states with much smaller number of gates. Moreover, when deploying AQCEL with a noisy intermediate scale quantum computer, it efficiently produces a quantum circuit that approximates the original circuit with high fidelity by truncating low-amplitude computational basis states below certain thresholds. Our technique is useful for a wide variety of quantum algorithms, opening up new possibilities to further simplify quantum circuits to be more effective for real devices.

Quantum expectation-value estimation by computational basis sampling

Measuring expectation values of observables is an essential ingredient in variational quantum algorithms. A practical obstacle is the necessity of a large number of measurements for statistical convergence to meet requirements of precision, such as chemical accuracy in the application to quantum chemistry computations. Here we propose an algorithm to estimate the expectation value based on its approximate expression as a weighted sum of classically-tractable matrix elements with some modulation, where the weight and modulation factors are evaluated by sampling appropriately prepared quantum states in the computational basis on quantum computers. Each of those states is prepared by applying a unitary transformation consisting of at most N CNOT gates, where N is the number of qubits, to a target quantum state whose expectation value is evaluated. Our algorithm is expected to require fewer measurements than conventional methods for a required statistical precision of the expectation value when the target quantum state is concentrated in particular computational basis states. We provide numerical comparisons of our method with existing ones for measuring electronic ground state energies (expectation values of electronic Hamiltonians for the lowest-energy states) of various small molecules. Numerical results show that our method can reduce the numbers of measurements to obtain the ground state energies for a targeted precision by several orders of magnitudes for molecules whose ground states are concentrated. Our results provide another route to measure expectation values of observables, which could accelerate the variational quantum algorithms.

Ising-like and Fibonacci anyons from KZ-equations

In this work we present solutions to Knizhnik-Zamolodchikov (KZ) equations corresponding to conformal block wavefunctions of non-Abelian Ising-like and Fibonacci Anyons. We solve these equations around regular singular points in configuration space in terms of hypergeometric functions and derive explicit monodromy representations of the braid group action. This confirms the correct non-Abelian statistics of the solutions. One novelty of our approach is that we explicitly keep track of spin basis states and identify conformal blocks uniquely with such states at relevant points in moduli space.

Juridical Analysis of Fintech Business Dispute Settlement Through Online Dispute Resolution (ODR)

The research used in this research process uses type of normative legal research. Online Dispute Resolution (ODR) as an alternative dispute resolution in fintech sector has an urgency to be constructed immediately. First, the philosophical basis states that state supports existence of increasingly developing technologies if they are considered good and bring benefits to society. Second, the sociological basis due for rapid growth of fintech is directly proportional to various legal issues related to fintech disputes. Third, the juridical basis is because regulations related to fintech and Alternative Dispute Resolution (APS) are deemed no longer in accordance with legal developments and community needs,so that stricter regulations are needed and in accordance with legal developments and community needs. The government, the Financial Services Authority, Bank Indonesia and other relevant regulators should pay attention to need to accommodate ODR as an alternative to fintech dispute resolution in various laws and regulations in Indonesia so that there is no legal vacuum (rechtvacuum) and to optimize the basic principles of consumers, namely for efficiency and effectiveness in fintech sector.

Invariant subspaces and elliptic spin-helix states in the integrable open spin- 12 XYZ chain

We derive a criterion under which splitting of all eigenstates of an open $\mathrm{XYZ}$ Hamiltonian with boundary fields into two invariant subspaces, spanned by chiral shock states, occurs. The splitting is governed by an integer number, which has the geometrical meaning of the maximal number of kinks in the basis states. We describe the generic structure of the respective Bethe vectors. We obtain explicit expressions for Bethe vectors, in the absence of Bethe roots, and those generated by one Bethe root, and we investigate the single-particle subspace. We also describe in detail an elliptic analog of the spin-helix state, appearing in both the periodic and the open $\mathrm{XYZ}$ model, and we derive the eigenstate condition. The elliptic analog of the spin-helix state is characterized by a quasiperiodic modulation of the magnetization profile, governed by Jacobi elliptic functions.

A partial least squares regression model based on variational quantum algorithm

Partial least squares regression (PLSR) is an essential multivariate correlation analysis method in machine learning field. In this paper, we propose a variational quantum algorithm for partial least regression (VQPLSR). By exploring the relationship between standard basis states and optimization, we design a cost function that can train regression parameters and weight vectors simultaneously. The VQPLS requires only one copy of variables as input, which reduces the complexity of quantum circuit implementation. Compared with PLSR, the VQPLSR achieves an exponential speed-up in the independent variable dimension n and dependent variable dimension w. Simulation results show that regression parameters and weight vectors can be constructed with the error ∼10−5 for 4 × 2 dimensional variable matrix. This algorithm inspires us to explore more quantum applications in machine learning.

Using quantum amplitude amplification in genetic algorithms

The selection mechanism of genetic algorithms can play a key role in leading the optimization process towards suitable solutions of a given problem, as their application can affect the trade-off between exploration and exploitation. However, some selection operators suffer from an excessive exploitation that may lead to the loss of population diversity and to a premature convergence, and others present an excessive exploration that may cause genetic algorithms to produce poor results near to random. As a consequence, there is a strong need to rethink how a mating pool is created and introduce alternative approaches to genetic selection. In this paper, a quantum algorithm, named Quantum Genetic Sampling (QGS), has been designed to replace selection operators so as to provide an increased population diversity in genetic evolution and reduce the possibility that the optimization process converge to low quality solutions. The proposed approach is based on two sequential steps. In the first step, QGS models a problem’s search space through a quantum state, where each quantum basis state is related to a possible solution of the problem. In the second step, QGS uses quantum amplitude amplification to properly adjust the probability of measuring an individual and placing it in the mating pool according to its fitness value. Unlike conventional selection operators, the quantum mechanical nature of the proposed approach allows for a non-zero probability of introducing new genetic material into the mating pool. Experiments based on well-known benchmark functions show the suitability of the proposed quantum operator for embedding in genetic algorithms, both in terms of accuracy and population diversity.

Construction of Binary Quantum Error-Correcting Codes from Orthogonal Array.

By using difference schemes, orthogonal partitions and a replacement method, some new methods to construct pure quantum error-correcting codes are provided from orthogonal arrays. As an application of these methods, we construct several infinite series of quantum error-correcting codes including some optimal ones. Compared with the existing binary quantum codes, more new codes can be constructed, which have a lower number of terms (i.e., the number of computational basis states) for each of their basis states.

Symplectic effective field theory for nuclear structure studies

A symplectic effective field theory that unveils the observed emergence of symplectic symmetry in atomic nuclei is advanced. Specifically, starting from a simple extension of the harmonic-oscillator Lagrangian, an effective field theory applied against symplectic basis states is shown to yield a Hamiltonian system with one fitted parameter. The scale of the system can be determined self-consistently as the ratio of the average volume of a nucleus assumed to be spherical to its volume as determined by the average number of oscillator quanta, which is stretched by the fact that the plane-wave solution satisfies the equations of motion at every order without the need for perturbative corrections. As an application of the theory, results for $^{20}\mathrm{Ne}$, $^{22}\mathrm{Ne}$, and $^{22}\mathrm{Mg}$ are presented that yield energy spectra, $B(E2)$ values, and matter radii in good agreement with experimentally measured results.

Variational approaches to constructing the many-body nuclear ground state for quantum computing

We explore the preparation of specific nuclear states on gate-based quantum hardware using variational algorithms. Large-scale classical diagonalizations of the nuclear shell model have reached sizes of ${10}^{9}--{10}^{10}$ basis states but are still severely limited by computational resources. Quantum computing can, in principle, solve such systems exactly with exponentially fewer resources than classical computing. Exact solutions for large systems require many qubits and large gate depth, but variational approaches can effectively limit the required gate depth. We use the unitary coupled cluster approach to construct approximations of the ground-state vectors, later to be used in dynamics calculations. The testing ground is the phenomenological shell model space, which allows us to mimic the complexity of the internucleon interactions. We find that often one needs to minimize over a large number of parameters, using a large number of entanglements that makes the application on existing hardware challenging. Prospects for rapid improvements with more capable hardware are, however, very encouraging.

Quantum transport for electron quasiparticles interacting with a disordered binary alloy: A Wigner approach

Quantum transport is developed in the Wigner function representation for a Bloch electron quasiparticle interacting with a disordered binary alloy in the presence of a homogeneous electric field of arbitrary time dependence and amplitude. The electron quasiparticle is described by a single-band effective Hamiltonian, and the homogeneous electric field is treated in the vector potential gauge. The methodology for the quantum transport analysis proceeds by first transforming the Liouville equation to one in which the interaction Hamiltonian (the binary alloy Hamiltonian) appears quadratically. The basis states employed in evaluating the requisite matrix elements are the instantaneous eigenstates of the electron quasiparticle Hamiltonian in the presence of the electric field. The Wigner quantum transport equations are derived, and the binary alloy collision term is suitably ensemble averaged over the disordered binary alloy matrix elements. In addition, the general drift and diffusion terms are exactly obtained, resulting in the complete Wigner-Boltzmann equation for the binary alloy system. In approximating the collision term for the two separate cases of parabolic energy dispersion and the long-wavelength limit, it is found that the reduced Wigner-Boltzmann equation includes the manifestation of the intracollisional field effect and other quantum generalities. As a contrast to the actual random alloy treatment, attention is given to the canonical problem of quantum transport for a virtual crystal (VC). As an alternative to the random binary alloy scattering problem, the VC Hamiltonian adopted for this treatment is derived by ensemble averaging the random binary alloy Hamiltonian. The resulting Wigner transport equation for the VC case is descriptive of Bloch dynamics in a graded semiconductor alloy.