Search Results (16)

Understanding the capabilities of quantum computer devices and computing the required resources to solve realistic tasks remain critical challenges associated with achieving useful quantum computational advantage. We present a study aimed at reducing the quantum resource overhead in quantum chemistry simulations using the variational quantum eigensolver (VQE). Our approach achieves up to a two-orders-of magnitude reduction in the required number of two-qubit operations for variational problem-inspired ansatzes. We propose and analyze optimization strategies that combine various methods, including molecular point-group symmetries, compact excitation circuits, different types of excitation sets, and qubit tapering. To validate the compatibility and accuracy of these strategies, we first test them on small molecules such as LiH and BeH₂, then apply the most efficient ones to restricted active-space simulations of methylamine. We complete our analysis by computing the resources required for full-valence, active-space simulations of methylamine (26 qubits) and formic acid (28 qubits) molecules. Our best-performing optimization strategy reduces the two-qubit gate count for methylamine from approximately 600,000 to about 12,000 and yields a similar order-of-magnitude improvement for formic acid. This resource analysis represents a valuable step towards the practical use of quantum computers and the development of better methods for optimizing computing resources. Full article

The structure, bonding, and properties of diradicals, triradicals, and polyradicals have been investigated using broken symmetry (BS) molecular orbital (MO) and BS density functional theory (DFT) methods, which are regarded as the first steps in the mean-field approach toward strongly correlated electron systems (SCES). The natural orbital (NO) analyses of the BS MO and BS DFT solutions were performed to elucidate the natural orbitals of their occupation numbers, which are used for derivations of the diradical character (y) and several chemical indices for the open-shell molecules under investigation. These chemical indices are also obtained using SCES, the next theoretical step, which uses symmetry-recovered resonating BS (RBS) and multi-determinant methods such as multi-reference (MR) configuration interaction (CI) and MR-coupled cluster (CC) methods that employ the NOs generated in the first step. The nonlinear optical response properties of organic open-shell species were theoretically investigated with several procedures, such as MR CI (CC), the numerical Liouville, and Monte Carlo wavefunction methods, as the third step to SCES. The second-order hyperpolarizability (γ) of diradicals such as a phenalenyl radical dimer were mainly investigated in relation to the generation of quantum squeezed lights, which are used for the construction of the quantum entangled states for quantum optical devices such as quantum sensing and quantum computation. Basic quantum mechanical concepts, such as the Pegg–Barnett quantum phase operator, were also revisited in relation to the design and chemical synthesis of stable diradicals and polyradicals such as optical quantum molecular materials and future molecular qubits materials. Full article

In this paper, we introduce waveguide Quantum Electrodynamics (wQED) for the description of tryptophans in microtubules representing data qubits for information storage and, possibly, information processing. We propose a Hamiltonian in wQED and derive Heisenberg equations for qubits and photons. Using the Heisenberg equations, we derive time-evolution equations for the probability of qubits and the distribution of photons both at zero and finite temperature. We then demonstrate the resultant sub-radiance with small decay rates, which is required to achieve robust data qubits for information storage by coupling tryptophan residues containing data qubits with water molecules as Josephson quantum filters (JQFs). We also describe an oscillation processes of qubits in a tubulin dimer through the propagation of excitations with changing decay rates of JQFs. Data qubits are found to retain initial values by adopting sub-radiant states involving entanglement with water degrees of freedom. Full article

We present the first step toward the quantum computing (QC) formulation of the electron nuclear dynamics (END) method within the variational quantum simulator (VQS) scheme: END/QC/VQS. END is a time-dependent, variational, on-the-flight, and non-adiabatic method to simulate chemical reactions. END represents nuclei with frozen Gaussian wave packets and electrons with a single-determinantal state in the Thouless non-unitary representation. Within the hybrid quantum/classical VQS, END/QC/VQS currently evaluates the metric matrix M and gradient vector V of the symplectic END/QC equations on the QC software development kit QISKIT, and calculates basis function integrals and time evolution on a classical computer. To adapt END to QC, we substitute the Thouless non-unitary representation with Fukutome unitary representation. We derive the first END/QC/VQS version for pure electronic dynamics in multielectron chemical models consisting of two-electron units with fixed nuclei. Therein, Fukutome unitary matrices factorize into triads of one-qubit rotational matrices, which leads to a QC encoding of one electron per qubit. We design QC circuits to evaluate M and V in one-electron diatomic molecules. In log2-log2 plots, errors and deviations of those evaluations decrease linearly with the number of shots and with slopes = −1/2. We illustrate an END/QC/VQS simulation with the pure electronic dynamics of H₂⁺ We discuss the present results and future END/QC/QVS extensions. Full article

Quantum simulation qubit models of electronic Hamiltonians rely on specific transformations in order to take into account the fermionic permutation properties of electrons. These transformations (principally the Jordan–Wigner transformation (JWT) and the Bravyi–Kitaev transformation) correspond in a quantum circuit to the introduction of a supplementary circuit level. In order to include the fermionic properties in a more straightforward way in quantum computations, we propose to use methods issued from Geometric Algebra (GA), which, due to its commutation properties, are well adapted for fermionic systems. First, we apply the Witt basis method in GA to reformulate the JWT in this framework and use this formulation to express various quantum gates. We then rewrite the general one and two-electron Hamiltonian and use it for building a quantum simulation circuit for the Hydrogen molecule. Finally, the quantum Ising Hamiltonian, widely used in quantum simulation, is reformulated in this framework. Full article

The Second Quantum Revolution refers to a contemporary wave of advancements and breakthroughs in the field of quantum physics that extends beyond the early developments of Quantum Mechanics that occurred in the 20th century. One crucial aspect of this revolution is the deeper exploration and practical application of quantum entanglement. Entanglement serves as a cornerstone in the ongoing revolution, contributing to quantum computing, communication, fundamental physics experiments, and advanced sensing technologies. Here, we present and discuss some of the recent applications of entanglement, exploring its philosophical implications and non-locality beyond Bell’s theorem, thereby critically examining the foundations of Quantum Mechanics. Additionally, we propose educational activities that introduce high school students to Quantum Mechanics by emphasizing entanglement as an essential concept to understand in order to become informed participants in the Second Quantum Revolution. Furthermore, we present the state-of-art developments of a largely unexplored and promising realization of real qubits, namely the molecular spin qubits. We review the available and suggested device architectures to host and use molecular spins. Moreover, we summarize the experimental findings on solid-state spin qubit devices based on magnetic molecules. Finally, we discuss how the Second Quantum Revolution might significantly transform law enforcement by offering specific examples and methodologies to address the evolving challenges in public safety and security. Full article

One-dimensional (1D) magnetic systems offer rich phenomena in the quantum limit, proving more chemically accessible than zero-dimensional or higher-dimensional frameworks. Single-walled carbon nanotubes (SWCNT) have recently been used to encapsulate trimetric nickel(II) acetylacetonate [Nanoscale, 2019, 11, 10615–10621]. Here, we investigate the magnetization on spin chains based on nickel trimers by Matrix Product State (MPS) simulations. Our findings reveal plateaus in the exchange/magnetic-field phase diagram for three coupling configurations, showcasing effective dimeric and trimeric spin-ordering with similar or staggered entanglement across chains. These ordered states allow the qubit-like tuning of specific local magnetic moments, exhibiting disengagement or uniform coupling in entanglement plateaus. This behavior is consistent with the experimental transition from frustrated (3D) to non-frustrated (1D) molecules, corresponding to large and smaller SWCNT diameters. Our study offers insights into the potential of 1D-confined trimers for quantum computation, extending beyond the confinement of trimetric nickel-based molecules in one dimension. Full article

Solving the eigenproblems of Hermitian matrices is a significant problem in many fields. The quantum resonant transition (QRT) algorithm has been proposed and demonstrated to solve this problem using quantum devices. To better realize the capabilities of the QRT with recent quantum devices, we improve this algorithm and develop a new procedure to reduce the time complexity. Compared with the original algorithm, it saves one qubit and reduces the complexity with error $ϵ$ from $O(1/{ϵ}^2)$ to $O(1/ϵ)$. Thanks to these optimizations, we can obtain the energy spectrum and ground state of the effective Hamiltonian of the water molecule more accurately and in only 20 percent of the time in a four-qubit processor compared to previous work. More generally, for non-Hermitian matrices, a singular-value decomposition has essential applications in more areas, such as recommendation systems and principal component analysis. The QRT has also been used to prepare singular vectors corresponding to the largest singular values, demonstrating its potential for applications in quantum machine learning. Full article

Nuclear magnetic resonance (NMR) is a spectroscopic method that can be applied to several areas. Currently, this technique is also being used as an experimental quantum simulator, where nuclear spins are employed as quantum bits or qubits. The present work is devoted to studying heavy metal complexes as possible candidates to act as qubit molecules. Nuclei such ¹¹³Cd, ¹⁹⁹Hg, ¹²⁵Te, and ⁷⁷Se assembled with the most common employed nuclei in NMR-QIP implementations (¹H, ¹³C, ¹⁹F, ²⁹Si, and ³¹P) could potentially be used in heteronuclear systems for NMR-QIP implementations. Hence, aiming to contribute to the development of future scalable heteronuclear spin systems, we specially designed four complexes, based on the auspicious qubit systems proposed in our previous work, which will be explored by quantum chemical calculations of their NMR parameters and proposed as suitable qubit molecules. Chemical shifts and spin–spin coupling constants in four complexes were examined using the spin–orbit zeroth-order regular approximation (ZORA) at the density functional theory (DFT) level, as well as the relaxation parameters ($T_1$ and $T_2$). Examining the required spectral properties of NMR-QIP, all the designed complexes were found to be promising candidates for qubit molecules. Full article

Quantum computers are reaching one crucial milestone after another. Motivated by their progress in quantum chemistry, we performed an extensive series of simulations of quantum-computer runs that were aimed at inspecting the best-practice aspects of these calculations. In order to compare the performance of different setups, the ground-state energy of the hydrogen molecule was chosen as a benchmark for which the exact solution exists in the literature. Applying the variational quantum eigensolver (VQE) to a qubit Hamiltonian obtained by the Bravyi–Kitaev transformation, we analyzed the impact of various computational technicalities. These included (i) the choice of the optimization methods, (ii) the architecture of the quantum circuits, as well as (iii) the different types of noise when simulating real quantum processors. On these, we eventually performed a series of experimental runs as a complement to our simulations. The simultaneous perturbation stochastic approximation (SPSA) and constrained optimization by linear approximation (COBYLA) optimization methods clearly outperformed the Nelder–Mead and Powell methods. The results obtained when using the $R_{\mathrm{y}}$ variational form were better than those obtained when the $R_{\mathrm{y}}{R}_{\mathrm{z}}$ form was used. The choice of an optimum entangling layer was sensitively interlinked with the choice of the optimization method. The circular entangling layer was found to worsen the performance of the COBYLA method, while the full-entangling layer improved it. All four optimization methods sometimes led to an energy that corresponded to an excited state rather than the ground state. We also show that a similarity analysis of measured probabilities can provide a useful insight. Full article

Magnetic molecules are prototypical systems to investigate peculiar quantum mechanical phenomena. As such, simulating their static and dynamical behavior is intrinsically difficult for a classical computer, due to the exponential increase of required resources with the system size. Quantum computers solve this issue by providing an inherently quantum platform, suited to describe these magnetic systems. Here, we show that both the ground state properties and the spin dynamics of magnetic molecules can be simulated on prototype quantum computers, based on superconducting qubits. In particular, we study small-size anti-ferromagnetic spin chains and rings, which are ideal test-beds for these pioneering devices. We use the variational quantum eigensolver algorithm to determine the ground state wave-function with targeted ansatzes fulfilling the spin symmetries of the investigated models. The coherent spin dynamics are simulated by computing dynamical correlation functions, an essential ingredient to extract many experimentally accessible properties, such as the inelastic neutron cross-section. Full article

Many concepts in mathematics are not fully defined, and their properties are implicit, which leads to paradoxes. New foundations of mathematics were formulated based on the concept of innate programs of behavior and thinking. The basic axiom of mathematics is proposed, according to which any mathematical object has a physical carrier. This carrier can store and process only a finite amount of information. As a result of the D-procedure (encoding of any mathematical objects and operations on them in the form of qubits), a mathematical object is digitized. As a consequence, the basis of mathematics is the interaction of brain qubits, which can only implement arithmetic operations on numbers. A proof in mathematics is an algorithm for finding the correct statement from a list of already-existing statements. Some mathematical paradoxes (e.g., Banach–Tarski and Russell) and Smale’s 18th problem are solved by means of the D-procedure. The axiom of choice is a consequence of the equivalence of physical states, the choice among which can be made randomly. The proposed mathematics is constructive in the sense that any mathematical object exists if it is physically realized. The consistency of mathematics is due to directed evolution, which results in effective structures. Computing with qubits is based on the nontrivial quantum effects of biologically important molecules in neurons and the brain. Full article

We present example quantum chemistry programs written with JaqalPaq, a python meta-programming language used to code in Jaqal (Just Another Quantum Assembly Language). These JaqalPaq algorithms are intended to be run on the Quantum Scientific Computing Open User Testbed (QSCOUT) platform at Sandia National Laboratories. Our exemplars use the variational quantum eigensolver (VQE) quantum algorithm to compute the ground state energies of the ${\mathrm{H}}_2$, ${\mathrm{HeH}}^{+}$, and $\mathrm{LiH}$ molecules. Since the exemplars focus on how to program in JaqalPaq, the calculations of the second-quantized Hamiltonians are performed with the PySCF python package, and the mappings of the fermions to qubits are obtained from the OpenFermion python package. Using the emulator functionality of JaqalPaq, we emulate how these exemplars would be executed on an error-free QSCOUT platform and compare the emulated computation of the bond-dissociation curves for these molecules with their exact forms within the relevant basis. Full article

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here, we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space specified by a set of computational bases. From this projection, an effective Hamiltonian is obtained. Furthermore, a process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given, whereby quantum entanglement and ancilla qubits are used. The effective Hamiltonian is then diagonalized on a classical computer using numerical algorithms to obtain the eigenvalues. The use case of this approach is demonstrated for ground state and excited states of BeH₂ and LiH molecules, and the density of states, which agrees well with exact solutions. Additionally, hardware demonstration is presented using IBM quantum devices for H₂ molecule. Full article

Vanadium(IV) complexes are actively studied as potential candidates for molecular spin qubits operating at room temperatures. They have longer electron spin decoherence times than many other transition ions, being the key property for applications in quantum information processing. In most cases reported to date, the molecular complexes were optimized through the design for this purpose. In this work, we investigate the relaxation properties of vanadium(IV) ions incorporated in complexes with lanthanides using electron paramagnetic resonance (EPR). In all cases, the VO₆ moieties with no nuclear spins in the first coordination sphere are addressed. We develop and implement the approaches for facile diagnostics of relaxation characteristics in individual VO₆ moieties of such compounds. Remarkably, the estimated relaxation times are found to be close to those of other vanadium-based qubits obtained previously. In the future, a synergistic combination of qubit-friendly properties of vanadium ions with single-molecule magnetism and luminescence of lanthanides can be pursued to realize new functionalities of such materials. Full article