arXiv subjects

Artur F. Izmaylov

Publications and source records attributed to Artur F. Izmaylov.

At least 37 records · Page 2Linked to original sources

arXiv2024

Simulating Vibrational Dynamics on Bosonic Quantum Devices

Bosonic quantum devices, which utilize harmonic oscillator modes to encode information, are emerging as a promising alternative to conventional qubit-based quantum devices, especially for the simulation of vibrational dynamics and spectroscopy. We present a framework for digital quantum simulation of vibrational dynamics under anharmonic potentials on these bosonic devices. In our approach the vibrational Hamiltonian is decomposed into solvable fragments that can be used for Hamiltonian simulation on currently available bosonic hardware. Specifically, we extended the Cartan subalgebra approach [T.C. Yen, A.F. Izmaylov, PRX Quantum 2, 040320 (2021)] -- a method for decomposing quantum Hamiltonians into solvable parts -- to bosonic operators, enabling us to construct anharmonic Hamiltonian fragments that can be efficiently diagonalized using Bogoliubov transforms. The approach is tested using a simulation of tunneling dynamics in a model two-dimensional double-well potential and calculations of vibrational eigenenergies for small molecules. Our fragmentation scheme provides a new approach for digital quantum simulations on bosonic quantum hardware for multi-mode anharmonic vibrational dynamics.

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arXiv2024

Majorana Tensor Decomposition: A unifying framework for decompositions of fermionic Hamiltonians to Linear Combination of Unitaries

Linear combination of unitaries (LCU) decompositions have appeared as one of the main tools for encoding operators on quantum computers, allowing efficient implementations of arbitrary operators. In particular, LCU approaches present a way of encoding information from the electronic structure Hamiltonian into a quantum circuit. Over the past years, many different decomposition techniques have appeared for the electronic structure Hamiltonian. Here we present the Majorana Tensor Decomposition (MTD), a framework that unifies existing LCUs and offers novel decomposition methods by using popular low-rank tensor factorizations.

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arXiv2024

Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.

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arXiv2024

Feasibility of accelerating homogeneous catalyst discovery with fault-tolerant quantum computers

The industrial manufacturing of chemicals consumes a significant amount of energy and raw materials. In principle, the development of new catalysts could greatly improve the efficiency of chemical production. However, the discovery of viable catalysts can be exceedingly challenging because it is difficult to know the efficacy of a candidate without experimentally synthesizing and characterizing it. This study explores the feasibility of using fault-tolerant quantum computers to accelerate the discovery of homogeneous catalysts for nitrogen fixation, an industrially important chemical process. It introduces a set of ground-state energy estimation problems representative of calculations needed for the discovery of homogeneous catalysts and analyzes them on three dimensions: economic utility, classical hardness, and quantum resource requirements. For the highest utility problem considered, two steps of a catalytic cycle for the generation of cyanate anion from dinitrogen, the economic utility of running these computations is estimated to be $200,000, and the required runtime for double-factorized phase estimation on a fault-tolerant superconducting device is estimated under conservative assumptions to be 139,000 QPU-hours. The computational cost of an equivalent DMRG calculation is estimated to be about 400,000 CPU-hours. These results suggest that, with continued development, it will be feasible for fault-tolerant quantum computers to accelerate the discovery of homogeneous catalysts.

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arXiv2024

Exactly solvable Hamiltonian fragments obtained from a direct sum of Lie algebras

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 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 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. 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 with previously used exactly solvable qubit Hamiltonians.

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arXiv2023

Probing Quantum Efficiency: Exploring System Hardness in Electronic Ground State Energy Estimation

We consider the question of how correlated the system hardness is between classical algorithms of electronic structure theory in ground state estimation and quantum algorithms. To define the system hardness for classical algorithms we employ empirical criterion based on the deviation of electronic energies produced by coupled cluster and configuration interaction methods from the exact ones along multiple bonds dissociation in a set of molecular systems. For quantum algorithms, we have selected the Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE) methods. As characteristics of the system hardness for quantum methods, we analyzed circuit depths for the state preparation, the number of quantum measurements needed for the energy expectation value, and various cost characteristics for the Hamiltonian encodings via Trotter approximation and linear combination of unitaries (LCU). Our results show that the quantum resource requirements are mostly unaffected by classical hardness, with the only exception being the state preparation part, which contributes to both VQE and QPE algorithm costs. However, there are clear indications that constructing the initial state with a significant overlap with the true ground state (>10%) is easier than obtaining the state with an energy expectation value within chemical precision. These results support optimism regarding the identification of a molecular system where a quantum algorithm excels over its classical counterpart, as quantum methods can maintain efficiency in classically challenging systems.

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arXiv2023

Block-Invariant Symmetry Shift: Preprocessing technique for second-quantized Hamiltonians to improve their decompositions to Linear Combination of Unitaries

Computational cost of energy estimation for molecular electronic Hamiltonians via Quantum Phase Estimation (QPE) grows with the difference between the largest and smallest eigenvalues of the Hamiltonian. In this work we propose a preprocessing procedure that reduces the norm of the Hamiltonian without changing its eigenspectrum for the target states of a particular symmetry. The new procedure, Block-Invariant Symmetry Shift (BLISS), builds an operator T such that the cost of implementing H-T is reduced compared to that of H, yet H-T acts on the subspaces of interest the same way as H does. BLISS performance is demonstrated for Linear Combination of Unitaries (LCU)-based QPE approaches on a set of small molecules. Using the number of electrons as the symmetry specifying the target set of states, BLISS provided a factor of 2 reduction of 1-norm for several LCU decompositions compared to their unshifted versions.

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arXiv2023

Extension of exactly-solvable Hamiltonians using symmetries of Lie algebras

Exactly-solvable Hamiltonians that can be diagonalized using relatively simple unitary transformations are of great use in quantum computing. They can be employed for decomposition of interacting Hamiltonians either in Trotter-Suzuki approximations of the evolution operator for the quantum phase estimation algorithm, or in the quantum measurement problem for the variational quantum eigensolver. One of the typical forms of exactly solvable Hamiltonians is a linear combination of operators forming a modest size Lie algebra. Very frequently such linear combinations represent non-interacting Hamiltonians and thus are of limited interest for describing interacting cases. Here we propose the extension where coefficients in these combinations are substituted by polynomials of the Lie algebra symmetries. This substitution results in a more general class of solvable Hamiltonians and for qubit algebras is related to the recently proposed non-contextual Pauli Hamiltonians. In fermionic problems, this substitution leads to Hamiltonians with eigenstates that are single Slater determinants but with different sets of single-particle states for different eigenstates. The new class of solvable Hamiltonians can be measured efficiently using quantum circuits with gates that depend on the result of a mid-circuit measurement of the symmetries.

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arXiv2023

Growth reduction of similarity transformed electronic Hamiltonians in qubit space

Accurately solving the electronic structure problem through the variational quantum eigensolver (VQE) is hindered by the available quantum resources of current and near-term devices. One approach to relieving the circuit depth requirements for VQE is to "pre-process" the electronic Hamiltonian by a similarity transformation incorporating some degree of electronic correlation, with the remaining correlation left to be addressed by the circuit ansatz. This often comes at the price of a substantial increase in the number of terms to measure in the similarity transformed Hamiltonian. In this work, we propose an efficient approach to sampling elements from the complete Pauli group for $N$ qubits which minimize the onset of new terms in the transformed Hamiltonian, while facilitating substantial energy lowering. We benchmark the growth-mitigating generator selection technique for ground state energy estimations applied to models of the H$_4$, N$_2$ and H$_2$O molecular systems. It is found that utilizing a selection procedure which obtains the growth-minimizing generator from the set of operators with maximal energy gradient is the most competitive approach to reducing the onset of Hamiltonian terms while achieving systematic energy lowering of the reference state.

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arXiv2023

Coherent control based on quantum Zeno and anti-Zeno effects: Role of coherences and timing

The quantum-Zeno and anti-Zeno effects (QZE/AZE) are known for a long time, in a quantum system with coupled levels, the measurement of a particular level population can lead to either acceleration (i.e. AZE) or retardation (i.e. QZE) of its population transfer to other levels. Here we consider how one can control the population flow from a coupled quantum state by measurement at a particular time, and what system parameters are responsible for that. We propose a framework for analysis of quantum Zeno dynamics based on time-dependent density matrix perturbation theory. This framework allows us to clearly separate state populations from their coherences and to predict appearance of either QZE or AZE. We illustrate our analysis on two model systems: 1) two coupled levels and 2) a level coupled to a continuum. In both cases dynamics of quantum coherences play a crucial role, and perturbative considerations allow us to predict the effect of projective measurements. In addition, we have extended our consideration to a closely related coherent control scenario, a unitary transformation flipping a sign of a state in a coherent superposition describing the system wavefunction.

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arXiv2023

Assessment of various Hamiltonian partitionings for the electronic structure problem on a quantum computer using the Trotter approximation

Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via Trotterization, where a sequence of short-time evolutions of fast-forwardable (i.e. efficiently diagonalizable) Hamiltonian fragments is used. Given multiple choices of possible Hamiltonian decompositions to fast-forwardable fragments, the accuracy of the Hamiltonian evolution depends on the choice of the fragments. We assess efficiency of multiple Hamiltonian partitioning techniques using fermionic and qubit algebras for the Trotterization. Use of symmetries of the electronic Hamiltonian and its fragments significantly reduces the Trotter error. This reduction makes fermionic-based partitioning Trotter errors lower compared to those in qubit-based techniques. However, from the simulation-cost standpoint, fermionic methods tend to introduce quantum circuits with a greater number of T-gates at each Trotter step and thus are more computationally expensive compared to their qubit counterparts.

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arXiv2023

Measurement optimization techniques for excited electronic states in near-term quantum computing algorithms

The variational quantum eigensolver (VQE) remains one of the most popular near-term quantum algorithms for solving the electronic structure problem. Yet, for its practicality, the main challenge to overcome is improving the quantum measurement efficiency. Numerous quantum measurement techniques have been developed recently, but it is unclear how these state-of-the-art measurement techniques will perform in extensions of VQE for obtaining excited electronic states. Assessing the measurement techniques' performance in the excited state VQE is crucial because the measurement requirements in these extensions are typically much greater than in conventional VQE, as one must measure the expectation value of multiple observables in addition to that of the electronic Hamiltonian. Here, we adapt various measurement techniques to two widely used excited state VQE algorithms: multi-state contraction and quantum subspace expansion. Then, the measurement requirements of each measurement technique are numerically compared. We find that the best methods for multi-state contraction are ones utilizing Hamiltonian data and wavefunction information to minimize the number of measurements. In contrast, randomized measurement techniques are more appropriate for quantum subspace expansion, with many more observables of vastly different energy scales to measure. Nevertheless, when the best possible measurement technique for each excited state VQE algorithm is considered, significantly fewer measurements are required in multi-state contraction than in quantum subspace expansion.

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arXiv2023

A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules

We propose a hybrid quantum-classical algorithm for solving the time-independent Schrödinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix by inverting the Hamiltonian matrix expressed in the basis of square-integrable functions. The computational bottleneck of the classical algorithm -- symmetric matrix inversion -- is addressed here using the variational quantum linear solver (VQLS), a recently developed noisy intermediate-scale quantum (NISQ) algorithm for solving systems of linear equations. We apply our algorithm to single and multichannel quantum scattering problems, obtaining accurate vibrational relaxation probabilities in collinear atom-molecule collisions. We also show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules. Our results demonstrate that it is possible to calculate scattering cross sections and rates for complex molecular collisions on NISQ quantum processors, opening up the possibility of scalable digital quantum computation of gas-phase bimolecular collisions and reactions of relevance to astrochemistry and ultracold chemistry.

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arXiv2023

Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches

We consider different Linear Combination of Unitaries (LCU) decompositions for molecular electronic structure Hamiltonians. Using these LCU decompositions for Hamiltonian simulation on a quantum computer, the main figure of merit is the 1-norm of their coefficients, which is associated with the quantum circuit complexity. It is derived that the lowest possible LCU 1-norm for a given Hamiltonian is half of its spectral range. This lowest norm decomposition is practically unattainable for general Hamiltonians; therefore, multiple practical techniques to generate LCU decompositions are proposed and assessed. A technique using symmetries to reduce the 1-norm further is also introduced. In addition to considering LCU in the Schrödinger picture, we extend it to the interaction picture, which substantially further reduces the 1-norm.

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arXiv2022

Fluid fermionic fragments for optimizing quantum measurements of electronic Hamiltonians in the variational quantum eigensolver

Measuring the expectation value of the molecular electronic Hamiltonian is one of the challenging parts of the variational quantum eigensolver. A widely used strategy is to express the Hamiltonian as a sum of measurable fragments using fermionic operator algebra. Such fragments have an advantage of conserving molecular symmetries that can be used for error mitigation. The number of measurements required to obtain the Hamiltonian expectation value is proportional to a sum of fragment variances. Here, we introduce a new method for lowering the fragments' variances by exploiting flexibility in the fragments' form. Due to idempotency of the occupation number operators, some parts of two-electron fragments can be turned into one-electron fragments, which then can be partially collected in a purely one-electron fragment. This repartitioning does not affect the expectation value of the Hamiltonian but has non-vanishing contributions to the variance of each fragment. The proposed method finds the optimal repartitioning by employing variances estimated using a classically efficient proxy for the quantum wavefunction. Numerical tests on several molecules show that repartitioning of one-electron terms lowers the number of measurements by more than an order of magnitude.

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arXiv2022

Improving quantum measurements by introducing "ghost" Pauli products

Reducing the number of measurements required to estimate the expectation value of an observable is crucial for the variational quantum eigensolver to become competitive with state-of-the-art classical algorithms. To measure complicated observables such as a molecular electronic Hamiltonian, one of the common strategies is to partition the observable into linear combinations (fragments) of mutually commutative Pauli products. The total number of measurements for obtaining the expectation value is then proportional to the sum of variances of individual fragments. We propose a method that lowers individual fragment variances by modifying the fragments without changing the total observable expectation value. Our approach is based on adding Pauli products ("ghosts") that are compatible with members of multiple fragments. The total expectation value does not change because a sum of coefficients for each "ghost" Pauli product introduced to several fragments is zero. Yet, these additions change individual fragment variances because of the non-vanishing contributions of "ghost" Pauli products within each fragment. The proposed algorithm minimizes individual fragment variances using a classically efficient approximation of the quantum wavefunction for variance estimations. Numerical tests on a few molecular electronic Hamiltonian expectation values show several-fold reductions in the number of measurements in the "ghost" Pauli algorithm compared to those in the other recently developed techniques.

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arXiv2022

Quantum Kinetic Rates within the Nonequilibrium Steady State

The nonequilibrium steady state (NESS) of a quantum network is central to a host of physical and biological scenarios. Examples include natural processes such as vision and photosynthesis, as well as technical devices such as photocells, both activated by incoherent light (e.g. sunlight) and leading to quantum transport. Here, a completely general approach to defining components of a quantum network in the NESS, and obtaining rates of processes between these components is provided. Quantum effects are explicitly included throughout, both in (a) defining network components via projection operators, and (b) in determining the role of coherences in rate processes. As examples, the methodology is applied to model cases, two versions of the V-level system, and to the spin-boson model, wherein the role of the environment and of internal system properties in determining the rates is examined. In addition, the role of Markovian vs. non-Markovian contributions is quantified, exposing conditions under which NESS rates can be obtained by perturbing the nonequilibrium steady state.

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arXiv2022

Fidelity overhead for non-local measurements in variational quantum algorithms

Measuring quantum observables by grouping terms that can be rotated to sums of only products of Pauli $\hat z$ operators (Ising form) is proven to be efficient in near term quantum computing algorithms. This approach requires extra unitary transformations to rotate the state of interest so that the measurement of a fragment's Ising form would be equivalent to measurement of the fragment for the unrotated state. These extra rotations allow one to perform a fewer number of measurements by grouping more terms into the measurable fragments with a lower overall estimator variance. However, previous estimations of the number of measurements did not take into account non-unit fidelity of quantum gates implementing the additional transformations. Through a circuit fidelity reduction, additional transformations introduce extra uncertainty and increase the needed number of measurements. Here we consider a simple model for errors introduced by additional gates needed in schemes involving grouping of commuting Pauli products. For a set of molecular electronic Hamiltonians, we confirm that the numbers of measurements in schemes using non-local qubit rotations are still lower than those in their local qubit rotation counterparts, even after accounting for uncertainties introduced by additional gates.

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