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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Natural evolutionary strategies for variational quantum computation

Abstract Natural evolutionary strategies (NES) are a family of gradient-free black-box optimization algorithms. This study illustrates their use for the optimization of randomly initialized parameterized quantum circuits (PQCs) in the region of vanishing gradients. We show that using the NES gradient estimator the exponential decrease in variance can be alleviated. We implement two specific approaches, the exponential and separable NES, for parameter optimization of PQCs and compare them against standard gradient descent. We apply them to two different problems of ground state energy estimation using variational quantum eigensolver and state preparation with circuits of varying depth and length. We also introduce batch optimization for circuits with larger depth to extend the use of ES to a larger number of parameters. We achieve accuracy comparable to state-of-the-art optimization techniques in all the above cases with a lower number of circuit evaluations. Our empirical results indicate that one can use NES as a hybrid tool in tandem with other gradient-based methods for optimization of deep quantum circuits in regions with vanishing gradients.

Anand, Abhinav (ORCID:0000000280812310)↗
DOE OSTI2023

Real-Time Krylov Theory for Quantum Computing Algorithms

Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, which applies to the VQPE algorithm as well as others. We establish an error bound that justifies the fast convergence of our spectral approximation. We also derive how the overlap with high energy eigenstates becomes suppressed from real-time subspace diagonalization and we visualize the process that shows the signature phase cancellations at specific eigenenergies. We investigate various algorithm implementations and consider performance when stochasticity is added to the target Hamiltonian in the form of spectral statistics. To demonstrate the practicality of such real-time evolution, we discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Classical optimization with imaginary-time block encoding on quantum computers: The MaxCut problem

Optimization problems in finance, physics, and computer science are typically very hard to tackle in classical computing; quantum computing could help speed up computations and provide efficient methods for tackling large problems. Typically, to treat a problem with a quantum computer, the optimal solution is cast as the ground state of a diagonal Hamiltonian. Here, we develop a method, called imaginary-time evolution block encoding (ITE-BE), based on a recent imaginary-time algorithm, which requires no variational parameter optimization, as all parameters can be derived analytically from the target Hamiltonian. We also demonstrate that our method can be successfully combined with other quantum algorithms such as the quantum approximate optimization algorithm (QAOA). For illustration, here we study the MaxCut problem. We find that the QAOA ansatz increases the postselection success of ITE-BE, and shallow QAOA circuits, when boosted with ITE-BE, achieve better performance than deeper QAOA circuits. For the special case of the transverse initial state, we adapt our block-encoding scheme to allow for a deterministic application of the first layer of the circuit.

Zhong, Dawei [University of Southern California, L↗
DOE OSTI2019

Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs

Quantum chemistry is a discipline which relies heavily on very expensive numerical computations. The scaling of correlated wave function methods lies, in their standard implementation, between O(N-5) and O(e(N)), where N is proportional to the system size. Therefore, performing accurate calculations on chemically meaningful systems requires (i) approximations that can lower the computational scaling and (ii) efficient implementations that take advantage of modern massively parallel architectures. QUANTUM PACKAGE is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multireference second-order perturbation theory (PT2). The determinant-driven framework allows the programmer to include any arbitrary set of determinants in the reference space, hence providing greater methodological freedom. The sCI method implemented in QUANTUM PACKAGE is based on the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm which complements the variational sCI energy with a PT2 correction. Additional external plugins have been recently added to perform calculations with multireference coupled cluster theory and range-separated density-functional theory. All the programs are developed with the IRPF90 code generator, which simplifies collaborative work and the development of new features. QUANTUM PACKAGE strives to allow easy implementation and experimentation of new methods, while making parallel computation as simple and efficient as possible on modern supercomputer architectures. Currently, the code enables, routinely, to realize runs on roughly 2 000 CPU cores, with tens of millions of determinants in the reference space. Moreover, we have been able to push up to 12 288 cores in order to test its parallel efficiency. In the present manuscript, we also introduce some key new developments: (i) a renormalized second-order perturbative correction for efficient extrapolation to the full CI limit and (ii) a stochastic version of the CIPSI selection performed simultaneously to the PT2 calculation at no extra cost.

Garniron, Yann↗
DOE OSTI2021

Variational quantum solver employing the PDS energy functional

In our previous work (J. Chem. Phys. 2020, 153, 201102),we reported a new class of quantum algorithms that are based on the quantum computation of the connected moment expansion to find the ground and excited state energies. In particular, the Peeters-Devreese-Soldatov (PDS) formulation is found variational and bearing the potential for further combining with the existing variational quantum infrastructure. Following this direction, here we propose a variational quantum solver employing the PDS energy gradient. In comparison with the usual variational quantum eigensolver (VQE) and the original static PDS approach, the proposed variational quantum solver offers an effective approach to achieve high ac-curacy at finding the ground state and its energy through the rotation of the trial wave function of modest quality guided by the low order PDS energy gradients, thus improves the ac-curacy and efficiency of the quantum simulation. We demonstrate the performance of the proposed variational quantum solver for toy models, H2molecule, and strongly correlated planar H4system in some challenging situations. In all the case studies, the proposed variational quantum approach out-performs the usual VQE and static PDS calculations even at the lowest order.

Peng, Bo↗
DOE OSTI2025

Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems

Strongly-correlated quantum many-body systems are difficult to study and simulate classically. We recently proposed a variational quantum eigensolver (VQE) based on the multiscale entanglement renormalization ansatz (MERA) with tensors constrained to certain Trotter circuits. Here, we determine the scaling of computation costs for various critical spin chains which substantiates a polynomial quantum advantage in comparison to classical MERA simulations based on exact energy gradients or variational Monte Carlo. Algorithmic phase diagrams suggest an even greater separation for higher-dimensional systems. Hence, the Trotterized MERA VQE is a promising route for the efficient investigation of strongly-correlated quantum many-body systems on quantum computers. Furthermore, we show how the convergence can be substantially improved by building up the MERA layer by layer in the initialization stage and by scanning through the phase diagram during optimization. For the Trotter circuits being composed of single-qubit and two-qubit rotations, it is experimentally advantageous to have small rotation angles. We find that the average angle amplitude can be reduced considerably with negligible effect on the energy accuracy. Benchmark simulations suggest that the structure of the Trotter circuits for the TMERA tensors is not decisive; in particular, brick-wall circuits and parallel random-pair circuits yield very similar energy accuracies.

Miao, Qiang [Duke Quantum Center, Duke University,↗
DOE OSTI2017

Explicit inclusion of electronic correlation effects in molecular dynamics

Here, we design a quantum molecular dynamics method for strongly correlated electron metals. The strong electronic correlation effects are treated within a real-space version of the Gutzwiller variational approximation (GA), which is suitable for the inhomogeneity inherent in the process of quantum molecular dynamics (MD) simulations. We also propose an efficient algorithm based on the second-moment approximation to the electronic density of states for the search of the optimal variation parameters, from which the renormalized interatomic MD potentials are fully determined. By considering a minimal one-correlated-orbital Anderson model with parameterized spatial dependence of tight-binding hopping integrals, this fast GA-MD method is benchmarked with that using exact diagonalization to solve the GA variational parameters. The efficiency and accuracy are illustrated. We have demonstrated the effect of temperature coupled with electronic correlation on structural properties simulated with MD. This method will open up an unprecedented opportunity enabling large-scale quantum MD simulations of strongly correlated electronic materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Quantum Davidson algorithm for excited states

Abstract Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in quantum phase estimation and the variational quantum eigensolver (VQE). Although VQE-type methods have been extended to explore excited states, these methods grapple with optimization challenges. In contrast, the quantum Krylov subspace (QKS) method has been introduced to address both ground and excited states, positioning itself as a cost-effective alternative to quantum phase estimation. However, conventional QKS methodologies depend on a pre-generated subspace through real or imaginary-time evolutions. This subspace is inherently expansive and can be plagued with issues like slow convergence or numerical instabilities, often leading to relatively deep circuits. Our research presents an economic QKS algorithm, which we term the quantum Davidson (QDavidson) algorithm. This innovation hinges on the iterative expansion of the Krylov subspace and the incorporation of a pre-conditioner within the Davidson framework. By using the residues of eigenstates to expand the Krylov subspace, we manage to formulate a compact subspace that aligns closely with the exact solutions. This iterative subspace expansion paves the way for a more rapid convergence in comparison to other QKS techniques, such as the quantum Lanczos. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems, spanning from the Heisenberg spin model to real molecules. Compared to the existing QKS methods, the QDavidson algorithm not only converges swiftly but also demands a significantly shallower circuit. This efficiency establishes the QDavidson method as a pragmatic tool for elucidating both ground and excited state properties on quantum computing platforms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Adaptive Quantum Generative Training using an Unbounded Loss Function

We propose a generative quantum learning algorithm using the Adaptive Derivative-Assembled Problem Tailored ansatz (ADAPT) framework in which the loss function to be minimized is the maximal quantum Rényi divergence of order two, an unbounded function that mitigates barren plateaus which inhibit training variational circuits. We benchmark this method against other state-of-the-art adaptive algorithms by learning random two-local thermal states. We perform numerical experiments of up to 12 qubits comparing our method learning algorithms that use linear objective functions and show that Rényi-ADAPT is capable of constructing shallow quantum circuits competitive with existing methods, while the gradients remain favorable resulting from the maximal Rényi divergence loss function.

quantum algorithms, quantum machine learning, quan↗
DOE OSTI2019

Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

The variational quantum eigensolver (VQE) has emerged as one of the most enticing near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. Yet, unlike the original classical UCC theory, implementation on a quantum computer requires a finite-order Suzuki-Trotter decomposition to separate the exponentials of the large sum of Pauli operators. While previous literature has recognized the non-uniqueness of different orderings of the operators in the Trotterized form of UCC methods, the question of whether or not different orderings matter at the chemical scale has not been addressed. In this letter, we explore the effect of operator ordering on the Trotterized UCCSD ansatz, as well as the much more compact k-UpCCGSD ansatz recently proposed by Lee et al. We observe a significant, system-dependent variation in the energies of Trotterizations with different operator orderings. The energy variations occur on a chemical scale, sometimes on the order of hundreds of kcal/mol. This letter establishes the need to define not only the operators present in the ansatz, but also the order in which they appear. This is necessary for adhering to the quantum chemical notion of a ``model chemistry'', in addition to the general importance of scientific reproducibility. As a final note, we suggest a useful strategy to select out of the combinatorial number of possibilities, a single well-defined and effective ordering of the operators.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Variational quantum simulation of the critical Ising model with symmetry averaging

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)–style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. Here, we propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.

1-dimensional spin chains↗
DOE OSTI2026

Self-consistent mean-field quantum approximate optimization

We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.

Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗
DOE OSTI2026

Self-consistent mean-field quantum approximate optimization

We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.

Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗
DOE OSTI2026

Self-consistent mean-field quantum approximate optimization

We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.

Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗
DOE OSTI2021

Prime factorization using quantum variational imaginary time evolution

The road to computing on quantum devices has been accelerated by the promises that come from using Shor’s algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and lack of robust error correction schemes. Here we explore a promising, alternative method for prime factorization that uses well-established techniques from variational imaginary time evolution. We create a Hamiltonian whose ground state encodes the solution to the problem and use variational techniques to evolve a state iteratively towards these prime factors. We show that the number of circuits evaluated in each iteration scales as \(O(n^{5}d)\) , where n is the bit-length of the number to be factorized and d is the depth of the circuit. We use a single layer of entangling gates to factorize 36 numbers represented using 7, 8, and 9-qubit Hamiltonians. We also verify the method’s performance by implementing it on the IBMQ Lima hardware to factorize 55, 65, 77 and 91 which are greater than the largest number (21) to have been factorized on IBMQ hardware.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Variational quantum state eigensolver

Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application of near-term quantum computers. The variational quantum eigensolver (VQE) treats the case when the matrix is a Hamiltonian. Here, we address the case when the matrix is a density matrix ρ. We introduce the variational quantum state eigensolver (VQSE), which is analogous to VQE in that it variationally learns the largest eigenvalues of ρ as well as a gate sequence V that prepares the corresponding eigenvectors. VQSE exploits the connection between diagonalization and majorization to define a cost function C=Tr(ρ~H) where H is a non-degenerate Hamiltonian. Due to Schur-concavity, C is minimized when ρ~=VρV† is diagonal in the eigenbasis of H. VQSE only requires a single copy of ρ (only n qubits) per iteration of the VQSE algorithm, making it amenable for near-term implementation. We heuristically demonstrate two applications of VQSE: (1) Principal component analysis, and (2) Error mitigation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states

Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. In conclusion, we demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error-correction codes.

McClean, Jarrod R.↗