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DOE OSTI2024

Red-QAOA: Efficient Variational Optimization through Circuit Reduction

The Quantum Approximate Optimization Algorithm (QAOA) provides a quantum solution for combinatorial optimization problems. However, the optimal parameter searching process of QAOA is greatly affected by noise, leading to non-optimal solutions. This paper introduces a novel approach to optimize QAOA by exploiting the energy landscape concentration of similar instances via graph reduction, thus addressing the effect of noise. We formalize the notion of similar instances in QAOA and develop a Simulated Annealing-based graph reduction algorithm, called Red-QAOA, to identify the most similar subgraph for efficient parameter optimization. Red-QAOA outperforms state-of-the-art Graph Neural Network (GNN) based graph pooling techniques in performance and demonstrates effectiveness on a diverse set of real-world optimization problems encompassing 3200 graphs. Red-QAOA reduced the node counts and edge counts by 28% and 37%, respectively, while maintaining a low mean square error of 2%. These enable the identification of an optimal parameter set that is closer to the ideal true optimal solution in the presence of noise. By substantially streamlining the search for QAOA parameters, our approach sets the stage for the practical application of quantum algorithms in solving complex optimization problems.

Wang, Meng↗
DOE OSTI2021

Gutzwiller hybrid quantum-classical computing approach for correlated materials

Rapid progress in noisy intermediate-scale quantum (NISQ) computing technology has led to the development of novel resource-efficient hybrid quantum-classical algorithms, such as the variational quantum eigensolver (VQE), that can address open challenges in quantum chemistry, physics, and material science. Proof-of-principle quantum chemistry simulations for small molecules have been demonstrated on NISQ devices. While several approaches have been theoretically proposed for correlated materials, NISQ simulations of interacting periodic models on current quantum devices have not yet been demonstrated. Here, we develop a hybrid quantum-classical simulation framework for correlated electron systems based on the Gutzwiller variational embedding approach. We implement this framework on Rigetti quantum processing units (QPUs) and apply it to the periodic Anderson model, which describes a correlated heavy electron band hybridizing with noninteracting conduction electrons. Our simulation results quantitatively reproduce the known ground state quantum phase diagram including metallic, Kondo and Mott insulating phases. This is the first fully self-consistent hybrid quantum-classical simulation of an infinite correlated lattice model executed on QPUs, demonstrating that the Gutzwiller hybrid quantum-classical embedding framework is a powerful approach to simulate correlated materials on NISQ hardware. This benchmark study also puts forth a concrete pathway towards practical quantum advantage on NISQ devices.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Quantum Search Approaches to Sampling-Based Motion Planning

In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse environments, we formulate the Quantum Full Path Search Algorithm (q-FPS), which creates a superposition of full random path solutions, manipulates probability amplitudes with Quantum Amplitude Amplification (QAA), and quantum measures a single obstacle free full path solution. For dense unstructured environments, we formulate the Quantum Rapidly Exploring Random Tree algorithm, q-RRT, that creates quantum superpositions of possible parent-child connections, manipulates probability amplitudes with QAA, and quantum measures a single reachable state, which is added to a tree. As performance depends on the number of oracle calls and the probability of measuring good quantum states, we quantify how these errors factor into the probabilistic completeness properties of the algorithm. We then numerically estimate the expected number of database solutions to provide an approximation of the optimal number of oracle calls in the algorithm. We compare the q-RRT algorithm with a classical implementation and verify quadratic run-time speedup in the largest connected component of a 2D dense random lattice. We conclude by evaluating a proposed approach to limit the expected number of database solutions and thus limit the optimal number of oracle calls to a given number.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Reverse annealing for nonnegative/binary matrix factorization

It was recently shown that quantum annealing can be used as an effective, fast subroutine in certain types of matrix factorization algorithms. The quantum annealing algorithm performed best for quick, approximate answers, but performance rapidly plateaued. In this paper, we utilize reverse annealing instead of forward annealing in the quantum annealing subroutine for nonnegative/binary matrix factorization problems. After an initial global search with forward annealing, reverse annealing performs a series of local searches that refine existing solutions. The combination of forward and reverse annealing significantly improves performance compared to forward annealing alone for all but the shortest run times.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantum annealing for jet clustering with thrust

Quantum computing holds the promise of substantially speeding up computationally expensive tasks, such as solving optimization problems over a large number of elements. In high-energy collider physics, quantum-assisted algorithms might accelerate the clustering of particles into jets. In this study, we benchmark quantum annealing strategies for jet clustering based on optimizing a quantity called “thrust” in electron-positron collision events. Here, we find that quantum annealing yields similar performance to exact classical approaches and classical heuristics, after tuning the annealing parameters. Without tuning, comparable performance can be obtained through a hybrid quantum/classical approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Practical quantum computation of chemical and nuclear energy levels using quantum imaginary time evolution and Lanczos algorithms

Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits or high-dimensional optimization in the presence of noise. The quantum imaginary-time evolution (QITE) and quantum Lanczos (QLanczos) methods proposed in Motta et al. (2020) eschew the aforementioned issues. In this study, we demonstrate the practical application of these algorithms to challenging quantum computations of relevance for chemistry and nuclear physics, using the deuteron-binding energy and molecular hydrogen binding and excited state energies as examples. With the correct choice of initial and final states, we show that the number of timesteps in QITE and QLanczos can be reduced significantly, which commensurately simplifies the required quantum circuit and improves compatibility with NISQ devices. We have performed these calculations on cloud-accessible IBM Q quantum computers. With the application of readout-error mitigation and Richardson error extrapolation, we have obtained ground and excited state energies that agree well with exact results obtained from diagonalization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantum JPEG

The joint photographic expert group algorithm compresses a digital image by filtering its high spatial-frequency components. Similarly, we introduce a quantum algorithm that uses the quantum Fourier transform to discard the high spatial-frequency qubits of an image, downsampling it to a lower resolution. This allows one to capture, compress, and send images even with limited quantum resources for storage and communication. We show under which conditions this protocol is advantageous with respect to its classical counterpart.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Particle Track Classification Using Quantum Associative Memory (Final Technical Report)

This project explored the use of quantum-assisted algorithms for pattern matching in sub-atomic physics experiments. Pattern matching algorithms are commonly employed to prune data of random noise and to help discriminate between signals generated by particle tracks of interest and signals generated by background events. The quantum-assisted algorithms explored in this project were based on an Ising formulation of quantum associative model (QAMM) recall and quantum content-addressable memory (QCAM) recall. The recall is performed by comparing a probe pattern with those stored in a library of patterns encoded in the QAMM/QCAM model. The classification accuracy of QAMM and QCAM recall was determined as a function of detector resolution, noise, and efficiency and pattern density, where pattern density is defined as the ratio of the number of reference signal patterns encoded in the library to each pattern’s length. We found that QAMM achieved high classification accuracy when applied to datasets with low pattern density. QCAM achieved high classification accuracy for datasets with high pattern density and was found to be more robust to detector noise. The project methodology and results are described in detail in our arXiv preprint (arXiv:2011.11848) . This project was conducted by scientists at the Johns Hopkins University Applied Physics Laboratory and Oak Ridge National Laboratory from August 2018 to August 2020 and was supported by DOE grant DE-SC0019497.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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 OSTI2021

Universal Compiling and (No-)Free-Lunch Theorems for Continuous-Variable Quantum Learning

Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the dynamics of an experimental system. While much attention has been paid to quantum compiling on discrete-variable hardware, less has been paid to compiling in the continuous-variable paradigm. Here we motivate several, closely related, short-depth continuous-variable algorithms for quantum compilation. We analyze the trainability of our proposed cost functions and numerically demonstrate our algorithms by learning arbitrary Gaussian operations and Kerr nonlinearities. We further make connections between this framework and quantum learning theory in the continuous-variable setting by deriving no-free-lunch theorems. These generalization bounds demonstrate a linear resource reduction for learning Gaussian unitaries using entangled coherent-Fock states and an exponential resource reduction for learning arbitrary unitaries using two-mode-squeezed states.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The Localized Active Space Method with Unitary Selective Coupled Cluster

Here, we introduce a hybrid quantum-classical algorithm, the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. Derived from the localized active space unitary coupled cluster (LAS-UCCSD) method, LAS-USCCSD first performs a classical LASSCF calculation, then selectively identifies the most important parameters (cluster amplitudes used to build the multireference UCC ansatz) for restoring interfragment interaction energy using this reduced set of parameters with the variational quantum eigensolver method. We benchmark LAS-USCCSD against LAS-UCCSD by calculating the total energies of (H 2 ) 2 , (H 2 ) 4 , and trans-butadiene, and the magnetic coupling constant for a bimetallic compound [Cr 2 (OH) 3 (NH 3 ) 6 ] 3+ . For these systems, we find that LAS-USCCSD reduces the number of required parameters and thus the circuit depth by at least 1 order of magnitude, an aspect which is important for the practical implementation of multireference hybrid quantum-classical algorithms like LAS-UCCSD on near-term quantum computers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Emulation of complex open quantum systems using superconducting qubits

With quantum computers being out of reach for now, quantum simulators are alternative devices for efficient and accurate simulation of problems that are challenging to tackle using conventional computers. Quantum simulators are classified into analog and digital, with the possibility of constructing “hybrid” simulators by combining both techniques. Here we focus on analog quantum simulators of open quantum systems and address the limit that they can beat classical computers. In particular, as an example, we discuss simulation of the chlorosome light-harvesting antenna from green sulfur bacteria with over 250 phonon modes coupled to each electronic state. Furthermore, we propose physical setups that can be used to reproduce the quantum dynamics of a standard and multiple-mode Holstein model. The proposed scheme is based on currently available technology of superconducting circuits consist of flux qubits and quantum oscillators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Coupled Cluster Downfolding Methods: the effect of double commutator terms on the accuracy of ground-state energies

Downfolding coupled cluster (CC) techniques have recently been introduced into quantum chemistry as a tool for the dimensionality reduction of the many-body quantum problem. As opposed to earlier formulations in physics and chemistry based on the concept of effective Hamiltonians, the appearance of the downfolded Hamiltonians is a natural consequence of the single-reference exponential parametrization of the wave function. In this paper, we discuss the impact of higher-order terms originating in double commutators. In analogy to previous studies, we consider the case when only one- and two-body interactions are included in the downfolded Hamiltonians. We demonstrate the efficiency of the many-body expansions involving single and double commutators for the unitary extension of the downfolded Hamiltonians on the example of the beryllium atom, and bond-breaking processes in the Li2 and H2O molecules. For the H2O system, we also analyze energies obtained with downfolding procedures as functions of the active space size.

quantum computing, quantum algorithms, electronic ↗
DOE OSTI2024

Continuous-variable quantum computation of the O(3) model in 1+1 dimensions

We formulate the $O(3)$ non-linear sigma model in $1+1$ dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous variable (CV) approach to quantum computing. Here we construct the ground state and excited states using the coupled cluster ansatz and find excellent agreement with the exact diagonalization results for a small number of lattice sites. We then present the simulation protocol for the time evolution of the model using CV gates, estimate the discretization error, and present numerical results obtained from a photonic quantum simulator. We expect that the methods developed in this work will be useful for exploring interesting dynamics for a wide class of sigma models and gauge theories, as well as for simulating scattering events on quantum hardware in the coming decade.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale

The numerical simulation of quantum circuits is an indispensable tool for development, verification, and validation of hybrid quantum-classical algorithms intended for near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. Here, we present a modernized version of the Tensor Network Quantum Virtual Machine (TNQVM) that serves as the quantum circuit simulation backend in the eXtreme-scale ACCelerator (XACC) framework. The new version is based on the scalable tensor network processing library ExaTN (Exascale Tensor Networks). It provides multiple configurable quantum circuit simulators that perform either an exact quantum circuit simulation via the full tensor network contraction or an approximate simulation via a suitably chosen tensor factorization scheme. Upon necessity, stochastic noise modeling from real quantum processors is incorporated into the simulations by modeling quantum channels with Kraus tensors. By combining the portable XACC quantum programming frontend and the scalable ExaTN numerical processing backend, we introduce an end-to-end virtual quantum development environment that can scale from laptops to future exascale platforms. We report initial benchmarks of our framework, which include a demonstration of the distributed execution, incorporation of quantum decoherence models, and simulation of the random quantum circuits used for the certification of quantum supremacy on Google’s Sycamore superconducting architecture.

Nguyen, Thien↗
DOE OSTI2016

Sanibel Symposium in the Petascale-Exascale Computational Era

The 56 th Sanibel Symposium was held February 14-19 2016 at the King and Prince Hotel, St. Simons Island, GA. It successfully brought quantum chemists and chemical and condensed matter physicists together in presentations, posters, and informal discussions bridging those two communities. The Symposium has had a significant role in preparing generations of quantum theorists. As computational potency and algorithmic sophistication have grown, the Symposium has evolved to emphasize more heavily computationally oriented method development in chemistry and materials physics, including nanoscience, complex molecular phenomena, and even bio-molecular methods and problems. Given this context, the 56 th Sanibel meeting systematically and deliberately had sessions focused on exascale computation. A selection of outstanding theoretical problems that need serious attention was included. Five invited sessions, two contributed sessions (hot topics), and a poster session were organized with the exascale theme. This was a historic milestone in the evolution of the Symposia. Just as years ago linear algebra, perturbation theory, density matrices, and band-structure methods dominated early Sanibel Symposia, the exascale sessions of the 56 th meeting contributed a transformative influence to add structure and strength to the computational physical science community in an unprecedented way. A copy of the full program of the 56 th Symposium is attached. The exascale sessions were Linear Scaling, Non-Adabatic Dynamics, Interpretive Theory and Models, Computation, Software, and Algorithms, and Quantum Monte Carlo. The Symposium Proceedings will be published in Molecular Physics (2017). Note that the Sanibel proceedings from 2015 and 2014 were published as Molecular Physics vol. 114, issue 3-4 (2016) and vol. 113, issue 3-4 (2015) respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Quantum Statistical Testing of a QRNG Algorithm

We present the algorithmic design of a quantum random number generator, the subsequent synthesis of a physical design and its verification using quantum statistical testing. We also describe how quantum statistical testing can be used to diagnose channel noise in QKD protocols.

quantum information↗
DOE OSTI2022

Experimental error mitigation using linear rescaling for variational quantum eigensolving with up to 20 qubits

Quantum computers have the potential to help solve a range of physics and chemistry problems, but noise in quantum hardware currently limits our ability to obtain accurate results from the execution of quantum-simulation algorithms. Various methods have been proposed to mitigate the impact of noise on variational algorithms, including several that model the noise as damping expectation values of observables. In this work, we benchmark various methods, including a new method proposed here. Here, we compare their performance in estimating the ground-state energies of several instances of the 1D mixed-field Ising model using the variational-quantum-eigensolver algorithm with up to 20 qubits on two of IBM's quantum computers. We find that several error-mitigation techniques allow us to recover energies to within 10% of the true values for circuits containing up to about 25 ansatz layers, where each layer consists of CNOT gates between all neighboring qubits and Y-rotations on all qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗