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IEEE International Conference on Quantum Computing and Engineering (QCE)

Quantum Resource Estimation for Quantum Chemistry Algorithms

Dmitry A. Fedorov, Matthew Otten, Byeol Kang, Anouar Benali, Salman Habib, Stephen K. Gray, Yuri Alexeev

Published Sep 1, 2022• 2 citations
Publisher

Abstract

Predicting the quantum resources for potential applications such as quantum chemistry plays a key role in the future development of quantum computers, and a systematic approach based on a reliable metric is needed for efficient resource estimation. In this work, we developed a Python software package QRE (Quantum Resource Estimator) for estimating quantum resources required to compute the properties of molecules. We define the key requirements for the quantum phase estimation (QPE) algorithm for molecules with different basis sets. We estimated the number of ancilla qubits, circuit depth, and time to solution. The input for QRE is the information about a molecule such as atom types, molecular geometries, charges, basis set, and level of theory. Also, we consider an error analysis scheme for QPE algorithm to calculate the number of ancilla qubits. As a part of the estimation, we calculate the number of rotation and CNOT gates for one Trotter step. Based on these results, the QRE program calculates costs for full QPE algorithms for the given gate time, fidelities of CNOT gates, and target success probability. It is expected that our work will contribute to a better understanding of the limitations of current and future quantum computers for quantum chemistry applications.

DOI
10.1109/qce53715.2022.00144

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Predicting the quantum resources for potential applications such as quantum chemistry plays a key role in the future development of quantum computers, and a systematic approach based on a reliable metric is needed for efficient resource estimation. In this work, we developed a Python software package QRE (Quantum Resource Estimator) for estimating quantum resources required to compute the properties of molecules. We define the key requirements for the quantum phase estimation (QPE) algorithm for molecules with different basis sets. We estimated the number of ancilla qubits, circuit depth, and time to solution. The input for QRE is the information about a molecule such as atom types, molecular geometries, charges, basis set, and level of theory. Also, we consider an error analysis scheme for QPE algorithm to calculate the number of ancilla qubits. As a part of the estimation, we calculate the number of rotation and CNOT gates for one Trotter step. Based on these results, the QRE program calculates costs for full QPE algorithms for the given gate time, fidelities of CNOT gates, and target success probability. It is expected that our work will contribute to a better understanding of the limitations of current and future quantum computers for quantum chemistry applications.
As quantum hardware continues to improve, more and more application scientists have entered the field of quantum computing. However, even with the rapid improvements in the last few years, quantum devices, especially for quantum chemistry applications, still struggle to perform calculations that classical computers could not calculate. In lieu of being able to perform specific calculations, it is important have a systematic way of estimating the resources necessary to tackle specific problems. Standard arguments about computational complexity provide hope that quantum computers will be useful for problems in quantum chemistry but obscure the true impact of many algorithmic overheads. These overheads will ultimately determine the precise point when quantum computers will perform better than classical computers. We have developed QREChem to provide logical resource estimates for ground state energy estimation in quantum chemistry through a Trotter-based quantum phase estimation approach. QREChem provides resource estimates which include the specific overheads inherent to problems in quantum chemistry by including heuristic estimates of the number of Trotter steps and number of necessary ancilla, allowing for more accurate estimates of the total number of gates. We utilize QREChem to provide logical resource estimates for a variety of small molecules in various basis sets, obtaining estimates in the range of 107–1015 for total number of T gates. We also determine estimates for the FeMoco molecule and compare all estimates to other resource estimation tools. Finally, we compare the total resources, including hardware and error correction overheads, demonstrating the need for fast error correction cycle times.
A number of exciting recent results have been seen in the field of quantum error correction. These include initial demonstrations of error correction on current quantum hardware and resource estimates which improve understanding of the requirements to run large-scale quantum algorithms for real-world applications. In this work, we bridge the gap between these two developments by performing careful estimation of the resources required to fault-tolerantly perform quantum phase estimation (QPE) on a minimal chemical example. Specifically, we describe a detailed compilation of the QPE circuit to lattice surgery operations for the rotated surface code, for a hydrogen molecule in a minimal basis set. We describe a number of optimizations at both the algorithmic and error correction levels. We find that implementing even a simple chemistry circuit requires 1000 qubits and 2300 quantum error correction rounds, emphasising the need for improved error correction techniques specifically targeting the early fault-tolerant regime. Published by the American Physical Society 2024
Quantum phase estimation (QPE) serves as a building block of many different quantum algorithms and finds important applications in computational chemistry problems. Despite the rapid development of quantum hardware, experimental demonstration of QPE for chemistry problems remains challenging due to its large circuit depth and the lack of quantum resources to protect the hardware from noise with fully fault-tolerant protocols. In the present work, we take a step towards fault-tolerant quantum computing by demonstrating a QPE algorithm on a Quantinuum trapped-ion computer. We employ a Bayesian approach to QPE and introduce a routine for optimal parameter selection, which we combine with a [[ n + 2 , n , 2 ]] quantum error detection code carefully tailored to the hardware capabilities. As a simple quantum chemistry example, we take a hydrogen molecule represented by a two-qubit Hamiltonian and estimate its ground state energy using our QPE protocol. In the experiment, we use the quantum circuits containing as many as 920 physical two-qubit gates to estimate the ground state energy within 6 × 10 − 3 hartree of the exact value. Published by the American Physical Society 2024
Determining properties of molecules and materials is one of the premier applications of quantum computing. A major question in the thesis is: how might we use long- and near-term quantum computers to solve problems of chemical interest? First, we give an overview of the standard model in electronic structure theory. Electronic structure methods have been improved significantly in the last decades; however, it is still a non-trivial task to fit experimental results for complex molecular systems. Second, we introduce quantum computation and quantum algorithms as an alternative device to solve the electronic structure problem. In the remaining part of the thesis, we describe the research projects. The thesis covers two (rather different) research directions: software and hardware projects. For the software part, we contribute with two new algorithms: Phase-Estimation Interval Target Energy Readout (PHILTER) and Recursive Variational Series Estimation (RVSE), where both are designed to be run on a quantum digital computer and extract materials and molecular properties. The PHILTER algorithm is a modification of the Quantum Phase Estimation and is designed to compute excited state energies within a target energy-interval for cases where good approximations for the states in the target energy-interval are either unknown or hard to prepare. For the RVSE algorithm, we pose the question: how might we use imperfect near-term quantum computers to solve problems of practical value? In this work, we introduce a method to compute expectation values of general functions of a Hamiltonian with respect to an input state using low depth quantum circuits suitable for noisy intermediate-scale quantum computers. For the hardware part, we propose a new chemical quantum computer by using molecular electronics as a basis for quantum computing. In this work, we pose the question: can scattering of electrons in molecules produce quantum gates? We construct one-qubit gates using one-electron scattering in molecules, and two-qubit controlled-phase gates using electron-electron scattering along metallic leads. We show initial applications of the framework by illustrating one-qubit gates using the molecular electronic structure of molecular hydrogen as a baseline model.
Quantum computers represent a radical technological advancement in the way information is processed by using the principles of quantum mechanics to solve very complex problems that exceed the capabilities of classical systems. However, in the current NISQ era (Noisy Intermediate-Scale Quantum devices), the available hardware presents several limitations, such as a limited number of qubits, high error rates, and reduced coherence times. Efficient management of quantum resources, both physical (qubits, error rates, connectivity) and logical (quantum gates, algorithms, error correction), becomes particularly relevant in the design and deployment of quantum algorithms. In this work, we analyze the role of resources in the various uses of NISQ devices today, identifying their relevance and implications for software engineering focused on the use of quantum computers. We propose a vision for runtime-aware quantum software development, identifying key challenges to its realization, such as limited introspection capabilities and temporal constraints in current platforms. As a proof of concept, we introduce Qonscious, a prototype framework that enables conditional execution of quantum programs based on dynamic resource evaluation. With this contribution, we aim to strengthen the field of Quantum Resource Estimation (QRE) and move towards the development of scalable, reliable, and resource-aware quantum software.
We compare several quantum phase estimation (QPE) protocols intended for early fault-tolerant (EFT) quantum computers in the context of models of their implementations on a surface code architecture. We estimate the logical and physical resources required to use these protocols to calculate the ground-state energy of molecular hydrogen in a minimal basis with error below ${10}^{\ensuremath{-}3}$ atomic units, in the presence of depolarizing logical errors. Accounting for the overhead of rotation synthesis and magic state distillation, we find that the total TTT-gate counts do not vary significantly among the EFT QPE protocols at fixed state overlap. In addition to reducing the number of ancilla qubits and circuit depth, the noise robustness of the EFT protocols can be leveraged to reduce resource requirements below those of textbook QPE, realizing an approximately 300-fold reduction in aggregate computational volume in some cases. We also compare resource requirements for QPE on Trotterized time evolution and qubitized walk operators, for this same minimal exemplar. We estimate the costs of these two approaches to be comparable, with the Trotter approach requiring slightly fewer physical qubits and the qubitized approach requiring slightly fewer code cycles. Even so, our estimates are well beyond the scale of existing early fault-tolerance demonstrations.