In recent years substantial research effort has been devoted to quantum algorithms for ground state energy estimation (GSEE) in chemistry and materials. Given the many heuristic and non-heuristic methods being developed, it is challenging to assess what combination of these will ultimately be used in practice. One important metric for assessing utility is runtime. For most GSEE algorithms, the runtime depends on the ground state preparation (GSP) method. Towards assessing the utility of various combinations of GSEE and GSP methods, we asked under which conditions a GSP method should be accepted over a reference method, such as the Hartree-Fock state. We introduce a criteria for accepting or rejecting a GSP method for the purposes of GSEE. We consider different GSP methods ranging from heuristics to algorithms with provable performance guarantees and perform numerical simulations to benchmark their performance on different chemical systems, starting from small molecules like the hydrogen atom to larger systems like the jellium. In the future this approach may be used to abandon certain VQE ansatzes and other heursitics. Yet so far our findings do not provide evidence against the use of VQE and more expensive heuristic methods, like the low-depth booster. This work sets a foundation from which to further explore the requirements to achieve quantum advantage in quantum chemistry.
In recent years substantial research effort has been devoted to quantum algorithms for ground state energy estimation (GSEE) in chemistry and materials. Given the many heuristic and non-heuristic methods being developed, it is challenging to assess what combination of these will ultimately be used in practice. One important metric for assessing utility is runtime. For most GSEE algorithms, the runtime depends on the ground state preparation (GSP) method. Towards assessing the utility of various combinations of GSEE and GSP methods, we asked under which conditions a GSP method should be accepted over a reference method, such as the Hartree-Fock state. We introduce a criteria for accepting or rejecting a GSP method for the purposes of GSEE. We consider different GSP methods ranging from heuristics to algorithms with provable performance guarantees and perform numerical simulations to benchmark their performance on different chemical systems, starting from small molecules like the hydrogen atom to larger systems like the jellium. In the future this approach may be used to abandon certain VQE ansatzes and other heursitics. Yet so far our findings do not provide evidence against the use of VQE and more expensive heuristic methods, like the low-depth booster. This work sets a foundation from which to further explore the requirements to achieve quantum advantage in quantum chemistry.
In recent years, substantial research effort has been devoted to quantum algorithms for ground-state-energy estimation (GSEE) in chemistry and materials. Given the many heuristic and nonheuristic methods being developed, it is challenging to assess what combination of these methods will ultimately be used in practice. One important metric for assessing utility is the runtime, which depends on the ground-state preparation (GSP) for most GSEE algorithms. Towards assessing the utility of various combinations of GSEE and GSP methods, we asked under which conditions a GSP method should be accepted over a reference method, such as the Hartree-Fock method. We introduce a criterion for accepting or rejecting a GSP method for the purposes of GSEE. We consider different GSP methods ranging from heuristics to algorithms with provable performance guarantees and perform numerical simulations to benchmark their performance on different chemical systems, starting from small molecules like the hydrogen molecule to larger systems like jellium. In the future, this approach may be used to abandon certain variational quantum eigensolver (VQE) ansatzes and other heuristics. Yet our findings do not provide evidence against using VQE and more expensive heuristic methods, like the low-depth booster. This work sets a foundation from which to further explore the requirements to achieve quantum advantage in quantum chemistry.
One promising field of quantum computation is the simulation of quantum systems, and specifically, the task of ground state energy estimation (GSEE). Ground state preparation (GSP) is a crucial component in GSEE algorithms, and classical methods like Hartree-Fock state preparation are commonly used. However, the efficiency of such classical methods diminishes exponentially with increasing system size in certain cases. In this study, we investigated whether in those cases quantum heuristic GSP methods could improve the overlap values compared to Hartree-Fock. Moreover, we carefully studied the performance gain for GSEE algorithms by exploring the trade-off between the overlap improvement and the associated resource cost in terms of T-gates of the GSP algorithm. Our findings indicate that quantum heuristic GSP can accelerate GSEE tasks, already for computationally affordable strongly-correlated systems of intermediate size. These results suggest that quantum heuristic GSP has the potential to significantly reduce the runtime requirements of GSEE algorithms, thereby enhancing their suitability for implementation on quantum hardware.
A major thrust in quantum algorithm development over the past decade has been the search for the quantum algorithms that will deliver practical quantum advantage first. Today's quantum computers---and even early fault-tolerant quantum computers---are limited in the number of operations they can implement per circuit. We introduce quantum algorithms for ground-state-energy estimation (GSEE) that accommodate this design constraint. The first algorithm estimates ground-state energies, offering a quadratic improvement on the ground-state overlap parameter compared to other methods in this regime. The second algorithm certifies that the estimated ground-state energy is within a specified error tolerance of the true ground-state energy, addressing the issue of gap estimation that beleaguers several ground-state preparation and energy estimation algorithms. We note, however, that the scaling of this certification technique is currently less favorable than that of the GSEE algorithm. To develop the certification algorithm, we propose an alternative use of quantum computers to facilitate rejection sampling. After a classical computer generates initial samples, the quantum computer is used to accept or reject these samples, resulting in a set of accepted samples that approximate draws from a target distribution. Although we apply this technique specifically for ground-state-energy certification, it may find broader applications. Our paper pushes the boundaries of what operation-limited quantum computers can achieve, bringing the prospect of quantum advantage closer to realization.
Recent progress in quantum computing is paving the way for the realization of early fault-tolerant quantum computers. To maximize the utility of these devices, it is important to develop quantum algorithms that match their capabilities and limitations. Motivated by this, recent work has developed low-depth quantum algorithms for ground state energy estimation (GSEE), an important subroutine in quantum chemistry and materials. We detail a new GSEE algorithm which, like recent work, uses a number of operations scaling as O(1/Δ) as opposed to the typical O(1/ε), at the cost of an increase in the number of circuit repetitions from O(1) to O(1/ε2). The relevant features of this algorithm come about from using a Gaussian window, which exponentially reduces contamination from excited states over the simplest GSEE algorithm based on the Quantum Fourier Transform (QFT). We adapt this algorithm to interpolate between the low-depth and full-depth regime by replacing Δ with anything between Δ and ε. At the cost of increasing the number of ancilla qubits from 1 to O(logΔ), our method reduces the upper bound on the number of circuit repetitions by a factor of four compared to previous methods.
Knowing the ground state energies of molecules and atoms gives scientists critical insight into these particles' behavior in reactions, thermodynamic and molecular properties, and excitation energies.However, due to the quantum mechanical nature of particles, finding the ground state of a system is intractable, both mathematically and experimentally.Computational methods are utilized to estimate the ground state energies.As we approach the limits of classical computers, quantum computers are viewed as promising alternatives that present a bright future for computational chemistry.In this paper, I review classical and quantum algorithms/methods for computational chemistry.Then, I discuss the current topics in using quantum computers for computational chemistry by analyzing the performance of the Variational Quantum Eigensolver (VQE) in different contexts on IBM's noisy quantum computer simulator, "QasmSimulator," and one of IBM's quantum computers, ibmq_belem.This review presents a theoretical and practical view of quantum computational chemistry.It allows the reader to learn the theory behind the algorithms and implement them with the guidance of the presented code and its detailed explanations.The purpose of this paper is to leave the reader with the necessary theory and adequate programming reference to implement the algorithms in various contexts.
Quantum algorithms for ground-state energy estimation of chemical systems require a high-quality initial state. However, initial state preparation is commonly either neglected entirely, or assumed to be solved by a simple product state like Hartree-Fock. Even if a nontrivial state is prepared, strong correlations render ground-state overlap inadequate for quality assessment. In this work, we address the initial state preparation problem with an end-to-end algorithm that and the quality of initial states, accomplishing the latter with a new metric—the energy distribution. To be able to prepare more complicated initial states, we introduce an implementation technique for states in the form of a sum of Slater determinants that exhibits significantly better scaling than all prior approaches. We also propose low-precision quantum phase estimation (QPE) for further state quality refinement. The complete algorithm is capable of generating high-quality states for energy estimation, and is shown in select cases to lower the overall estimation cost by several orders of magnitude when compared with the best single product state ansatz. More broadly, the energy distribution picture suggests that the goal of QPE should be reinterpreted as generating improvements compared to the energy of the initial state and other classical estimates: such an improvement can still be achieved even if QPE does not project directly onto the ground state. Finally, we show how the energy distribution can help in identifying potential quantum advantage. Published by the American Physical Society 2024