Adaptive variational quantum simulation algorithms use information from a quantum computer to dynamically create optimal trial wave functions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wave functions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an Adaptive Derivative-Assembled Problem-Tailored Ansatz Variational Quantum Eigensolver (ADAPT-VQE) calculation on a smaller instance of the problem using a large, but computationally inefficient, operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems. Published by the American Physical Society 2024
Adaptive variational quantum simulation algorithms use information from a quantum computer to dynamically create optimal trial wave functions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wave functions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an Adaptive Derivative-Assembled Problem-Tailored Ansatz Variational Quantum Eigensolver (ADAPT-VQE) calculation on a smaller instance of the problem using a large, but computationally inefficient, operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems. Published by the American Physical Society 2024
Adaptive quantum variational algorithms are particularly promising for simulating strongly correlated systems on near-term quantum hardware, but they are not yet viable due, in large part, to the severe coherence time limitations on current devices. In this paper, we introduce an algorithm called TETRIS-ADAPT-VQE (tiling efficient trial circuits with rotations implemented simultaneously adaptive derivative-assembled problem-tailored variational quantum eigensolver), which iteratively builds up variational a few operators at a time in a way dictated by the problem being simulated. This algorithm is a modified version of the ADAPT-VQE algorithm, in which the one-operator-at-a-time rule is lifted to allow for the addition of multiple operators with disjoint supports in each iteration. TETRIS-ADAPT-VQE results in denser but significantly shallower circuits, without increasing the number of controlled- gates or variational parameters. Its advantage over the original algorithm in terms of circuit depths increases with the system size. Moreover, the expensive step of measuring the energy gradient with respect to each candidate unitary at each iteration is performed only a fraction of the time compared with ADAPT-VQE. These improvements bring us closer to the goal of demonstrating a practical quantum advantage on quantum hardware. Published by the American Physical Society 2024
Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ansätze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number n of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size 2n−2 can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such "complete" pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings.
The adaptive derivative-assembled problem-tailored variational quantum eigensolver (ADAPT-VQE) is one of the most widely used algorithms for electronic structure calculations in quantum computers. It adaptively selects operators based on their gradient, constructing ansätze that continuously evolve to match the energy landscape, helping avoid local traps and barren plateaus. However, this flexibility in reoptimization can lead to the inclusion of redundant or inefficient operators that have almost zero parameter value, barely contributing to the ansatz. We identify three phenomena responsible for the appearance of these operators: poor operator selection, operator reordering, and fading operators. In this work, we propose an automated, cost-free refinement method that removes unnecessary operators from the ansatz without disrupting convergence. Our approach evaluates each operator after ADAPT-VQE optimization by using a function that considers both its parameter value and position in the ansatz, striking a balance between eliminating low-coefficient operators while preserving the natural reduction of coefficients as the ansatz grows. Additionally, a dynamic threshold based on the parameters of recent operators enables efficient convergence. We apply this method to several molecular systems and find that it reduces ansatz size and accelerates convergence, particularly in cases with flat energy landscapes. The refinement process incurs, at most, a small additional computational cost and consistently improves or maintains ADAPT-VQE performance.
The adaptive derivative-assembled problem-tailored variational quantum eigensolver (ADAPT-VQE) is one of the most widely used algorithms for electronic structure calculations in quantum computers. It adaptively selects operators based on their gradient, constructing ansätze that continuously evolve to match the energy landscape, helping avoid local traps and barren plateaus. However, this flexibility in reoptimization can lead to the inclusion of redundant or inefficient operators that have almost zero parameter value, barely contributing to the ansatz. We identify three phenomena responsible for the appearance of these operators: poor operator selection, operator reordering, and fading operators. In this work, we propose an automated, cost-free refinement method that removes unnecessary operators from the ansatz without disrupting convergence. Our approach evaluates each operator after ADAPT-VQE optimization by using a function that considers both its parameter value and position in the ansatz, striking a balance between eliminating low-coefficient operators while preserving the natural reduction of coefficients as the ansatz grows. Additionally, a dynamic threshold based on the parameters of recent operators enables efficient convergence. We apply this method to several molecular systems and find that it reduces ansatz size and accelerates convergence, particularly in cases with flat energy landscapes. The refinement process incurs, at most, a small additional computational cost and consistently improves or maintains ADAPT-VQE performance.
Abstract Variational Quantum Eigensolver (VQE) methods aim to maximize the resources of existing noisy devices. However, they encounter difficulties in simulating molecules of industrially-relevant sizes, such as constructing the efficient ansatz. Adaptive variational algorithms (ADAPT-VQE) can solve this problem but with a significant increase in the number of measurements. Here, we reduce the measurement overhead of ADAPT-VQE via adding operator batches to the ansatz while keeping it compact. We reformulate the previously proposed qubit pool completeness criteria for the tapered qubit space and propose an automated pool construction procedure. Our numerical results indicate that reducing the qubit pool size from polynomial to linear conversely increases the number of measurements. We simulate a set of molecules, participating in the carbon monoxide oxidation processes using the statevector simulator and compare the results with VQE-UCCSD and classical methods. Our results pave the way towards usage of variational approaches for solving practically relevant chemical problems.
The ADAPT-VQE (adaptive derivative-assembled pseudo-Trotter Ansatz variational quantum eigensolver) approach is used to solve the neutron-proton pairing problem in atomic nuclei. This variational approach is considered today to be one of the most powerful methods to iteratively find the ground state of a many-body problem, provided a performing set of operators, called the pool of operators, is used to explore the Hilbert space of many-body wave-functions. Three different pools of operators, which might eventually break one or several symmetries of the Hamiltonian during the descent to the ground state, are tested for the neutron-proton pairing problem. We observe that the breaking of some symmetries during the optimization of the trial wave function might, in general, help to speed up the convergence towards the ground state. Still, we rejected the pool of operators that might explicitly break the total particle number because they become uncontrollable during the optimization process. Overall, we observed that the iterative optimization process rapidly becomes a delicate problem when the number of parameters to build the Ansatz increases, and the energy might get stuck at energies higher than the ground state energy. To improve the convergence in this case, several techniques have been proposed, with some better controlling the symmetries during the energy minimization. Among the proposed methods, two have proved effective: one based on an embedding technique and the other on a randomized preparation of the initial state. We conclude that the ADAPT-VQE, complemented by these techniques, can provide a very accurate description of the neutron-proton pairing problem, and can outperform other standardly used techniques that break the particle number symmetry and restore afterwards.