1/10/2024 0 Comments Sto potential energy entanglerTo minimize the circuit complexity of this approach, we propose a strategy for efficiently measuring the Hamiltonian and overlap matrix elements between states parametrized by circuits that commute more » with the total particle number operator. This allows for the systematic improvement of a logical wavefunction ansatz without a significant increase in circuit complexity. We present an extension to the variational quantum eigensolver that approximates the ground state of a system by solving a generalized eigenvalue problem in a subspace spanned by a collection of parametrized quantum states. Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. Nevertheless, we argue that these methods lay a foundation for the use of quantum algorithms to study finite-energy-density properties of many-body systems. Here, we also study the scaling of the number of variational parameters with system size, finding that an exponentially large number of parameters may be necessary to approximate individual highly excited states. In particular, an operator pool including long-range two-body gates accelerates the convergence of both algorithms in the nonintegrable regime. For both methods, we find a strong dependence of the algorithm's performance on the choice of operator pool used for the adaptive construction of the ansatz. We also compare the performance of adaptive VQE-X to an adaptive variant of the folded-spectrum method. We benchmark the method by applying it to an Ising spin chain with integrable and nonintegrable regimes, where we calculate more » various quantities of interest, including the total energy, magnetization density, and entanglement entropy. We propose an adaptive variational quantum eigensolver (VQE) for excited states (X) that self-generates a variational ansatz for arbitrary eigenstates of a many-body Hamiltonian H by attempting to minimize the energy variance with respect to H. In this work, we explore the potential of variational quantum algorithms to approximate such states. Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization that challenge classical computational methods due to their volume-law entanglement content. In particular, we demonstrate the beneficial effect of qubit permutations to build fermionic–adaptive derivative assembled pseudo-Trotter ansatz on a linear qubit connectivity architecture with nearly a twofold reduction of the number of controlled not gates. The main ideas can also be applied to simulate molecules with other ansatz as well as variational quantum algorithms beyond the VQE. ![]() The approach is designed for hardware-efficient ansatz of any qubit connectivity, and examples are demonstrated for linear and two-dimensional grid architectures. Here, we believe that our method paves a new way for adaptive construction of ansatz circuits for variational quantum = $$, and N 2, we demonstrate that placing entangled qubits in close proximity leads to shallower depth circuits required to reach a given eigenvalue-eigenvector accuracy. Our numerical experiments show that a reduced entangler pool with a small portion of the original entangler pool can achieve same numerical accuracy. We corroborate our method numerically on small molecules. The density matrix renormalization group method is employed for classical precomputation in this work. ![]() Our method uses mutual information between the qubits in classically approximated ground state to rank and screen the entanglers. In this work, we propose a way to construct entangler pools with reduced size by leveraging classical algorithms. ![]() Those algorithms aim to build up optimal circuits for a certain problem and ansatz circuits are adaptively constructed by selecting and adding entanglers from a predefined pool. Adaptive construction of ansatz circuits offers a promising route towards applicable variational quantum eigensolvers on near-term quantum hardware.
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