Improved Iterative Quantum Algorithm for Ground‐State Preparation

Abstract

Finding the ground state of a Hamiltonian system is of great significance in many‐body quantum physics and quantum chemistry. An improved iterative quantum algorithm to prepare the ground state of a Hamiltonian is proposed. The crucial point is to optimize a cost function on the state space via the quantum gradient descent (QGD) implemented on quantum devices. Practical guideline on the selection of the learning rate in QGD are provided by finding a fundamental upper bound and establishing a relationship between the algorithm and the first‐order approximation of the imaginary time evolution. Furthermore, a variational quantum state preparation method is adapted as a subroutine to generate an ancillary state by utilizing only polylogarithmic quantum resources. The performance of the algorithm is demonstrated by numerical calculations of the deuteron molecule and Heisenberg model without and with noises. Compared with the existing algorithms, the approach has advantages including the higher success probability at each iteration, the measurement precision‐independent sampling complexity, the lower gate complexity, and only quantum resources are required when the ancillary state is well prepared.

Assisted quantum simulation of open quantum systems

“…Case 2 and 3 generalize the result of 39 to an arbitrary vector. The construction of Equations 10 and 17 is motivated by the work 48 in which only real-value vector is considered.…”

“…All negative vector is covered by adding a global phase . Algorithm 1 , first presented in, 39 shows the detailed process of a hybrid quantum-classical algorithm to prepare state .

Variational quantum state preparation (VQSP) Input: an initial state and a PQC .

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“…Furthermore, we have developed a VQSP to prepare an amplitude encoding state of arbitrary classical data. The preparation algorithm generalized the result of the recent work 39 in which only positive classical data is considered. We have shown that any classical vector with size can be loaded into a d -qubit quantum state with a shallow depth circuit using only single- and two-qubit gates.…”

“…For exponential dimension vector, our method would require exponential measurement cost like other works. 39 , 46 …”

Unified multivariate trace estimation and quantum error mitigation

“…Therefore, a variety of quantum error mitigation (QEM) approaches [10][11][12][13][14][15][16][17] for NISQ algorithms have been presented instead for QEC. Different from QEC, QEM focuses on recovering the ideal measurement statistics (usually the expectation values) [18] and can be directly employed in the ground state preparation [19,20]. For instance, the error extrapolation technique utilizes different error rates to the zero noise limit [21][22][23].…”