Quantum Merging Algorithms

Hayata Yamasaki, Mio Murao

Recent advances in quantum technology facilitate the realization of information processing using quantum computers at least on the small and intermediate scales of up to several dozens of qubits. We investigate entanglement cost required for one-shot quantum state merging, aiming at quantum state transformation on these scales. In contrast to existing coding algorithms achieving nearly optimal approximate quantum state merging on a large scale, we construct algorithms for exact quantum state merging so that the algorithms are applicable to any given state of an arbitrarily small-dimensional system. In the algorithms, the entanglement cost can be reduced depending on a structure of the given state derived from the Koashi-Imoto decomposition. We also provide improved converse bounds for exact quantum state merging achievable for qubits but not necessarily achievable in general. As for approximate quantum state merging, we obtain algorithms and improved converse bounds by applying smoothing to those for exact state merging. Our results are applicable to distributed quantum information processing and multipartite entanglement transformation on small and intermediate scales.

Madhusudan Singh Irish Singh, Bharat S. Rawal

Debora Ramacciotti, Martin Steinbach, Bence Temesi +2 more

Sparse quantum state preparation is a common subroutine in quantum algorithms, where classical data with few nonzero entries must be loaded into a quantum state. In this work, we consider the Grover-Rudolph algorithm, which has recently been shown to efficiently prepare sparse states, and we propose two improvements. First, we extend an existing gate-merging procedure by allowing rotations to merge with virtual zero-angle gates on unreachable branches of the preparation tree, reducing the number of CNOTs and control qubits. Second, we introduce an approximate variant in which rotations with similar but not identical angles are merged at the cost of a small, controllable error in the prepared state. We derive a classically computable estimate of the resulting overlap with the target state, which is used to guide the merging decisions.

Daowen Qiu

Tatsuhiko Shirai, Nozomu Togawa

A merge process is proposed to engineer a multi-spin flip in an Ising machine. The merge process deforms the Hamiltonian (energy function) of the Ising model. We prove a theorem for the merge process and show that a single-spin flip in the deformed Hamiltonian is equivalent to a multi-spin flip in the original Hamiltonian. A merge process induces a transition within the subspace of feasible solutions. We propose a hybrid simulated annealing (SA) algorithm with the merge process. The hybrid algorithm outperforms the conventional SA algorithm, genetic algorithm, and tabu search in the binary quadratic knapsack problems (QKP) and the quadratic assignment problems (QAP). Finally, the hybrid merge process is used in a real Ising machine. The performance is improved in QKP and QAP instances. The merge process is generally applicable to existing Ising machine hardware because the deformed Hamiltonian keeps the format of the Ising model.