Embedding quantum and random optics in a larger field theory

Improving solutions by embedding larger subproblems in a D-Wave quantum annealer

Quantum annealing is a heuristic algorithm that solves combinatorial optimization problems, and D-Wave Systems Inc. has developed hardware implementation of this algorithm. However, in general, we cannot embed all the logical variables of a large-scale problem, since the number of available qubits is limited. In order to handle a large problem, qbsolv has been proposed as a method for partitioning the original large problem into subproblems that are embeddable in the D-Wave quantum annealer, and it then iteratively optimizes the subproblems using the quantum annealer. Multiple logical variable…

Perils of Embedding for Quantum Sampling

Given quantum hardware that enables sampling from a family of natively implemented Hamiltonians, how well can one use that hardware to sample from a Hamiltonian outside that family? A common approach is to minor embed the desired Hamiltonian in a native Hamiltonian. In Phys. Rev. Research 2, 023020 (2020) it was shown that minor embedding can be detrimental for classical thermal sampling. Here, we generalize these results by considering quantum thermal sampling in the transverse-field Ising model, i.e. sampling a Hamiltonian with non-zero off diagonal terms. To study these systems numerically …

量子退火硬件中奇偶约束的可扩展嵌入

Scalable embedding of parity constraints in quantum annealing hardware

本文提出固定、模块化且可扩展的奇偶映射嵌入方法，用于将任意伊辛哈密顿量表示的组合优化问题嵌入量子退火硬件，并验证嵌入后哈密顿量的物理性质与原问题一致。

On definition of quantum tomography via the Sobolev embedding theorem

We obtain sufficient conditions on kernels of quantum states under which Wigner functions, optical quantum tomograms and linking their formulas are correctly defined. Our approach is based upon the Sobolev embedding theorem. The transition probability formula and the fractional Fourier transform are discussed in this framework.

使用并行量子退火求解更大的最大团问题

Solving Larger Maximum Clique Problems Using Parallel Quantum Annealing

针对D-Wave量子退火器规模有限且需次要嵌入、难以求解大型优化问题的限制，提出并行量子退火结合图分解的混合方法，并在多达120个节点、6395条边的图上准确求解最大团问题。

Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model

It is possible to simulate the dynamics of a single spin-$1/2$ ($\mathsf{PT~}$ symmetric) system by conveniently embedding it into a subspace of a larger Hilbert space with unitary dynamics. Our goal is to formulate a many body generalization of this idea i.e., embedding many body non-Hermitian dynamics. As a first step in this direction, we investigate embedding of "$N$" non-interacting spin-$1/2$ ($\mathsf{PT~}$ symmetric) degrees of freedom, thereby unfolding the complex nature of such an embedding procedure. It turns out that the resulting Hermitian Hamiltonian represents a cluster of $N+1…