Techniques for converting an optimization functional for a binary optimization problem into a cost function for a quantum computation

Abstract

Abstract The disclosure relates to method of converting an optimization functional for a binary optimization problem into a cost function for a quantum computation. The method 5 comprises representing a first optimization variable among a plurality of binary optimization variables of the optimization functional as a first product of binary transformed variables, wherein the first product comprises a first plurality of factors, wherein each factor among the first plurality of factors corresponds to a subset of the plurality of optimization variables that includes the first optimization variable. The method further comprises converting each of the 10 binary optimization variables or the binary transformed variables into a continuous variable; converting the optimization functional into the cost function, wherein the cost function comprises the transformed and continuous variables; and selecting a plurality of the subsets for the quantum computation. 15 (Fig. 5) Abstract 10 20 26 20 02 06 14 J an 2 02 6 1 4 J a n 2 0 2 6 2 0 2 6 2 0 0 2 0 6 1 0 5 / 7 Variational Quantum Circuit: Ising ground state: min E(Z) QC() Z E {-1,1} [0,2]²NL Nq = [log 11 - number of qubits n- - number of bits L- number of layers Local minima of the relaxed E are local minima of the initial E Quantum state: wrt 1-neighborhood search () E L C H²N H²N, , is Hilbert space Continuous relaxation: Local minima of the auxiliary E min E(t) are local minima of E [-1,1] Probability distribution: the initial E P() E P C [0, 1]²^ wrt local search over l groups Auxiliary function: : min E(q) N - number of shots Measurement statistic p (hyperparameter) 1- number of groups differentiable transformation with hyperparameters Fig. 5 R and M R 20 26 20 02 06 14 J an 2 02 6 2 0 2 6 2 0 0 2 0 6 1 4 J a n 2 0 2 6 Ising ground state: n- - number of bits L o c a l m i n i m a of the relaxed E are local minima of t h e i n i t i a l E wrt 1-neighborhood search Continuous relaxation: L o c a l m i n i m a o f t h e a u x i l i a r y E are local minima of t h e i n i t i a l E wrt local search o v e r l g r o u p s Auxiliary function: : 1 - number of groups

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