How do we obtain the expectation value between 2 qubits?
In the Science paper, Phase transitions in a programmable quantum spin glass simulator, they mention that the D-wave processor can easily determine the correlation function between two spins (see eqn. 4, and figure S11).
What are the commands to specify this output?
Comments
In Fig. S11 we discuss the spin spin correlations found from classical samples taken at the end of a quenched anneal. To calculate this let us start with some notation. Take a set of C classical samples, call them S^i for i in 1..C (^ meaning superscript). The value of a spin j in sample S^i is referred to as S^i_j (_j being subscript) and can be +1 or -1. Then, to calculate the spin spin correlation of spin m with spin n calculate sum_{i = 1..C} (S^i_m * S^j_n) / C. For a perfect anti-ferromagnetic and averaged across all nearest neighbor pairs you should get -1. For a perfect ferromagnetic, you should get 1. Eqn. 4, on the other hand, describes how to calculate a more interesting parameter, the spin spin overlap where one calculates intersample correlations for each spin instead of intrasample correlations between spins.
The high level work flow is setup a set of couplings to describe the spin system you want, then take a set of samples using either a simple forward anneal over some time, or a more complicated pause / quench. Then calculate the above on the results.
Thank you for the response, Andrew. It definitely clears everything up.
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