Can bipolar disorder be considered a malfunction of the "love circuit" in the human brain?
A Love Circuit?

The idea that there is a "love circuit" has little evidence (for or against it). But in general studies that look at "love" (however defined) reveal broad activation across multiple intrinsic neural networks that are involved in many different cognitive processes (in favor of a constructivist view of emotions). 

Consider the image from a meta-analysis (Cacioppo et al., 2012) of functional imaging studies on sexual desire and love:



Both sexual desire and love are associated with greater activation of the insula, hypothalamus, ventral striatum, VTA, amygdala, thalamus, hippocampus, anterior cingulate, and other limbic/cortical areas.  These regions are involved in interoception, memory, conceptualization, core affect, somatosensory integration, motivation, salience detection, and more.  

Note, however, that these areas are not specific to love; instead, they are involved in emotional experience more broadly (fear, disgust, anger, happiness, etc.; Touroutoglou, Lindquist, Dickerson, &amp; Barrett, 2015). It's still possible that the above pattern of activation is unique to love; however, this has not been tested (to my knowledge)--nor does it seem plausible in light of other evidence (i.e., Touroutoglou et al., 2015).

Because these brain areas are involved in many cognitive processes, we might imagine that dysfunction in at least some of them is associated with bipolar disorder. 

Bipolar Disorder

Consider the image below from a meta-analysis (Chen, Suckling, Lennox, Ooi, &amp; Bullmore, 2011) of functional imaging in bipolar patients:



Compared to healthy controls, bipolar disorder seems to be associated with decreased inferior frontal gyrus activation in response to cognitive or emotional tasks and increased limbic activity (amygdala, hippocampus, parahippocampal gyrus, basal ganglia) in response to emotional tasks.

Conclusion

As you can see, there is some overlap with the areas activated for love/sexual desire and bipolar disorder (e.g., limbic structures).  

However, this is not compelling evidence that BD somehow involves dysfunction in a "love circuit," as the limbic system is involved in all emotions, not just love. If anything, this suggests that BD is associated with dysfunction in emotion regulation/processing/reactivity (and executive function more broadly; Robinson et al., 2006).