Inclusion Criteria:

• have an authorized parent/legal guardian who understands the nature of the study and who provides written informed consent. Additionally, each subject must provide assent to the study;
• be fluent in English;
• be 12 to 20 years of age, inclusive;
• be using a medically accepted means of contraception (i.e., oral contraceptives, medroxyprogesterone acetate injectable suspension, abstinence) if female and of menarche;
• have a diagnosis of bipolar I disorder in a current manic or mixed episode, in addition to a cannabis use disorder (which includes abuse or dependence) within 28 days prior to screening, as determined by the WASH-U-KSADS;
• have an initial YMRS total score of >16 at screening and baselines.

Exclusion Criteria:

• have a diagnosis of mental retardation, as defined by the Weschler Abbreviated Scale of Intelligence (WASI)38 score of <70;
• are acutely intoxicated, and thus impaired;
• have manic or depressive symptoms resulting entirely from acute medical illness or acute intoxication or withdrawal from drugs or alcohol, as determined by medical evaluation and rapid symptom resolution;
• have clinically significant alcohol or other drug withdrawal symptoms, as determined by vital signs, The Clinical Institute Withdrawal Assessment for Alcohol Scale - Revised (CIWA-Ar)24, and physician interview;
• have any unstable medical or neurological illness;
• have laboratory abnormalities >3 times upper limits of established normal values;
• as females, have a positive urine pregnancy test, are lactating, or are not practicing a reliable form of birth control;
• have a history of nephrolithiasis, since topiramate has been associated with an elevated risk of kidney stones;
• have concurrent treatment with mood stabilizers, anticonvulsants, psychostimulants, or antidepressants, so that we can examine the effects of topiramate vs. placebo in combination with QT in a controlled study
• have significant suicidal ideation, as defined by a score of > 3 on the Children's Depression Rating Scale-Revised CDRS34 suicide item, or any serious suicide attempt within the prior 60 days as judged by the investigator so that we do not include patients with a high risk for suicide attempts during study participation
• have been treated for a substance use disorder during 28 days prior to screening or are court-ordered to treatment for substance use to ensure that, if we detect a change in use with topiramate treatment, it is likely not due to these other confounding factors that might influence substance use.
• have been diagnosed or treated for an eating disorder, to make sure any weight loss does not contribute to an already underlying condition