Born in Perm in 1984. Studied at the College of Music of the Moscow State Tchaikovsky Conservatoire and at the Moscow Conservatoire itself. In 2012 he completed a postgraduate study with distinction at the Moscow Conservatoire and in 2013 he completed a second postgraduate study at the UniversitätfürMusik und DarstellendeKunst in Graz (class of Boris Kuschnir). He is currently a student at the Vienna Konservatorium(class of Lidia Baich). He has twice been a grant-recipient of the St Petersburg House of Music and Bank Rossiya.
In 2008 he took part in a meeting of young musicians with President Vladimir Putin of the Russian Federation.
Prize-winner at international competitions in Tolyatti (1st prize, 2002), KlosterSchöntal (2nd prize, 2003), Astana (Grand Prix, 2008), Seoul (2nd prize, 2012), the International Robert Canetti Competition (1st prize, 2005), the Vibrarte international competition in Paris (1st prize, 2008), the David Oistrakh Competition in Moscow (2nd prize, 2008) and the Aram Khachaturian Competition in Yerevan (1st prize, 2012).
In June 2015 Milyukov won the 3rd prize at the XV International Tchaikovsky Competition.
Gives master-classes throughout Russia. Tours to Austria, Belgium, Germany, Hungary, Greece, Italy, Spain, South and North Korea, China, Finland, Sweden and Switzerland. Has worked with such conductors as Valery Gergiev, Vladimir Spivakov, Vladimir Fedoseyev, Mikhail Pletnev, Maxim Fedotov, Yuri Simonov, Pavel Kogan, Alexander Sladkovsky, EvgenyBushkov, Robert Canetti, Maria Eklund, Kristjan Järvi and Oswald Sallaberger. Performs the Ex-Szigeti violin crafted by Pietro Guarneri, on generous loan from the Swiss foundation. Since 2008 he has been a permanent soloist of the St Petersburg House of Music. Since 2012 he has been a soloist with the Moscow Philharmonic.
In 2016 he was awarded the Order of Friendship.