At a recent conference, it was suggested that Magnetars, a type of super-magnetic neutron star, could be a Quark star.  It is too soon to say whether this hypothesis will come to anything.  To the right is a diagram showing a comparison between a neutron star and the hypothetical composition of a quark star. 
Firstly, it must be said that the evidence for the existence of quark stars is controversial.  If they exist, they comprise free quark matter, either in whole or in part.  The most likely scenario is that there would be quark matter in the center of heavy neutron stars.  In terms of density, the star would be between a neutron star and a black hole. 

A neutron star already has a preponderance of free neutrons in its core.  Under sufficient pressure from gravity, the neutrons may break down into their constituent "up" and "down" quarks; this is called quark "deconfinement".  Some of these light quarks may then become strange quarks.  Thus, there would be a plasma of "up", "down" and "strange" quarks, gluons and some electrons.  The deconfinement process would release a stupendous amount of energy, particularly as gamma rays; far more than a supernova explosion. 

While quark stars are hypothetical, two candidates have been detected that were previously thought to be neutron stars. One seems to be rather smaller than expected, while the other, pulsar 3C58, is rather too cool, implying a higher density than expected from normal neutron star material.  However, in the second case a more feasible explanation is that there is a high neutrino flux in the star's core that is carrying away large amounts of energy, causing the cooling.   See picture (below left) taken by the Chandra X-Ray Observatory. 

A supernova that occurred in 1987 (SN1987A) has also been touted as a possible quark star.  This is because, to date, it has not been possible to find the remnant which was expected to be a neutron star.  It could be, however, that the neutron star is shrouded by especially dense dust clouds, or that there was matter sufficient to produce a black hole. 

Very recently, some researchers suggested another state; the Electroweak star.  If the temperature of the star exceeds that where the electromagnetic and weak forces combine into the electroweak force, it is possible that the quarks can change into leptons.  This releases vast amounts of energy as neutrinos drain away the energy from the core of the star.  This is likely to happen only when the quark star is becoming a black hole, having captured sufficient additional mass. 

Quark Stars

Pulsar 3C58, about 10,000 light-years away.  Initially thought to be the result of supernova SN 1181, some observers suggest that it may be much older. 

Astronomy & Cosmology -

Stars - Life & Death of Stars