In order to delineate which minimalistic physical primitives can enable the full power of universal quantum computing, it has been fruitful to consider various measurement based architectures which reduce or eliminate the use of coherent unitary evolution, and also involve operations that are physically natural. In this context previous works had shown that the triplet-singlet measurement of two qubit angular momentum (or equivalently two qubit exchange symmetry) yields the power of quantum computation given access to a few additional different single qubit states or gates. However, Freedman, Hastings and Shokrian-Zini1 recently proposed a remarkable conjecture, called the ‘STP=BQP’ conjecture, which states that the two-qubit singlet/triplet measurement is quantum computationally universal given only an initial ensemble of maximally mixed single qubits. In this work we prove this conjecture. This provides a method for quantum computing that is fully rotationally symmetric (i.e. reference frame independent), using primitives that are physically very-accessible, naturally resilient to certain forms of error, and provably the simplest possible. It has been conjectured that an alternative model of quantum computation—in which one only applies two-qubit singlet-vs-triplet measurements to almost any source of input qubits—is as powerful as the usual gate-based model. Here, the authors prove this conjecture, ending up with a model where computations are independent from the way in which one picks the axes of the Bloch sphere.

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The article proves the STP=BQP conjecture, which states that the two-qubit singlet/triplet measurement is quantum computationally universal given only an initial ensemble of maximally mixed single qubits. The approach involves two steps: the preparation of maximally-mixed symmetric states and the relative localization of multiple sources.

The two-qubit singlet/triplet measurement is universal for quantum computing given only maximally-mixed initial states