Symmetry Protected Quantum Computation

TL;DR

This paper introduces a quantum computation model based on symmetry-protected measurements of singlet and triplet states, demonstrating its potential universality and equivalence to known complexity classes under certain conditions.

Contribution

It proposes a symmetry-protected measurement model for quantum computation, showing its universality with minimal overhead and its equivalence to PostBQP with postselection.

Findings

Capable of universal quantum computation with polylogarithmic overhead using additional single-qubit gates.

At least as powerful as permutational quantum computation without extra gates.

Equivalent to PostBQP when combined with postselection.

Abstract

We consider a model of quantum computation using qubits where it is possible to measure whether a given pair are in a singlet (total spin $0$) or triplet (total spin $1$) state. The physical motivation is that we can do these measurements in a way that is protected against revealing other information so long as all terms in the Hamiltonian are $SU(2)$-invariant. We conjecture that this model is equivalent to BQP. Towards this goal, we show: (1) this model is capable of universal quantum computation with polylogarithmic overhead if it is supplemented by single qubit $X$ and $Z$ gates. (2) Without any additional gates, it is at least as powerful as the weak model of "permutational quantum computation" of Jordan [14, 18]. (3) With postselection, the model is equivalent to PostBQP.