Symmetry Protected Quantum Computation

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.

arXiv commentTo be published in Quantum Journal

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Cited by in corpus (7)

• Circuit Complexity in Topological Quantum Field Theory
• Splitting and connecting singlets in atomic quantum circuits
• Noncommuting charges can remove non-stationary quantum many-body dynamics
• Hybrid Exchange Measurement-Based Qubit Operations in Semiconductor Double Quantum Dot Qubits
• Quantum Computation by Spin Parity Measurements with Encoded Spin Qubits
• Exchange-Symmetrized Qudit Bell Bases and Bell-State Distinguishability
• Protected hybrid superconducting qubit in an array of gate-tunable Josephson interferometers