Fermion lattices can be simulated on same-size qubit lattices with O(1) interaction overhead by dynamically reorienting the Jordan-Wigner transformation.
Roads towards fault-tolerant universal quantum computation
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abstract
Current experiments are taking the first steps toward noise-resilient logical qubits. Crucially, a quantum computer must not merely store information, but also process it. A fault-tolerant computational procedure ensures that errors do not multiply and spread. This review compares the leading proposals for promoting a quantum memory to a quantum processor. We compare magic state distillation, color code techniques and other alternative ideas, paying attention to relative resource demands. We discuss the several no-go results which hold for low-dimensional topological codes and outline the potential rewards of using high-dimensional quantum (LDPC) codes in modular architectures.
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Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.
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Fermion lattices can be simulated by same-size qubit lattices with $\mathcal{O}(1)$ interaction overhead
Fermion lattices can be simulated on same-size qubit lattices with O(1) interaction overhead by dynamically reorienting the Jordan-Wigner transformation.
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Magic and Non-Clifford Gates in Topological Quantum Field Theory
Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.