Abstract
Magic states are eigenstates of non-Pauli operators. One way of suppressing errors present in magic states is to perform parity measurements in their non-Pauli eigenbasis and postselect on even parity. Here we develop new protocols based on non-Pauli parity checking, where the measurements are implemented with the aid of pre-distilled multiqubit resource states. This leads to a two step process: pre-distillation of multiqubit resource states, followed by implementation of the parity check. These protocols can prepare single-qubit magic states that enable direct injection of single-qubit axial rotations without subsequent gate-synthesis and its associated overhead. We show our protocols are more efficient than all previous comparable protocols with quadratic error reduction, including the protocols of Bravyi and Haah.
Highlights
Magic states are eigenstates of non-Pauli operators
We can circumvent the need for synthesis if we instead prepare magic states tailored for injecting specific gates
Here we focus on the second step — the main technical contribution of this work — by showing that a pre-distilled |CCZ#N can be used to parity check on 2N magic states
Summary
If the angle is θ = π/2 for integer R(θ) belongs in the th level of the Clifford hierarchy [23]. Unitaries inside the Clifford hierarchy are special because they can be realised using state-injection and a bounded number of appropriate magic states. All the analysis in this paper holds for any θ, even values corresponding to unitaries and magic states not connected to the Clifford hierarchy. The relevant magic states are eigenstates of W (θ) and sit on the equator of the Bloch sphere. When U is a diagonal gate (acting on n qubits) we use |U := U (|+ ⊗n). In this notation, the familiar T state is |R(π/8).
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