Quantum Computing with Hermitian Gates
- URL: http://arxiv.org/abs/2402.12356v1
- Date: Mon, 19 Feb 2024 18:36:09 GMT
- Title: Quantum Computing with Hermitian Gates
- Authors: Ben Zindorf and Sougato Bose
- Abstract summary: We show that any single-qubit operator may be implemented as two Hermitian gates.
We show that a gate set comprised of pi rotations about two fixed axes, along with the CNOT gate, is universal for quantum computation.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Universal gate sets for quantum computation, when single and two qubit
operations are accessible, include both Hermitian and non-Hermitian gates. Here
we show that any single-qubit operator may be implemented as two Hermitian
gates, and thus a purely Hermitian universal set is possible. An
implementational convenience can be that non-identity single-qubit Hermitian
gates are equivalent to pi rotations up to a global phase. We show that a gate
set comprised of pi rotations about two fixed axes, along with the CNOT gate,
is universal for quantum computation. Moreover, we show that two pi rotations
can transform the axis of any multi-controlled unitary, a special case being a
single CNOT sufficing for any controlled pi rotation. These gates simplify the
process of circuit compilation in view of their Hermitian nature. Further, the
insights are used to design an efficient circuit for a controlled-U(4) gate
with any arbitrary operator on two target qubits.
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