On the power quantum computation over real Hilbert spaces

Abstract

We consider the power of various quantum complexity classes with the restriction that states and operators are defined over a real, rather than complex, Hilbert space. It is well know that a quantum circuit over the complex numbers can be transformed into a quantum circuit over the real numbers with the addition of a single qubit. This implies that BQP retains its power when restricted to using states and operations over the reals. We show that the same is true for QMA(k), QIP(k), QMIP, and QSZK.

Significant improvements from previous version, in particular showing both containments (eg. QMA_R is in QMA and vice versa)

References in corpus (4)

• Simulating quantum systems using real Hilbert spaces
• Testing product states, quantum Merlin-Arthur games and tensor optimisation
• Generalized self-testing and the security of the 6-state protocol
• Quantum Information Processing with Adversarial Devices

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• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks