Quantum-gate characterization in an extended Hilbert space (5 pages)

Dmitry Solenov

Peter P. Rohde, Geoff J. Pryde, Jeremy L. O’Brien +1 more

We describe an approach for characterizing optical quantum gates, by constructing models which incorporate mode-matching effects. Quantum process tomography is then performed on the model. The techniques can be generalized to other quantum computing architectures.

Peter P. Rohde, Geoff J. Pryde, Jeremy L. O’Brien +1 more

We describe an approach for characterizing the process performed by a quantum gate using quantum process tomography, by first modeling the gate in an extended Hilbert space, which includes nonqubit degrees of freedom. To prevent unphysical processes from being predicted, present quantum process tomography procedures incorporate mathematical constraints, which make no assumptions as to the actual physical nature of the system being described. By contrast, the procedure presented here assumes a particular class of physical processes, and enforces physicality by fitting the data to this model. This allows quantum process tomography to be performed using a smaller experimental data set, and produces parameters with a direct physical interpretation. The approach is demonstrated by example of mode matching in an all-optical controlled-NOT gate. The techniques described are general and could be applied to other optical circuits or quantum computing architectures.

Yibin He, Li Wang

Sergey A. Podoshvedov

Philipp A. Höhn, Andrea Russo, Alexander R. H. Smith

We explore the canonical description of a scalar field as a parameterized field theory on an extended phase space that includes additional embedding fields that characterize spacetime hypersurfaces $\mathsf{X}$ relative to which the scalar field is described. This theory is quantized via the Dirac prescription and physical states of the theory are used to define conditional wave functionals $|ψ_ϕ[\mathsf{X}]\rangle$ interpreted as the state of the field relative to the hypersurface $\mathsf{X}$, thereby extending the Page-Wootters formalism to quantum field theory. It is shown that this conditional wave functional satisfies the Tomonaga-Schwinger equation, thus demonstrating the formal equivalence between this extended Page-Wootters formalism and standard quantum field theory. We also construct relational Dirac observables and define a quantum deparameterization of the physical Hilbert space leading to a relational Heisenberg picture, which are both shown to be unitarily equivalent to the Page-Wootters formalism. Moreover, by treating hypersurfaces as quantum reference frames, we extend recently developed quantum frame transformations to changes between classical and nonclassical hypersurfaces. This allows us to exhibit the transformation properties of a quantum field under a larger class of transformations, which leads to a frame-dependent particle creation effect.