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Usually, the hyperparallel quantum computation can speed up quantum computing, reduce the quantum resource consumed largely, resist to noise, and simplify the storage of quantum information. Here, we present the first scheme for the self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom of photon systems simultaneously. It can prevent bit-flip errors from happening with an imperfect nonlinear interaction in the nearly realistic condition. We give the way to design the universal hyperparallel photonic quantum controlled-NOT (CNOT) gate on a two-photon system, resorting to the nonlinear interaction between the circularly polarized photon and the electron spin in the quantum dot in a double-sided microcavity system, by taking the imperfect interaction in the nearly realistic condition into account. Its self-error-corrected pattern prevents the bit-flip errors from happening in the hyperparallel quantum CNOT gate, guarantees the robust fidelity, and relaxes the requirement for its experiment. Meanwhile, this scheme works in a failure-heralded way. Also, we generalize this approach to achieve the self-error-corrected hyperparallel quantum CNOT$^N$ gate working on a multiple-photon system. These good features make this scheme more useful in the photonic quantum computation and quantum communication in the future.
We present an original self-error-rejecting photonic qubit transmission scheme for both the polarization and spatial states of photon systems transmitted over collective noise channels. In our scheme, we use simple linear-optical elements, including
We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results. Still, we argu
I obtain the quantum correction $Delta V_mathrm{eff}= (hbar^2/8m) [(1- 4xi frac{d+1}{d})(mathcal{S})^2 + 2(1-4xi)mathcal{S}]$ that appears in the effective potential whenever a compact $d$-dimensional subspace (of volume $propto exp[mathcal{S}(x)]$)
Whenever variables $phi=(phi^1,phi^2,ldots)$ are discarded from a system, and the discarded information capacity $mathcal{S}(x)$ depends on the value of an observable $x$, a quantum correction $Delta V_mathrm{eff}(x)$ appears in the effective potenti
We employ spherical $t$-designs for the systematic construction of solids whose rotational degrees of freedom can be made robust to decoherence due to external fluctuating fields while simultaneously retaining their sensitivity to signals of interest