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Abstract
Quantum systems are important resources for quantum computer. Different from previous encoding forms using quantum systems with one degree of freedom (DoF) or two DoFs, we investigate the possibility of photon systems encoding with three DoFs consisting of the polarization DoF and two spatial DoFs. By exploring the optical circular birefringence induced by an NV center in a diamond embedded in the photonic crystal cavity, we propose several hybrid controlled-NOT (hybrid CNOT) gates operating on the two-photon or one-photon system. These hybrid CNOT gates show that three DoFs may be encoded as independent qubits without auxiliary DoFs. Our result provides a useful way to reduce quantum simulation resources by exploring complex quantum systems for quantum applications requiring large qubit systems.
Highlights
Quantum computer has shown its superiority for solving difficult problems such as the large integer decomposition[1,2,3] and data searching[4,5]
The single-electron and nuclear-spin states can be faithfully detected even under ambient conditions[40,41], when the electron spin of the NV defect center couples to nearby 13C nuclear spins. Another diamond NV− center is proposed with six electrons from the nitrogen and three carbons surrounding the vacancy[42], which is confined in a microtoroidal resonator (MTR)[43] with the quantized whispering-gallery mode (WGM)
To show the encoding independence of the polarization degree of freedom (DoF) and two spatial DoFs of each photon, it is necessary to prove that all quantum transformations in SU(2n) may be implemented on these DoFs
Summary
Quantum computer has shown its superiority for solving difficult problems such as the large integer decomposition[1,2,3] and data searching[4,5]. After one Hadamard operation Ha on the NV center e1 in the NV1, the photon A2 from each spatial mode evolves as Hp →CPBS →NV1 →CPBS →Hp to complete the following hybrid CNOT gate
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