Proposal for a destructive controlled phase gate using linear optics

Knill, Laflamme, and Milburn showed that linear optics techniques could be used to implement a nonlinear sign gate. They also showed that two of their nonlinear sign gates could be combined to implement a controlled-phase gate, which has a number of practical applications. Here we describe an alternative implementation of a controlled-phase gate for a single-rail target qubit that only requires the use of a single nonlinear sign gate. This gives a much higher average probability of success when the required ancilla photons are generated using heralding techniques. This implementation of a controlled-phase gate destroys the control qubit, which is acceptable in a number of applications where the control qubit would have been destroyed in any event, such as in a postselection process.

Path-optimized nonadiabatic geometric quantum computation on superconducting qubits

Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric Phase, $\pi/8$ and Hadamard gates can be obtained as $99.93\%$, $99.95\%$ and $99.95\%$, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as $99.87\%$. Therefore, our scheme provides a new perspective for geometric quantum computation, making it more promising in the application of large-scale fault-tolerant quantum computation.

Giant cross-Kerr nonlinearity in a four-level Y-type atomic system

We found the analytical expression for cross-Kerr nonlinear coefficient in a four-level Y-type atomic system. The analytical model is applied to 85Rb atoms and shown that under electromagnetically induced transparency, cross-Kerr nonlinear coefficient is enhanced by several orders of magnitude. At the same time, the amplitude and the sign of cross-Kerr nonlinear coefficient are controlled with respect to the intensity and the frequency of the coupling laser field. The analytical model can be useful to explain the experimental results and to study related effects in nonlinear optics. Full Text: PDF ReferencesC. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, P. Tombesi, "Polarization Qubit Phase Gate in Driven Atomic Media", Phys. Rev. Lett. 90, 197902 (2003). CrossRef C. Zhu, G. Huang, "Giant Kerr Nonlinearity, Controlled Entangled Photons and Polarization Phase Gates in Coupled Quantum-Well Structures", Opt. Express 19, 23364 (2011). CrossRef C. Hang, G. Huang, "Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet", Opt. Express 18(3), 2952 (2010). CrossRef M. Fleischhauer, I. Mamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media", Rev. Mod. Phys. 77, 633 (2005). CrossRef H. Schmidt, And A. Imamogdlu, "Giant Kerr nonlinearities obtained by electromagnetically induced transparency", Opt. Lett., 21(23), 1936 (1996). CrossRef H. Kang And Y. Zhu, Phys. "Observation of Large Kerr Nonlinearity at Low Light Intensities", Rev. Lett., 91, 093601 (2003). CrossRef J. Kou, R. G. Wan, Z. H. Kang, H. H. Wang, L. Jiang, X. J. Zhang, Y. Jiang, and J. Y. Gao, "EIT-assisted large cross-Kerr nonlinearity in a four-level inverted-Y atomic system", J. Opt. Soc. Am. B. 27(10), 2035 (2010). CrossRef X. Yang, S. Li, C. Zhang, and H. Wang, "Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system", J. Opt. Soc. Am. B. 26(7), 1423 (2009). CrossRef C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti and P. Tombesi, "Polarization Qubit Phase Gate in Driven Atomic Media", Phys. Rev. Lett. 90, 197902 (2003). CrossRef H. Sun, Y. Niu, S. Jin and S. Gong, "Phase control of cross-phase modulation with electromagnetically induced transparency", J. Phys. B: At. Mol. Opt. Phys. 40, 3037 (2007). CrossRef L.V. Doai, P.V. Trong, D.X. Khoa, and N.H. Bang, "Electromagnetically induced transparency in five-level cascade scheme of 85Rb atoms: An analytical approach", Optik, 125, 3666 (2014). CrossRef D. X. Khoa, P. V. Trong, L. V. Doai and N. H. Bang, "Electromagnetically induced transparency in a five-level cascade system under Doppler broadening: an analytical approach", Phys, Scr. 91, 035401 (2016). CrossRef D.X. Khoa, L.C. Trung, P.V. Thuan, L.V. Doai and N.H. Bang, "Measurement of dispersive profile of a multiwindow electromagnetically induced transparency spectrum in a Doppler-broadened atomic medium", J. Opt. Soc. Am. B 34 (6), 1255 (2017). CrossRef D. X. Khoa, L. V. Doai, D. H. Son, and N. H. Bang, "Enhancement of self-Kerr nonlinearity via electromagnetically induced transparency in a five-level cascade system: an analytical approach", J. Opt. Soc. Am. B., 31, 1330 (2014). CrossRef L.V. Doai, N.L.T. An, D.X. Khoa, V.N. Sau and N.H. Bang, "Manipulating giant cross-Kerr nonlinearity at multiple frequencies in an atomic gaseous medium", J. Opt. Soc. Am. B 36, 2856 (2019). CrossRef D. X. Khoa, L. V. Doai, L. N. M. Anh, L. C. Trung, P. V. Thuan, N. T. Dung, and N. H. Bang, "Optical bistability in a five-level cascade EIT medium: an analytical approach", J. Opt. Soc. Am. B, Vol. 33, 735 (2016). CrossRef N. T. Anh, L. V. Doai, and N. H. Bang, "Manipulating multi-frequency light in a five-level cascade-type atomic medium associated with giant self-Kerr nonlinearity", J. Opt. Soc. Am. B 35, 1233 (2018). CrossRef N. T. Anh, L. V. Doai, D. H. Son, and N. H. Bang, "Manipulating multi-frequency light in a five-level cascade EIT medium under Doppler broadening", Optik 171, 721 (2018). CrossRef D.A. Steck, Rb85 D Line Data: http://Steck.Us/Alkalidata/rubidium85numbers.pdf CrossRef

Destructive Controlled-Phase Gate using Linear Optics

Knill, Laflamme, and Milburn showed that linear optics techniques could be used to implement a nonlinear sign gate. They also showed that two of their nonlinear sign gates could be combined to implement a controlled-phase gate, which has a number of practical applications. Here we describe an alternative implementation of a controlled-phase gate that only requires the use of a single nonlinear sign gate. This gives a much higher average probability of success when the required ancilla photons are generated using heralding techniques. This implementation of a controlled-phase gate destroys the control qubit, which is acceptable in a number of applications where the control qubit would have been destroyed in any event, such as in a postselection process.

Optimal two-qubit circuits for universal fault-tolerant quantum computation

We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS = diag(1, 1, 1, i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes through magic state distillation. Since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is often desirable to construct circuits that use few CS gates. In the present paper, we introduce an efficient and optimal synthesis algorithm for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and outputs a Clifford+CS circuit for U, which uses the least possible number of CS gates. Because the algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for that operator. We give an explicit description of these normal forms and use this description to derive a worst-case lower bound of $$5{{\rm{log}}}_{2}(\frac{1}{\epsilon })+O(1)$$ 5 log 2 ( 1 ϵ ) + O ( 1 ) on the number of CS gates required to ϵ-approximate elements of SU(4). Our work leverages a wide variety of mathematical tools that may find further applications in the study of fault-tolerant quantum circuits.