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Conference on Lasers and Electro-Optics

Quantum gates and entanglement

Schmidt-Kaler, Haffiier, Riebe, Deuschle, Benhelm, Lancaster, Becher, Hansel, Roos, Blatt

Published Jan 1, 2004• 0 citations
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Abstract In the circuit model of quantum computation, an entangling two-qubit gate and a set of single-qubit gates are used as universal gate set or basis gates for doing quantum computation. CNOT and iSWAP gates, the perfect entanglers that can create maximally entangled two-qubit states in one application, are broadly used entangling two-qubit basis gates in quantum computers. In this paper, we analyze the potentiality of B gate, an unexplored non-perfect entangler of the form, exp i π ( σ ˆ x ⨂ σ ˆ x ) 8 + i π ( σ ˆ y ⨂ σ ˆ y ) 16 , as an entangling two-qubit basis gate in quantum computers by studying its ability to generate other two-qubit gates. We derive a necessary condition for a two-qubit gate to be generated by n applications of B gate. Using this condition, we show that the gates that can be generated by two and three applications of B gate are contained in the 50% and 92.97% of the volume of Weyl chamber of two-qubit gates, respectively. We prove that two applications of B gate can generate both SWAP and SWAP

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study to produce eight entangled states of a quantum circuit consisting of four qubits using quantum gates

مصطفى حسين موسى, أ.م.د مزهر باقر صالح, أ.د. اسماعيل عبدالله اخلاطي

Study of a quantum circuit consisting of four qubits that produces an output state consisting of eight entangled states through the CNOT –gates and the three Hadamard gates. targeting the gates to |q0q1q2q3> to show the other entangled states, We used quantum gates that give the same arrangement as the circuit gates and for the same inputs, taking into account the output of a quantum circuit that contains entangled states. As a general case, we used an X-gate and a SWAP-gate, For inputs|0000> .We obtained a general change to the output state while keeping the eight states maximally entangled.

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New Two-Qubit Gate Library with Entanglement

Md. Belayet Ali, Takashi Hirayama, Katsuhisa Yamanaka +1 more

The NCV (NOT, CNOT and Controlled-V/V) gate set is most commonly used for the realization of classical reversible functions and implementation of quantum circuits. Logic operations in quantum circuits are performed by individual gates or can be expressed as matrix-vector multiplication. Thispaper presents a two-qubit quantum gate library which consists most commonly used elementary quantum gates NOT, CNOT, Controlled-V and Controlled-V. The new library contains all possible two-qubit quantum gates which do not produce entangled states in the final output state. Two approaches have been appliedto generate the new two-qubit quantum gate library because it hasbeen observed that some entangled gates act like non-entangledif those entangled gates are merged with other valid gates in thelibrary. The experimental result shows the difference betweenthe libraries with and without considering entangled gates in theprocess of generating new gates.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)•May 1, 2016•1 citation
Abstract In the circuit model of quantum computation, an entangling two-qubit gate and a set of single-qubit gates are used as universal gate set or basis gates for doing quantum computation. CNOT and iSWAP gates, the perfect entanglers that can create maximally entangled two-qubit states in one application, are broadly used entangling two-qubit basis gates in quantum computers. In this paper, we analyze the potentiality of B gate, an unexplored non-perfect entangler of the form, exp i π ( σ ˆ x ⨂ σ ˆ x ) 8 + i π ( σ ˆ y ⨂ σ ˆ y ) 16 , as an entangling two-qubit basis gate in quantum computers by studying its ability to generate other two-qubit gates. We derive a necessary condition for a two-qubit gate to be generated by n applications of B gate. Using this condition, we show that the gates that can be generated by two and three applications of B gate are contained in the 50% and 92.97% of the volume of Weyl chamber of two-qubit gates, respectively. We prove that two applications of B gate can generate both SWAP and SWAP
Study of a quantum circuit consisting of four qubits that produces an output state consisting of eight entangled states through the CNOT –gates and the three Hadamard gates. targeting the gates to |q0q1q2q3> to show the other entangled states, We used quantum gates that give the same arrangement as the circuit gates and for the same inputs, taking into account the output of a quantum circuit that contains entangled states. As a general case, we used an X-gate and a SWAP-gate, For inputs|0000> .We obtained a general change to the output state while keeping the eight states maximally entangled.
The NCV (NOT, CNOT and Controlled-V/V) gate set is most commonly used for the realization of classical reversible functions and implementation of quantum circuits. Logic operations in quantum circuits are performed by individual gates or can be expressed as matrix-vector multiplication. Thispaper presents a two-qubit quantum gate library which consists most commonly used elementary quantum gates NOT, CNOT, Controlled-V and Controlled-V. The new library contains all possible two-qubit quantum gates which do not produce entangled states in the final output state. Two approaches have been appliedto generate the new two-qubit quantum gate library because it hasbeen observed that some entangled gates act like non-entangledif those entangled gates are merged with other valid gates in thelibrary. The experimental result shows the difference betweenthe libraries with and without considering entangled gates in theprocess of generating new gates.