Online 3D Simulator for Visualization of the Bloch Sphere Using VPython

T.S. Smirnova, Mikhail V. Shvetskiy

Büşra Özcan, Abdullah Ateş

Ali Al-Bayaty, Marek A. Perkowski

The Bloch sphere is a geometrical 3D sphere that visualizes the states of a qubit after a series of quantum gates are applied to it. For that, the Bloch sphere is mainly used as a geometrical visualization (and verification) tool. On the other hand, in this protocol, we introduce the Bloch sphere as a geometrical design tool for building cost-effective quantum gates based on their rotational quantum operations in the XY-plane, which is the 2D circular top-view of the Bloch sphere. Collectively, the Bloch sphere and its XY-plane are termed the Bloch sphere approach (BSA). With the BSA, various generic and cost-effective quantum gates and libraries are designed for IBM quantum computers, using the symmetrical and semi-symmetrical structures [1-5], Clifford+T gates, and IBM native gates ( , , , and ), as follows. Quantum libraries (GALA-n [3, 6] and CALA-n [4, 7]), which have become part of the IBM Qiskit ecosystem [8] n-bit Toffoli gate [2-4] n-bit Boolean gates (AND, NAND, OR, NOR, implication, and inhibition) [3, 4] n-bit controlled- ( ) and controlled- ( ) gates [3, 4] n-bit Fredkin gate [3, 4] n-bit Miller gate [3, 4] Boolean-Phase SWAP gate (p-SWAP) [4, 5] Because the quantum operations of all IBM native "basis" gates mainly rotate around the X-axis and Z-axis of the Bloch sphere, we propose the XY-plane of the Bloch sphere for the BSA. However, the BSA can also be utilized to build generic and cost-effective quantum gates for other quantum computers, e.g., Intel, Google, and Rigetti, using different projectional planes of the Bloch sphere, e.g., the XZ-plane and the YZ-plane, based on the supported native gates for such quantum computers. Therefore, in this protocol, we introduce the BSA as an open geometrical framework for prospective quantum computing research.

K Thirupathi Reddy

Ali Al-Bayaty, Marek A. Perkowski

The Bloch sphere is a geometrical 3D sphere that visualizes the states of a qubit after a series of quantum gates are applied to it. In quantum computing, the Bloch sphere is mainly used as a geometrical visualization (and verification) tool. On the other hand, in this protocol, we introduce the Bloch sphere as a geometrical design tool for building cost-effective quantum gates based on their rotational quantum operations in the XY, XZ, and/or YZ planes, which are the 2D circular projections of the Bloch sphere. Collectively, the Bloch sphere and its planes are termed the Bloch sphere approach (BSA). With the BSA, various generic and cost-effective quantum gates and libraries are designed for IBM quantum computers, using the symmetrical and semi-symmetrical structures [1-5], Clifford+T gates, and IBM native "basis" gates ( , , , and ). Our designed generic and cost-effective quantum gates and libraries are listed as follows, where 2 n 5 qubits. Quantum libraries: GALA-n [3, 6] and CALA-n [4, 7], which have become part of the IBM Qiskit ecosystem [8] n-bit Toffoli gate [2-4] n-bit Boolean gates (AND, NAND, OR, NOR, implication, and inhibition) [3, 4] n-bit controlled- ( ) and controlled- ( ) gates [3, 4] n-bit Fredkin gate [3, 4] n-bit Miller gate [3, 4] Boolean-Phase SWAP gate: p-SWAP [4, 5] Because the quantum operations of all IBM native gates mainly rotate around the X-axis and Z-axis of the Bloch sphere, the XY-plane of the Bloch sphere is utilized here for the BSA. However, the BSA can also be utilized to build generic and cost-effective quantum gates for other quantum computers, e.g., Intel, Google, and Rigetti, using other projectional planes of the Bloch sphere, i.e., the XZ and YZ planes, based on the supported native gates for such quantum computers. Therefore, in this protocol, we introduce the BSA as a generic and open geometrical framework for prospective quantum computing research for building interesting and innovative quantum gates and circuits.

Thirupathi Kandadi