Optimal Quantum Circuits for General Two-Qubit Gates

By Farrokh Vatan, Colin P. Williams. 2003

426 citations recorded by the source corpus.

In order to demonstrate nontrivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortestpossible sequence of one-qubit and two-qubit gates. We contribute to this effort by providing a method to construct an optimal quantum circuit for a general two-qubit gate that requires at most 3 controlled-NOT (CNOT) gates and 15 elementary one-qubit gates. Moreover, if the desired two-qubit gate corresponds to a purely real unitary transformation, we provide a construction that requries at most 2 CNOT and 12 one-qubit gates. We then prove that these constructions are optimal with respect to the family of CNOT, y-rotation, z-rotation, and phase gates.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/521de4e15b6ef74ee7baa7c308154bd7381a2fe0

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum convolutional neural network for classical data classification (2021, background): “Circuit 9 represents the parameterization of an arbitrary SU(4) gate [20, 30].”
Synthesis of quantum-logic circuits (2004, positive): “while three CNOT gates are necessary and sufficient in the worst case [28], [29], [35], [36].”
Absence of Barren Plateaus in Quantum Convolutional Neural Networks (2020, methodology): “[57] Farrokh Vatan and Colin Williams, “Optimal quantum circuits for general two-qubit gates,” Physical Review A 69, 032315 (2004).”
Quantum-assisted quantum compiling (2018, methodology): “This decomposition is known to be optimal [35], i.e., it uses the least number of continuous parameters and CNOT gates.”
Quantum Generative Adversarial Networks for learning and loading random distributions (2019, methodology): “As shown in [56], the action of circuit (a) is equivalent to the action of circuit (b), which only utilizes 2 CX gates.”
Realization of a programmable two-qubit quantum processor (2009, background): “Since realising gates acting on two or more qubits tends to be more experimentally challenging[8], much attention has been focused on using them optimally in the creation of entanglement[11] and on finding decompositions minimizing the number of times they are applied[7, 12, 13, 14, 15].”
Geometric (2019, background): “Thus, there were eight global patterns formed by local dot motion, with four patterns exhibiting a right-tilted contour ( No. 1 –”
Demonstration of quantum volume 64 on a superconducting quantum computing system (2020, background): “While the question of ‘optimal’ SU(4) decomposition has been extensively studied, the optimality criteria has usually been the number of two-qubit gates [23, 24].”