Minimal universal two-qubit controlled-NOT-based circuits

Abstract

We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to a global phase. For several quantum gate libraries we prove that gate counts are optimal in the worst and average cases. Our lower and upper bounds compare favorably to previously published results. Temporary storage is not used because it tends to be expensive in physical implementations. For each gate library, the best gate counts can be achieved by a single universal circuit. To compute the gate parameters in universal circuits, we use only closed-form algebraic expressions, and in particular do not rely on matrix exponentials. Our algorithm has been coded in C++.

Efficient Grover search with Rydberg blockade

“…A general k-qubit unitary operation is described by a 2 k × 2 k matrix, and the theoretical lower bound on the number of C-NOT gates needed, together with arbitrary singlequbit gates, to form an arbitrary unitary operation scales as 4 k [27]. A practical, constructive protocol reaching this limit is presented, e.g., in [28].…”

Quantum-process tomography: Resource analysis of different strategies

“…The operator Ω has maximal Schmidt number and generally cannot be simulated using a polynomial number of elementary gates. It is known that, in general, O(4 N ) elementary singleand two-qubit gates are necessary to simulate many-body operations acting on N qubits [48] (see also Ref. [34] for different measures of complexity of a given quantum dynamics, and Ref.…”

Characterization of two-qubit perfect entanglers

“…In fact, there is a vast literature on this topic with many remarkable findings [22,23,24,25,26,27,28,29,30,31,32,33,34,35]. It has been known that a general (multi-qubit) quantum gate can be simulated using a quantum circuit built of elementary gates which operate on single and two qubits [23].…”