Low-Cost Fredkin Gate with Auxiliary Space

Abstract

Effective quantum information processing is tantamount in part to the minimization the quantum resources needed by quantum logic gates. Here, we propose an optimization of an n-controlled-qubit Fredkin gate with a maximum of 2n + 1 two-qubit gates and 2n single-qudit gates by exploiting auxiliary Hilbert spaces. The number of logic gates required improves on earlier results on simulating arbitrary n-qubit Fredkin gates. In particular, the optimal result for one-controlled-qubit Fredkin gate (which requires three qutrit-qubit partial-swap gates) breaks the theoretical nonconstructive lower bound of five two-qubit gates. Furthermore, using an additional spatial-mode degree of freedom, we design a possible architecture to implement a polarization-encoded Fredkin gate with linear optical elements.

Universal Quantum Multi‐Qubit Entangling Gates with Auxiliary Spaces

“…simplified a Fredkin gate from eight CNOTs to five CNOTs [ 38 ] or three qubit–qudit gates. [ 39 ] In addition, higher‐dimensional quantum systems have also been studied [ 40,41 ] and applied in quantum computing, [ 42–45 ] quantum communication, [ 46–53 ] and quantum metrology. [ 54 ]…”

Multiple‐Qubit CkUm Logic Gates of Rydberg Atoms via Optimized Geometric Quantum Operations

“…The traditional multiple-qubit logic gates are constructed by a combination of single qubit gates and two qubit gates. [89][90][91][92][93] However, this traditional construction method will cause a waste of quantum resources. For example, if a Toffoli gate is implemented in this way, six two-qubit quantum CNOT gates and nine single-qubit quantum gates need to be combined.…”

Negative controlled Fredkin gate circuits with mirrors

“…One is a positive control, which performs SWAP operation with control input as 'logic-1' and the other is a negative control, which performs SWAP operation with control input as 'logic-0' [3]. Controlled SWAP gate has been proposed by many authors by all-optical nonlinear martial based switch [4][5][6][7], Photonic crystal based circuit [8], linear optical materials in quantum mechanical approach [9][10][11][12], nanocomputational circuit [13], DNA based circuit [14] and CMOS based circuit [15]. Among them the optical circuit has several advantages like high bandwidth, low cross talk, low noise than electrical circuit, parallel operation, ability to operate at room temperature, etc.…”