It is known that SWAP operation for quantum systems of arbitrary dimension can be implemented using various qudit gates. In this paper, equivalence of some important qudit operations is demonstrated. Equivalence of the qudit operations is exploited to minimize the circuit complexity in the previously proposed qudit SWAP gate constructions. Further, constructions of qudit SWAP operation with minimum number of qudit gates are also proposed. Importantly, these circuit constructions of SWAP retain its properties like symmetry and simplicity.It is known that SWAP operation for quantum systems of arbitrary dimension can be implemented using various qudit gates. In this paper, equivalence of some important qudit operations is demonstrated. Equivalence of the qudit operations is exploited to minimize the circuit complexity in the previously proposed qudit SWAP gate constructions. Further, constructions of qudit SWAP operation with minimum number of qudit gates are also proposed. Importantly, these circuit constructions of SWAP retain its properties like symmetry and simplicity.

Physics Research InternationalAug 5, 20149 citations

Moving quantum states without swap via intermediate higher-dimensional qudits

Amit Saha, Debasri Saha, Amlan Chakrabarti

Quantum algorithms can be realized in the form of a quantum circuit. To map a quantum circuit for a specific quantum algorithm to quantum hardware, qubit mapping is an imperative technique based on the qubit topology. Due to the neighborhood constraint of qubit topology, the implementation of the quantum algorithm rightly, is essential for moving information around in a quantum computer. Swapping of qubits using a swap gate moves the quantum state between two qubits and solves the neighborhood constraint of qubit topology. Although, one needs to decompose the swap gate into three controlled-not gates to implement the swap gate efficiently, but unwillingly quantum cost with respect to the gate count and depth increases. In this paper, a formalism of moving quantum states without using swap operation is introduced. Moving quantum states through qubits have been attained with the adoption of temporary intermediate qudit states. This introduction of intermediate qudit states has exhibited a three times reduction in quantum cost with respect to the gate count and approximately two times reduction with respect to circuit depth compared to the state-of-the-art approach of the swap gate insertion. We also exhibit that the adoption of the intermediate qudit makes the approach sublimer than the existing works by obtaining a better fidelity. Furthermore, the proposed approach is generalized to any finite-dimensional quantum system.Quantum algorithms can be realized in the form of a quantum circuit. To map a quantum circuit for a specific quantum algorithm to quantum hardware, qubit mapping is an imperative technique based on the qubit topology. Due to the neighborhood constraint of qubit topology, the implementation of the quantum algorithm rightly, is essential for moving information around in a quantum computer. Swapping of qubits using a swap gate moves the quantum state between two qubits and solves the neighborhood constraint of qubit topology. Although, one needs to decompose the swap gate into three controlled-not gates to implement the swap gate efficiently, but unwillingly quantum cost with respect to the gate count and depth increases. In this paper, a formalism of moving quantum states without using swap operation is introduced. Moving quantum states through qubits have been attained with the adoption of temporary intermediate qudit states. This introduction of intermediate qudit states has exhibited a three times reduction in quantum cost with respect to the gate count and approximately two times reduction with respect to circuit depth compared to the state-of-the-art approach of the swap gate insertion. We also exhibit that the adoption of the intermediate qudit makes the approach sublimer than the existing works by obtaining a better fidelity. Furthermore, the proposed approach is generalized to any finite-dimensional quantum system.

arXiv:2106.09089Physical Review AJul 21, 20223 citations

Towards an optimal swap gate

Colin Wilmott, Peter Wild

Quantum Information ProcessingMar 18, 20143 citations

On interchanging the states of a pair of qudits

Colin Wilmott, Peter Wild

The qubit SWAP gate has been shown to be an integral component of quantum circuitry design. It permutes the states of two qubits and allows for the storage quantum information, teleportation of atomic or ionic states, and is a fundamental element in the circuit implementation of Shor's algorithm. We consider the problem of generalising the SWAP gate beyond the qubit setting. We show that quantum circuit architectures completely described by instances of the CNOT gate can not implement a transposition of a pair of qudits for dimensions $d \equiv 3 (mod 4)$ . The task of constructing generalised SWAP gates based on transpositions of qudit states is argued in terms of the signature of a permutation.The qubit SWAP gate has been shown to be an integral component of quantum circuitry design. It permutes the states of two qubits and allows for the storage quantum information, teleportation of atomic or ionic states, and is a fundamental element in the circuit implementation of Shor's algorithm. We consider the problem of generalising the SWAP gate beyond the qubit setting. We show that quantum circuit architectures completely described by instances of the CNOT gate can not implement a transposition of a pair of qudits for dimensions $d \equiv 3 (mod 4)$. The task of constructing generalised SWAP gates based on transpositions of qudit states is argued in terms of the signature of a permutation.

arXiv:0811.1545Nov 10, 20080 citations

Blind encoding into qudits

Jesni Shamsul Shaari, Mohamed Ridza Wahiddin, Stefano Mancini

arXiv:quant-ph/0701055Physics Letters ANov 9, 200710 citations

d \equiv 3 (mod 4)

. The task of constructing generalised SWAP gates based on transpositions of qudit states is argued in terms of the signature of a permutation.