Moving quantum states without swap via intermediate higher-dimensional qudits

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.

Figure 1

cnot swapping circuit.

Figure 2

(a) Example: circuit, (b) example: qubit topology, and (c) swap insertion.

Figure 3

Moving of a quantum state via intermediate qudits.

Figure 4

(a) Example: circuit in binary quantum systems; (b) example: qubit topology; (c) swap insertion; (d) swap depth optimization; (e) proposed approach.

Figure 5

Qudit swapping circuit.

Figure 6

(a) Example: circuit in $d$-ary quantum systems; (b) example: qudit topology; (c) swap insertion; (d) swap depth optimization; (e) proposed approach.

Figure 7

(a) Gate count vs number of qubits and qudits for proposed work (lower curve) and conventional work (upper curve), (b) circuit depth vs number of qubits and qudits for proposed work (lower curve) and conventional work (upper curve).

Figure 8

Probability of success for the proposed method (upper curve) vs the conventional method (lower curve).

Figure 9

(a) Five-qubit circuit and (b) six-qubit circuit.