We run continuous-time quantum walks with perfect and peak state transfer on a present-day superconducting quantum processor, IBM Quantum's $156$ -qubit Heron device ibm_kingston, deliberately without error correction or error mitigation. Perfect state transfer and its relaxations have been studied extensively in algebraic graph theory, where one can prove exactly which graphs move a quantum state from one vertex to another with probability one (or with the largest probability the graph allows, in the case of peak state transfer), and at what time. Our experiments cover perfect state transfer on the hypercubes $Q_2 = C_4$ and $Q_3$ , and on the Hamming-weighted paths $\mathrm{HP}_n$ , the equitable-partition quotients of the hypercubes $Q_n$ , for $n$ up to $20$ ; peak state transfer on the $X_n$ family for $n$ up to $11$ ; and, for comparison, moving the state along a path of qubits by a sequence of SWAP gates.We run continuous-time quantum walks with perfect and peak state transfer on a present-day superconducting quantum processor, IBM Quantum's $156$-qubit Heron device ibm_kingston, deliberately without error correction or error mitigation. Perfect state transfer and its relaxations have been studied extensively in algebraic graph theory, where one can prove exactly which graphs move a quantum state from one vertex to another with probability one (or with the largest probability the graph allows, in the case of peak state transfer), and at what time. Our experiments cover perfect state transfer on the hypercubes $Q_2 = C_4$ and $Q_3$, and on the Hamming-weighted paths $\mathrm{HP}_n$, the equitable-partition quotients of the hypercubes $Q_n$, for $n$ up to $20$; peak state transfer on the $X_n$ family for $n$ up to $11$; and, for comparison, moving the state along a path of qubits by a sequence of SWAP gates.

quant-pharXiv:2610.20855Oct 16, 20260 citations

Perfect state transfer using Markovian quantum walk

Supriyo Dutta

arXiv:2212.11699Annals of PhysicsFeb 20, 20260 citations

Perfect quantum state transfer on the Johnson scheme

Bahman Ahmadi, Mohammad Hassan Shirdareh Haghighi, Ahmad Mokhtar

arXiv:1710.09096Linear Algebra and its ApplicationsSep 24, 201912 citations

The perfect state transfer and the success probability of finding the marked vertex on the N -fold star power graph G ⋆ N

Qi Han, Rong Zhang, Jingyi Zhang +2 more

Abstract In this paper, within the framework of continuous-time quantum walks (CTQWs), we decompose graphs into disjoint strata by adopting the idea of equitable partitions. Based on the thought, we investigate the success probability of finding marked vertices on the N -fold star power graph G ⋆ N (where G is a cycle graph with three vertices), as well as the time required for perfect state transfer. Additionally, we explore the time for perfect state transfer on G ⋆ N under partition conditions from the perspective of quantum probability. Specifically, we surprisingly discover an interesting result: the times for perfect state transfer under quantum probability-based partitions and equitable partitions are completely consistent when the coupling strength J = 1 and the parameter λ = 1.Abstract In this paper, within the framework of continuous-time quantum walks (CTQWs), we decompose graphs into disjoint strata by adopting the idea of equitable partitions. Based on the thought, we investigate the success probability of finding marked vertices on the N -fold star power graph G ⋆ N (where G is a cycle graph with three vertices), as well as the time required for perfect state transfer. Additionally, we explore the time for perfect state transfer on G ⋆ N under partition conditions from the perspective of quantum probability. Specifically, we surprisingly discover an interesting result: the times for perfect state transfer under quantum probability-based partitions and equitable partitions are completely consistent when the coupling strength J = 1 and the parameter λ = 1.

Physica ScriptaDec 1, 20250 citations

Perfect swap and transfer of arbitrary quantum states

Yusef Maleki, Aleksei M. Zheltikov

Optics CommunicationsFeb 17, 202110 citations

We run continuous-time quantum walks with perfect and peak state transfer on a present-day superconducting quantum processor, IBM Quantum's

156

-qubit Heron device ibm_kingston, deliberately without error correction or error mitigation. Perfect state transfer and its relaxations have been studied extensively in algebraic graph theory, where one can prove exactly which graphs move a quantum state from one vertex to another with probability one (or with the largest probability the graph allows, in the case of peak state transfer), and at what time. Our experiments cover perfect state transfer on the hypercubes

Q_2 = C_4

and

Q_3

, and on the Hamming-weighted paths

\mathrm{HP}_n

, the equitable-partition quotients of the hypercubes

Q_n

, for

n

up to

20

; peak state transfer on the

X_n

family for

n

up to

11

; and, for comparison, moving the state along a path of qubits by a sequence of SWAP gates.