Perfect state transfer on hypercubes and its implementation using superconducting qubits

Singh, Siddhant; Adhikari, Basudam; Dutta, Supriyo; Zueco, David

doi:10.1103/physreva.102.062609

Cited by 6 publications

(5 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Beyond the difficulties presented by the Heisenberg model and the QST of arbitrary onequbit states, there is a bonanza de new proposals. Among these novel propositions are the transfer of multilevel states [19,[40][41][42][43][44][45][46], also called d-levels states, transfer protocols dealing with multiple qubit states [47][48][49][50], perfect transfer in graphs or two-or three-dimensional settings [9,51,52], and the transfer of several quantum states in parallel using only a single channel [53]. The works dealing with these ideas are both theoretical and experimental.…”

Section: Introductionmentioning

confidence: 99%

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Serra¹,

Ferrón²,

Osenda³

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We construct the exact solution for a family of one-half spin chains explicitly. The spin chains Hamiltonian corresponds to an isotropic Heisenberg Hamiltonian, with staggered exchange couplings that take only two diﬀerent values. We work out the exact solutions in the one- excitation sub-space. Regarding the problem of quantum state transfer, we use the solution and some theorems concerning the approximation of irrational numbers, to show the appearance of conclusive pretty good transmission for chains with particular lengths. We present numerical evidence that pretty good transmission is achieved by chains whose length is not a power of two. The set of spin chains that shows pretty good transmission is a subset of the family with an exact solution. Using perturbation theory, we thoroughly analyze the case when one of the exchange coupling strengths is orders of magnitude larger than the other. This strong coupling limit allows us to study, in a simple way, the appearance of pretty good transmission. The use of analytical closed expressions for the eigenvalues, eigenvectors, and transmission probabilities allows us to obtain the precise asymptotic behavior of the time where the pretty good transmission is observed. Moreover, we show that this time scales as a power law whose exponent is an increasing function of the chain length. We also discuss the crossover behavior obtained for the pretty good transmission time between the regimes of strong coupling limit and the one observed when the exchange couplings are of the same order of magnitude.

show abstract

Section: Introductionmentioning

confidence: 99%

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Serra¹,

Ferrón²,

Osenda³

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…We can accomplish simultaneous tunability of the coupling strengths by exploiting the magnetic-field gradients. The goals of Hamiltonian engineering is summarized as follows [30,31]:…”

Section: Hamiltonian Engineeringmentioning

confidence: 99%

Quantum routing in planar graph using perfect state transfer

Dutta¹

2023

Preprint

View full text Add to dashboard Cite

In this article, we consider a spin-spin interaction network governed by XX + Y Y Hamiltonian. The vertices and edges of the network represent the spin objects and their interactions, respectively. We take a privilege to switch on or off any interaction, that assists us to perform multiple perfect state transfers in a graph simultaneously. We also build up a salable network allowing quantum communication between two arbitrary vertices. Later we utilize the combinatorial characteristics of hypercube graphs to propose a static routing schema to communicate simultaneously between a set of senders and a set of receivers in a planar network. Our construction is new and significantly powerful. We elaborate multiple examples of planar graphs supporting quantum routing where classical routing is not possible.

show abstract

“…Quantum computing is poised to provide supremacy over classical computing using quantum mechanical phenomena such as superposition, interference and entanglement. Physical systems like, superconducting circuits 1 – 4 , nuclear magnetic resonance (NMR) systems 5 – 9 , ion traps 10 , 11 , ultra-cold atoms in optical lattice 12 , 13 and photonics 14 – 18 have been successfully engineered to demonstrate small scale quantum processors and implement quantum simulations and computational tasks. The noisy-intermediate scale quantum processors we have today are still far from the one that can be used for performing useful tasks that are inaccessible by the existing powerful classical computers.…”

Section: Introductionmentioning

confidence: 99%

Multi-qubit quantum computing using discrete-time quantum walks on closed graphs

Chawla,

Singh,

Agarwal

et al. 2023

Sci Rep

View full text Add to dashboard Cite

Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of the scheme is demonstrated by using a set of walk operations on a closed lattice form to implement the universal set of quantum gates on multi-qubit system. We also present a set of experimentally realizable walk operations that can implement Grover’s algorithm, quantum Fourier transformation and quantum phase estimation algorithms. An elementary implementation of error detection and correction is also presented. Analysis of space and time complexity of the scheme highlights the advantages of quantum walk based model for quantum computation on systems where implementation of quantum walk evolution operations is an inherent feature of the system.

show abstract

Perfect state transfer on hypercubes and its implementation using superconducting qubits

Cited by 6 publications

References 65 publications

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Quantum routing in planar graph using perfect state transfer

Multi-qubit quantum computing using discrete-time quantum walks on closed graphs

Contact Info

Product

Resources

About