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Chinese Physics B

Using a quantum dot system to realize perfect state transfer

Li Ji, Shi-Hai Wu, Wen-Wen Zhang, Xiao-Qiang Xi

Published Oct 1, 2011• 4 citations
Publisher

Abstract

There are some disadvantages to Nikolopoulos et al. 's protocol [Nikolopoulos G M, Petrosyan D and Lambropoulos P 2004 Europhys. Lett. 65 297] where a quantum dot system is used to realize quantum communication. To overcome these disadvantages, we propose a protocol that uses a quantum dot array to construct a four-qubit spin chain to realize perfect quantum state transfer (PQST). First, we calculate the interaction relation for PQST in the spin chain. Second, we review the interaction between the quantum dots in the Heitler—London approach. Third, we present a detailed program for designing the proper parameters of a quantum dot array to realize PQST.

DOI
10.1088/1674-1056/20/10/100308

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There are some disadvantages to Nikolopoulos et al. 's protocol [Nikolopoulos G M, Petrosyan D and Lambropoulos P 2004 Europhys. Lett. 65 297] where a quantum dot system is used to realize quantum communication. To overcome these disadvantages, we propose a protocol that uses a quantum dot array to construct a four-qubit spin chain to realize perfect quantum state transfer (PQST). First, we calculate the interaction relation for PQST in the spin chain. Second, we review the interaction between the quantum dots in the Heitler—London approach. Third, we present a detailed program for designing the proper parameters of a quantum dot array to realize PQST.
We review the subject of perfect state transfer — how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time. The perfect state transfer systems are then used as a constructive tool to design Hamiltonian implementations of other primitive protocols such as entanglement generation and signal amplification in measurements, before showing that, in fact, universal quantum computation can be implemented in this way.
We present a communication protocol for chains of permanently coupled qubits which achieves perfect quantum state transfer and which is efficient with respect to the number of chains employed in the scheme. The system consists of M uncoupled identical quantum chains. Local control (gates, measurements) is only allowed at the sending/receiving end of the chains. Under a quite general hypothesis on the interaction Hamiltonian of the qubits, a theorem can be proved which shows that the receiver is able to asymptotically recover the messages by repetitive monitoring of his qubits. We show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than P in a Heisenberg chain of N spin-1/2 particles can be achieved in a time scale of the order of [Formula: see text].
We present a communication protocol for chains of permanently coupled qubits which achieves perfect quantum state transfer and which is efficient with respect to the number of chains employed in the scheme. The system consists of M uncoupled identical quantum chains. Local control (gates, measurements) is only allowed at the sending/receiving end of the chains. Under a quite general hypothesis on the interaction Hamiltonian of the qubits, a theorem is proved which shows that the receiver is able to asymptotically recover the messages by repetitive monitoring of his qubits.
Perfect quantum state transfer is achievable in different settings, including linear qubit chains, bi-dimensional arrays, ladders, etc. The most studied case contemplates transferring arbitrary one-qubit pure states in systems with homogeneous interactions. These restrictions allow finding numerous examples of systems that show perfect transfer but in geometries that are not implementable or are very difficult to implement in actual experimental settings. Relaxing the homogeneity of the interactions and inspired by the XXXXXX qubit chains that show perfect transmission, we present a simple scheme based on the Givens Transformations to analyse and obtain a class of qubit graphs that possess perfect quantum state transmission. We present some simple examples and show how it is possible to generalize them for longer transmission lengths.
In quantum computation and quantum information processing, the manipulation and engineering of quantum systems to suit certain purposes are an ongoing task. One such example is quantum state transfer (QST), an essential requirement for both quantum communication and large-scale quantum computation. Here we engineer a chain of four superconducting qubits with tunable couplers to realize the perfect state transfer (PST) protocol originally proposed in quantum spin networks and successfully demonstrate the efficient transfer of an arbitrary single-qubit state from one end of the chain to the other, achieving a high fidelity of 0.986 in just 25 ns. This demonstrated QST is readily to extend to larger chain and multi-node configurations, thus serving as a desirable tool for scalable quantum information processing.
Semiconductor quantum-dot spin qubits are a promising platform for quantum computation, because they are scalable and possess long coherence times. In order to realize this full potential, however, high-fidelity information transfer mechanisms are required for quantum error correction and efficient algorithms. Here, we present evidence of adiabatic quantum-state transfer in a chain of semiconductor quantum-dot electron spins. By adiabatically modifying exchange couplings, we transfer single- and two-spin states between distant electrons in less than 127 ns. We also show that this method can be cascaded for spin-state transfer in long spin chains. Based on simulations, we estimate that the probability to correctly transfer single-spin eigenstates and two-spin singlet states can exceed 0.95 for the experimental parameters studied here. In the future, state and process tomography will be required to verify the transfer of arbitrary single qubit states with a fidelity exceeding the classical bound. Adiabatic quantum-state transfer is robust to noise and pulse-timing errors. This method will be useful for initialization, state distribution, and readout in large spin-qubit arrays for gate-based quantum computing. It also opens up the possibility of universal adiabatic quantum computing in semiconductor quantum-dot spin qubits.