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International Journal of Quantum Information

EFFICIENT AND PERFECT STATE TRANSFER IN QUANTUM CHAINS

Daniel Klaus Burgarth, Sougato Bose, Vittorio Giovannetti

Published Jun 1, 2006• 16 citations
Publisher

Abstract

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].

DOI
10.1142/s0219749906001876

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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.
We suggest a protocol for perfect quantum communication through spin-chain channels. By combining a dual-rail encoding with measurements only at the receiving end, we can get conclusively perfect state transfer, whose probability of success can be made arbitrarily close to unity. As an example of such an amplitude-delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than PPP in a Heisenberg chain of NNN spin-12\frac{1}{2}21​ particles can be achieved in a timescale of the order of $(0.33\ensuremath{\hbar}∕J){N}^{1.7}\ensuremath{\mid}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}P\ensuremath{\mid}$. We demonstrate that our scheme is more robust to decoherence and nonoptimal timing than any scheme using single spin chains.
We suggest a protocol for the transfer of quantum information in spin chain channels with a finite recurrence time. By combining a dual-rail encoding with certain measurements at the receiving end, we can get arbitrarily perfect state transfer, i.e. by performing sufficiently many measurements at the receiving end, we can make the probability of perfect state transfer arbitrary close to unity. As an example of such an amplitude delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires in solid state quantum computers. Perfect state transfer with a probability of failure lower than delta in a Heisenberg chain of N spin-1/2 particles can be achieved in a timescale of the order of N^(7/3)*|ln(delta)|. Furthermore, the same scheme can be implemented using a single SU(n) chain which is realizable in quantum dot arrays.
We present an introductory overview of the use of spin chains as quantum wires, which has recently developed into a topic of lively interest. The principal motivation is in connecting quantum registers without resorting to optics. A spin chain is a permanently coupled 1D system of spins. When one places a quantum state on one end of it, the state will be dynamically transmitted to the other end with some efficiency if the spins are coupled by an exchange interaction. No external modulations or measurements on the body of the chain, except perhaps at the very ends, is required for this purpose. For the simplest (uniformly coupled) chain and the simplest encoding (single qubit encoding), however, dispersion reduces the quality of transfer. We present a variety of alternatives proposed by various groups to achieve perfect quantum state transfer through spin chains. We conclude with a brief discussion of the various directions in which the topic is developing.
We present an introductory overview of the use of spin chains as quantum wires, which has recently developed into a topic of lively interest. The principal motivation is in connecting quantum registers without resorting to optics. A spin chain is a permanently coupled 1D system of spins. When one places a quantum state on one end of it, the state will be dynamically transmitted to the other end with some efficiency if the spins are coupled by an exchange interaction. No external modulations or measurements on the body of the chain, except perhaps at the very ends, is required for this purpose. For the simplest ( uniformly coupled) chain and the simplest encoding (single qubit encoding), however, dispersion reduces the quality of transfer. We present a variety of alternatives proposed by various groups to achieve perfect quantum state transfer through spin chains. We conclude with a brief discussion of the various directions in which the topic is developing.