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Physics Today

Entangled two-spin qubits

Richard J. Fitzgerald

Published Jun 1, 2012• 0 citations
Publisher

Abstract

For quantum computation, qubits need to be isolated from their environment but connected to each other. For one kind of spin qubits, a means to achieve both has now been demonstrated.
DOI
10.1063/pt.3.1593

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Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the computer, and forcing their joint quantum state to be completely symmetric. On the other hand, isolated errors can be corrected by quantum codewords that represent a logical qubit in a redundant way, by several physical qubits. If one of the physical qubits is perturbed, for example if it gets entangled with an unknown environment, there still is enough information encoded in the other physical qubits to restore the logical qubit, and disentangle it from the environment. The recovery procedure may consist of unitary operations, without the need of actually identifying the error.
A quantum computer would exploit the phenomena of quantum superposition and entanglement in its functioning and with them offer pathways to solving problems that are too hard or complex to even the best classical computers built today. The implementation of a large-scale working quantum computer could bring about a change in our society rivaling the one started by the digital computer. However, the field is still in its infancy and there are many theoretical and practical issues needing to be solved before large-scale quantum computing can become reality. In digital computers, data is stored in bits. The quantum equivalent is called a qubit (quantum bit) and it is basically a quantum mechanical two-level system that can be in a superposition of its two basis states. There are many different proposals for implementing qubits, but one of the most promising ones is to encode the qubit using electron spins trapped in semiconductor quantum dots. Singlet-triplet qubits are spin qubits where the two-electron spin eigenstates are used as the qubit's basis. The required one and two-qubit operations have already been demonstrated experimentally by several research groups around the world in this qubit architecture. The most severe factor limiting the implementation of larger systems of qubits is decoherence. The qubits are not isolated systems, they interact with their environment, which can lead to the loss of quantum information. Few-electron systems can be simulated accurately using first principle methods that become too taxing when the particle number increases. The topic of this thesis is the simulation of quantum dot singlet-triplet qubit systems using accurate exact diagonalization based methods. The emphasis is on the realistic description of qubit operations, both single-qubit ones and those involving the interaction between neighboring qubits. The decoherence effects are also discussed alongside with certain proposals to alleviate their effects.
We study the dynamical behavior of two initially entangled qubits, each locally coupled to an environment embodied by an interacting spin chain. We consider energy-exchange qubit–environment couplings resulting in rich and highly non-trivial entanglement dynamics. We obtain exact results for the time evolution of the concurrence between the two qubits and find that, by tuning the interaction parameters, one can freeze the dynamics of entanglement, therefore inhibiting their relaxation into the spin environments, as well as activate a sudden-death phenomenon. We also discuss the effects of an environmental quantum phase transition on the features of the two-qubit entanglement dynamics.