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arXiv:quant-ph/9703040 · Physical Review Letters

Preserving Coherence in Quantum Computation by Pairing Quantum Bits

L.-M. Duan, Guang‐Can Guo

Published Sep 8, 1997• 556 citations
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Abstract

A scheme for protecting quantum states from both independent and cooperative decoherence is proposed. The scheme operates by pairing each qubit (two-state quantum system) with an ancilla qubit and by encoding the states of the qubits into corresponding coherence-preserving states of qubit pairs. In this scheme, amplitude damping (loss of energy) as well as phase damping (dephasing) is prevented by a strategy called ``free-Hamiltonian elimination.'' We further extend the scheme to include quantum gate operations and show that loss and decoherence during such operations can also be prevented.

DOI
10.1103/physrevlett.79.1953

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Acta Physica Sinica•Jan 1, 2016•4 citations
A scheme for protecting quantum states from both independent and cooperative decoherence is proposed. The scheme operates by pairing each qubit (two-state quantum system) with an ancilla qubit and by encoding the states of the qubits into corresponding coherence-preserving states of qubit pairs. In this scheme, amplitude damping (loss of energy) as well as phase damping (dephasing) is prevented by a strategy called ``free-Hamiltonian elimination.'' We further extend the scheme to include quantum gate operations and show that loss and decoherence during such operations can also be prevented.
Cooperative effects in the loss (the amplitude damping) and decoherence (the phase damping) of the qubits (two-state quantum systems) due to the inevitable coupling to the same environment are investigated. It is found that the qubits undergo the dissipation coherently in this case. In particular, for a special kind of input states (called the coherence-preserving states), whose form depends on the type of the coupling, loss and decoherence in quantum memory are much reduced. Based on this phenomenon, a scheme by encoding the general input states of the qubits into the corresponding coherence-preserving states is proposed for reducing the cooperative loss and decoherence in quantum computation or communication.
A scheme is presented for protecting one-qubit quantum information against decoherence due to a general environment and local exchange interactions. The scheme operates essentially by distributing information over two pairs of qubits and through error-prevention procedures. In the scheme, quantum information is encoded through a decoherence-free subspace for collective phase errors and exchange errors affecting the qubits in pairs; leakage out of the encoding space due to amplitude damping is reduced by quantum Zeno effect. In addition, how to construct decoherence-free states for n-qubit information against phase and exchange errors is discussed.
When a quantum system interacts with its environment, the so-called decoherence effect will normally destroy the coherence in the quantum state and the entanglement between its subsystems. We propose a feedback control strategy based on quantum weak measurements to protect coherence and entanglement of the quantum state against environmental disturbance. For a one-qubit quantum system under amplitude damping and dephasing decoherence channels, our strategy can preserve the coherence based on the measured information about the population difference between its two levels. For a two-qubit quantum system disentangled by independent amplitude damping and dephasing decoherence channels, the designed feedback control can preserve coherence between the ground state and the highest excited states by tuning the coupling strength between the two qubits, and at the same time minimize the loss of entanglement between the two qubits. As a consequence of dynamic symmetry, the generalization of these results derives the concept of control-induced decoherence-free observable subspace, for which several criteria are provided.
Abstract Quantum information encoded into the superposition of coherent states is an illustrative representation of practical applications of macroscopic quantum coherence possessing. However, these states are very sensitive to energy loss, losing their non-classical aspects of coherence very rapidly. An available deterministic strategy to slow down this decoherence process is to apply a Gaussian squeezing transformation prior to the loss as a protective step. Here, we propose a deterministic hybrid protection scheme utilizing strong but feasible interactions with two-level ancillas immune to spontaneous emission. We verify the robustness of the scheme against the dephasing of qubit ancilla. Our scheme is applicable to complex superpositions of coherent states in many oscillators, and remarkably, the robustness to loss is enhanced with the amplitude of the coherent states. This scheme can be realized in experiments with atoms, solid-state systems, and superconducting circuits.
Entanglement is a vital resource for many quantum information processes. However, the unavoidable interaction between quantum system and its environment will lead to quantum decoherence. So protecting remote entanglement against decoherence is of great importance for realizing quantum information and quantum communication. In fact, there are many types of decoherences. Besides the depolarization and phase damping, amplitude damping is a typical decoherence mechanism. If we monitor the environments to guarantee that no excitation escapes from the system, the amplitude damping is modified into a weak measurement induced amplitude damping of the system. Amplitude damping decoherence can affect both single-qubit quantum states and multipartite entangled states. However, in most of previous quantum state protection schemes, the authors only pay attention to the single-qubit system or two-qubit system. Compared with bipartite entangled states, multipartite entangled states possess many advantages, but the entanglement property of multipartite entangled state is much more complicated than bipartite entanglement, so bipartite entanglement reversal (protection) scheme may not be suitable for multipartite case. Thus, in this paper, according to local pulse series and weak measurement, we propose an effective scheme for protecting two multipartite entangled states against amplitude damping, and these two multipartite states are Cluster state and Maximal slice (MS) state. Cluster state and MS state are two typical classes of multipartite entangled states, which play important roles in quantum computation and communication, respectively. These two states cannot be converted into each other with local operation and classical communication. Owing to its good operational and computable properties, here we choose negativity as a measure to quantify the multipartite entanglement. For the case of MS sate, no matter what the initial parameter is, when the local pulses are exerted on all qubits, the entanglement can be fixed around the entanglement of the initial state. Similarly, in the four-qubit cluster state case, if a series of flip operations is exerted on all qubits, it is shown that the multipartite entanglement can be recovered to the maximum 1.0. All these results show that this protocol can protect remote multipartite entanglement effectively. The physical mechanism behind this scheme is that the weak measurement combining with flip operation can balance the weight of different terms of the state, and move the entanglement toward the initial value. To summarize, our scheme is much simpler and feasible, which may warrant its experimental realization. Moreover, our scheme could be extended to protect other multipartite states.