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arXiv:1502.07815

Scaling Behavior in the Decoherence of Decoupled Multi-spin System

Jun Jing, Xuedong Hu

Published Feb 27, 2015• 0 citations
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Abstract

We study the scaling of decoherence of decoupled electron spin qubits due to hyperfine interaction. For a superposed state consisting of product states from a single Zeeman manifold, both $T_2^*(n)$ and $T_2(n)$ are scale-free with respect to $n$ and the number of basis states, $m$. For a superposed state made up of states from different Zeeman manifolds, both $T_2(n)$ and $T_2^*(n)$ are roughly inversely proportional to $\sqrt{n}$. Our results can be extended to other decoherence mechanisms, including in the presence of dynamical decoupling, which allow meaningful discussions on the scalability of spin-based coherent solid state quantum technology.

DOI
10.48550/arxiv.1502.07815

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We study the scaling of decoherence of decoupled electron spin qubits due to hyperfine interaction. For a superposed state consisting of product states from a single Zeeman manifold, both T2∗(n)T_2^*(n)T2∗​(n) and T2(n)T_2(n)T2​(n) are scale-free with respect to nnn and the number of basis states, mmm. For a superposed state made up of states from different Zeeman manifolds, both T2(n)T_2(n)T2​(n) and T2∗(n)T_2^*(n)T2∗​(n) are roughly inversely proportional to n\sqrt{n}n​. Our results can be extended to other decoherence mechanisms, including in the presence of dynamical decoupling, which allow meaningful discussions on the scalability of spin-based coherent solid state quantum technology.
Significant experimental progresses in recent years have generated continued interest in quantum computation. A practical quantum computer would employ thousands if not millions of coherent qubits, and maintaining coherence in such a large system would be imperative for its utility. As an attempt at understanding the quantum coherence of multiple qubits, here we study decoherence of a multi-spin-qubit state under the influence of hyperfine interaction, and clearly demonstrate that the state structure is crucial to the scaling behavior of n-spin decoherence. Specifically, we find that coherence times of a multi-spin state at most scale with the number of qubits n as √n, while some states with higher symmetries have scale-free coherence with respect to n. Statistically, convergence to these scaling behavior is generally determined by the size of the Hilbert space m, which is usually much larger than n (up to an exponential function of n), so that convergence rate is very fast as we increase the number of qubits. Our results can be extended to other decoherence mechanisms, including in the presence of dynamical decoupling, which allow meaningful discussions on the scalability of spin-based quantum coherent technology.
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The dynamics and decoherence of an electronic spin-1/2 qubit coupled to a bath of nuclear spins via hyperfine interactions in a quantum dot is studied. We show how exact results from the integrable solution can be used to understand the dynamic behavior of the qubit. It is possible to predict the main frequency contributions and their broadening for relatively general initial states analytically, leading to an estimate of the corresponding decay times, which are related to T1{T}_{1}T1​ of the electron. Furthermore, for a small bath polarization, a distinct low-frequency time scale is observed.
The dominant source of decoherence for an electron spin in a quantum dot is the hyperfine interaction with the surrounding bath of nuclear spins. The decoherence process may be slowed down by subjecting the electron spin to suitable sequences of external control pulses. We investigate the performance of a variety of dynamical decoupling protocols using exact numerical simulation. Emphasis is given to realistic pulse delays and the long-time limit, beyond the domain where available analytical approaches are guaranteed to work. Our results show that both deterministic and randomized protocols are capable to significantly prolong the electron coherence time, even when using control pulse separations substantially larger than what expected from the upper cutoff frequency of the coupling spectrum between the electron and the nuclear spins. In a realistic parameter range, the total width of such a coupling spectrum appears to be the physically relevant frequency scale affecting the overall quality of the decoupling.