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Scientific Reports

Scaling of decoherence for a system of uncoupled spin qubits

Jun Jing, Xuedong Hu

Published Nov 23, 2015• 3 citations
Publisher

Abstract

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.

DOI
10.1038/srep17013

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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.
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.
Decoherence causes the decay of the quantum information that is stored in highly correlated states during quantum computation. It is thus a limiting factor for all implementations of a quantum computer. Because a scalable quantum computer with hundreds or thousands of qubits is not available yet, experimental data about decoherence rates was restricted to small quantum registers. With solid state nuclear magnetic resonance we create highly correlated multiqubit states that serve as a model quantum register and measure their decay. By measuring the decay as a function of the system size, we determined the scaling of the decoherence rate with the number of qubits. Using the same system, we also used decoupling techniques to reduce the coupling between system and environment and thereby the decoherence rate by more than an order of magnitude, independent of the system size. For the free decay as well as for the decoupled case, we found a relatively weak scaling with system size, which could be fitted to a power law $\ensuremath{\propto}{\overline{K}}^{p}$ with an exponent $p\ensuremath{\approx}1∕2$. This raises the prospect for large-scale quantum computation.
We address the quantum dynamics of a system composed of a qubit globally coupled to a many-body system characterized by short-range interactions. We employ a dynamic finite-size scaling framework to investigate the out-of-equilibrium dynamics arising from the sudden variation (turning on) of the interaction between the qubit and the many-body system, in particular when the latter is in proximity to a quantum first-order or continuous-phase transition. Although the approach is quite general, we consider ddd-dimensional quantum Ising spin models in the presence of transverse and longitudinal fields as paradigmatic quantum many-body systems. To characterize the out-of-equilibrium dynamics, we focus on a number of quantum-information-oriented properties of the model. Namely, we concentrate on the decoherence features of the qubit, the energy interchange between the qubit and the many-body system during the out-of-equilibrium dynamics, and the work distribution associated with the quench. The scaling behaviors predicted by the dynamic finite-size scaling theory are verified through extensive numerical computations for the one-dimensional Ising model, which reveal a fast convergence to the expected asymptotic behavior with increasing system size.
Decoherence, i.e. the decay of coherences in a quantum system due to the coupling to an environment with many uncontrolled degrees of freedom, plays a key role in the transition from quantum mechanics to classical mechanics. Decoherence is also one of the main obstacles on the road to a large scale quantum computer, and the question whether or not one will be able in principle to maintain and manipulate coherent superpositions of an exponentially large number of states of a few thousand qubits, has become of fundamental interest. Here I show that the decoherence of superpositions of many-qubit code words in a quantum memory is governed by a generalized Hamming distance (called ``decoherence metric'') between the code words, with a time dependent metric tensor that is specific for the heat bath. The decoherence metric allows for the complete characterization of the decoherence of all possible superpositions of code-words, and for an optimization of the over-all decoherence. I apply the theory to quantum memories based on neutral atoms in optical lattices and in atomic gases, interacting with black body radiation as source of decoherence. Additional atoms, which are not addressed in the memory, can become an important source of decoherence.
Among the most important parameters for the usefulness of quantum computers are the size of the quantum register and the decoherence time for the quantum information. The decoherence time is expected to get shorter with the number of correlated qubits, but experimental data are only available for small numbers of qubits. Solid-state nuclear magnetic resonance allows one to correlate large numbers of qubits (several hundred) and measure their decoherence rates. We use a modified magnetic dipole-dipole interaction to correlate the proton spins in a solid sample and observe the decay of the resulting highly correlated states. By systematically varying the number of correlated spins, we measure the increase of the decoherence rate with the size of the quantum register.
Abstract — We review results in theoretical modeling of quantum systems in support of the studies of decoherence and qubit interactions for quantum information processing. The developed modeling tools have been applied to semiconductor materials and nanostructures that show promise for implementation of coherent, controlled quantum dynamics at the level of registers of several quantum bits (qubits), such as spins. Field-theoretical techniques have been utilized to address decoherence and more generally the origin and effects of quantum noise and the loss of entanglement in quantum dynamics of qubits and several-qubit registers. Qubit coupling mechanisms via the indirect exchange interaction have been investigated, and quantum computing designs have been evaluated for scalability. We also describe general and specific research challenges, the solution of which will advance the field of modeling “open quantum systems ” to further our understanding of how environmental influences affect quantum coherence and its loss during quantum dynamics.