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Chinese Control Conference (CCC)

Controlling decoupled quantum system

Yu Pan, Zairong Xi, Wei Cui

Published Jul 29, 2010• 0 citations
OpenAlex

Abstract

Dynamical decoupling (DD) eliminates qubit-bath coupling by applying a sequence of instantaneous pulses. While qubit-bath couplings generally lead to qubit relaxation and dephasing, qubit-qubit couplings are often used to manipulate or control quantum states. We investigate the available control operations in two DD schemes, named periodic DD (PDD) and Uhrig DD (UDD), to see whether universal quantum computation can be realized in these decoupled systems. We find that universal control is possible using Heisenberg interaction in both periodically decoupled system and Uhrig decoupled system, and the available control operations under two kinds of DD sequences obey the same commutation relation. In the UDD case, we also derive a rough bound for control errors.

Related papers

Dynamical decoupling in common environment

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Dynamical decoupling (DD) sequences were invented to eliminate the direct coupling between a qubit and its environment. We further investigate the possibility of decoupling the indirect qubit–qubit interaction induced by a common environment, and successfully find simplified solutions that preserve the bipartite quantum states to arbitrary order. Through analysing the exact dynamics of the controlled two-qubit density matrix, we have proven that applying independent Uhrig DD (UDD) on each qubit will effectively eliminate both the qubit–environment and indirect qubit–qubit couplings to the same order as in the single-qubit case, only if orders of the two UDD sequences have different parities. More specifically, UDD( n ) on one qubit with UDD( m ) on another are able to produce min ( n , m )th-order suppression while n + m is odd. Our results can be used to reduce the pulse number in relevant experiments for protecting bipartite quantum states, or dynamically manipulating the indirect interaction within a certain quantum gate and quantum bus.

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动态去耦(DD ) 消除由使用即时脉搏的一个序列联合的 qubit 洗澡。当时 qubit 洗澡 couplings 通常导致 qubit 松驰和 dephasing， qubit-qubit couplings 经常被用来操作或控制量状态。我们在二个 DD 计划，命名周期的 DD (PDD ) 和 Uhrig DD (UDD ) 调查可得到的控制操作，到看通用的量计算是否能在这些 decoupled 系统被认识到。我们发现通用控制周期性地用在两个的海森堡相互作用是可能的 decoupled 系统和 Uhrig decoupled 系统，和在二种 DD 序列下面的可得到的控制操作服从一样的交换关系。在 UDD 案例中，我们也为控制错误导出不平的界限。

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Dynamical decoupling of a qubit with always-on control fields

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Dynamical decoupling (DD) emerges as a promising tool to suppress decoherence of quantum systems by eliminating the system-environment coupling. We investigate its power in combating pure dephasing of a qubit under random classical noise. Interestingly, the decoherence rate can be viewed as the interplay between noise spectrum and a controllable filter function. More specifically, the filter function is determined by the DD sequence we employed. Here we take Uhrig DD (UDD) as a benchmark sequence to illustrate the filtering process. We find that UDD sequence works as a perfect dynamical filter for low-frequency noise. For spectrum with hard cutoff, UDD increases the performance order by order with linearly increased number of pulses. However, for noise spectrum with soft cutoff, the required pulse number grows exponentially.

Chinese Control Conference (CCC)•Jul 22, 2011•0 citations
Dynamical decoupling (DD) eliminates qubit-bath coupling by applying a sequence of instantaneous pulses. While qubit-bath couplings generally lead to qubit relaxation and dephasing, qubit-qubit couplings are often used to manipulate or control quantum states. We investigate the available control operations in two DD schemes, named periodic DD (PDD) and Uhrig DD (UDD), to see whether universal quantum computation can be realized in these decoupled systems. We find that universal control is possible using Heisenberg interaction in both periodically decoupled system and Uhrig decoupled system, and the available control operations under two kinds of DD sequences obey the same commutation relation. In the UDD case, we also derive a rough bound for control errors.
Dynamical decoupling (DD) sequences were invented to eliminate the direct coupling between a qubit and its environment. We further investigate the possibility of decoupling the indirect qubit–qubit interaction induced by a common environment, and successfully find simplified solutions that preserve the bipartite quantum states to arbitrary order. Through analysing the exact dynamics of the controlled two-qubit density matrix, we have proven that applying independent Uhrig DD (UDD) on each qubit will effectively eliminate both the qubit–environment and indirect qubit–qubit couplings to the same order as in the single-qubit case, only if orders of the two UDD sequences have different parities. More specifically, UDD( n ) on one qubit with UDD( m ) on another are able to produce min ( n , m )th-order suppression while n + m is odd. Our results can be used to reduce the pulse number in relevant experiments for protecting bipartite quantum states, or dynamically manipulating the indirect interaction within a certain quantum gate and quantum bus.
Dynamical decoupling (DD) sequences were invented to eliminate the direct coupling between a qubit and its environment. We further investigate the possibility of decoupling the indirect qubit–qubit interaction induced by a common environment, and successfully find simplified solutions that preserve the bipartite quantum states to arbitrary order. Through analysing the exact dynamics of the controlled two-qubit density matrix, we have proven that applying independent Uhrig DD (UDD) on each qubit will effectively eliminate both the qubit–environment and indirect qubit–qubit couplings to the same order as in the single-qubit case, only if orders of the two UDD sequences have different parities. More specifically, UDD(n) on one qubit with UDD(m) on another are able to produce min (n, m)th-order suppression while n + m is odd. Our results can be used to reduce the pulse number in relevant experiments for protecting bipartite quantum states, or dynamically manipulating the indirect interaction within a certain quantum gate and quantum bus.
动态去耦(DD ) 消除由使用即时脉搏的一个序列联合的 qubit 洗澡。当时 qubit 洗澡 couplings 通常导致 qubit 松驰和 dephasing， qubit-qubit couplings 经常被用来操作或控制量状态。我们在二个 DD 计划，命名周期的 DD (PDD ) 和 Uhrig DD (UDD ) 调查可得到的控制操作，到看通用的量计算是否能在这些 decoupled 系统被认识到。我们发现通用控制周期性地用在两个的海森堡相互作用是可能的 decoupled 系统和 Uhrig decoupled 系统，和在二种 DD 序列下面的可得到的控制操作服从一样的交换关系。在 UDD 案例中，我们也为控制错误导出不平的界限。
We consider dynamical decoupling schemes in which the qubit is continuously manipulated by a control field at all times. Building on the theory of the Uhrig dynamical decoupling (UDD) sequence and its connections to Chebyshev polynomials, we derive a method of always-on control by expressing the UDD control field as a Fourier series. We then truncate this series and numerically optimize the series coefficients for decoupling, constructing the Chebyshev and Fourier expansion sequence. This approach generates a bounded, continuous control field. We simulate the decoupling effectiveness of our sequence versus a continuous version of UDD for a qubit coupled to fully-quantum and semi-classical dephasing baths and find comparable performance. We derive filter functions for continuous-control decoupling sequences, and we assess how robust such sequences are to noise on control fields. The methods we employ provide a variety of tools to analyze continuous-control dynamical decoupling sequences.
In this paper, we first present a brief derivation of the dynamical decoupling condition by means of designing control Hamiltonians, which is used to preserve arbitrary quantum states in the case of interactions with environment. According to different time intervals between the adjacent pulses, two important dynamical decoupling schemes: periodic dynamical decoupling (PDD) and Uhrig dynamical decoupling (UDD) are analyzed. Based on the comparison between PDD and UDD, we propose our optimized dynamical decoupling scheme with different time intervals between adjacent pulses which follow a normal distribution. At last numerical simulations are carried out in a three-level atom in Ξ -configuration, we select the non-diagonal element of density matrix as a reference index to compare the performances of suppressing the decoherence of these three strategies, and the results indicate that dynamical decoupling strategy proposed has better performances than that of PDD and UDD have under some low range of the loss of the quantum coherence.
Dynamical decoupling (DD) emerges as a promising tool to suppress decoherence of quantum systems by eliminating the system-environment coupling. We investigate its power in combating pure dephasing of a qubit under random classical noise. Interestingly, the decoherence rate can be viewed as the interplay between noise spectrum and a controllable filter function. More specifically, the filter function is determined by the DD sequence we employed. Here we take Uhrig DD (UDD) as a benchmark sequence to illustrate the filtering process. We find that UDD sequence works as a perfect dynamical filter for low-frequency noise. For spectrum with hard cutoff, UDD increases the performance order by order with linearly increased number of pulses. However, for noise spectrum with soft cutoff, the required pulse number grows exponentially.