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Chinese Control Conference (CCC)

Constructing noise filter by dynamical decoupling

Yu Pan, Zairong Xi, Wei Cui

Published Jul 22, 2011• 0 citations
OpenAlex

Abstract

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.

Related papers

Optimized dynamical decoupling sequences in protecting two-qubit states

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Aperiodic dynamical decoupling (DD) sequences of π pulses are of great interest to decoherence control and have been recently extended from single-qubit to two-qubit systems. If the environmental noise power spectrum is made available, then one may further optimize aperiodic DD sequences to reach higher efficiency of decoherence suppression than known universal schemes. This possibility is investigated in this work for the protection of two-qubit states, using an exactly solvable pure dephasing model including both local and nonlocal noise. The performance of optimized DD sequences in protecting two-qubit states is compared with that achieved by nested Uhrig's DD (nested-UDD) sequences, for several different types of noise spectrum. Except for the cases with noise spectrum decaying slowly in the high-frequency regime, optimized DD sequences with tens of control pulses can perform orders of magnitude better than that of nested-UDD. A two-qubit system with highly unbalanced local noise is also examined to shed more light on a recent experiment. Possible experiments that may be motivated by this work are discussed.

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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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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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Controlling decoupled quantum system

Yu Pan, Zairong Xi, Wei Cui

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.

Chinese Control Conference (CCC)•Jul 29, 2010•0 citations
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.
Aperiodic dynamical decoupling (DD) sequences of π pulses are of great interest to decoherence control and have been recently extended from single-qubit to two-qubit systems. If the environmental noise power spectrum is made available, then one may further optimize aperiodic DD sequences to reach higher efficiency of decoherence suppression than known universal schemes. This possibility is investigated in this work for the protection of two-qubit states, using an exactly solvable pure dephasing model including both local and nonlocal noise. The performance of optimized DD sequences in protecting two-qubit states is compared with that achieved by nested Uhrig's DD (nested-UDD) sequences, for several different types of noise spectrum. Except for the cases with noise spectrum decaying slowly in the high-frequency regime, optimized DD sequences with tens of control pulses can perform orders of magnitude better than that of nested-UDD. A two-qubit system with highly unbalanced local noise is also examined to shed more light on a recent experiment. Possible experiments that may be motivated by this work are discussed.
In quantum information processing, it is vital to protect the coherence of qubits in noisy environments. Dynamical decoupling (DD), which applies a sequence of flips on qubits and averages the qubit-environment coupling to zero, is a promising strategy compatible with other desired functionalities, such as quantum gates. Here, we review the recent progresses in theories of dynamical decoupling and experimental demonstrations. We give both semiclassical and quantum descriptions of the qubit decoherence due to coupling to noisy environments. Based on the quantum picture, a geometrical interpretation of DD is presented. The periodic Carr-Purcell-Meiboom-Gill DD and the concatenated DD are reviewed, followed by a detailed exploration of the recently developed Uhrig DD, which employs the least number of pulses in an unequally spaced sequence to suppress the qubit-environment coupling to a given order of the evolution time. Some new developments and perspectives are also discussed.
Abstract Dynamical decoupling (DD) is a quantum error-mitigation technique based on applying sequences of control pulses to suppress decoherence. Here we perform a numerical study to compare different DD protocols, namely Carr-Purcell-Meiboom-Gill (CPMG), Periodic Dynamical Decoupling (PDD), Concatenated Dynamical Decoupling (CDD) and Uhrig Dynamical Decoupling (UDD) applied to three commonly used noise power spectral densities: (i) white, (ii) 1/f, (iii) 1/f 2 and their hybrid combinations. By ignoring qubit relaxation, we simulate these protocols focusing purely on dephasing noise. We then consider independent multi-axial noise with uniaxial control pulses. The effective coherence times T2,eff are extracted for each case and compared with the baseline free induction decay T ∗ 2 [6]. In all these simulations, the time-domain decoherence profiles follow a stretched exponential form ∼ exp −(t/T2,eff) β with the effective coherence times dependent on the noise spectrum considered, the strength of the noise, and the DD sequence employed. An exception is observed for the UDD under specific noise conditions where it cannot be described by a simple stretched exponential decay form.
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.
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.