Physical Review A

Scalability of decoherence control in entangled systems

Goren Gordon, Gershon Kurizki

Published Mar 30, 2011• 17 citations

Abstract

We investigate the scaling of decoherence rates and their dynamical suppression with the number $N$ of qubits in various entangled states. Remarkably, for sufficiently large $N$, coherence time is always in the Zeno regime. This changes the scaling to the square root of the Markov-regime scaling. We find that a simple and effective control strategy is to locally modulate the individual qubits and thereby not only suppress the decoherence rate of each qubit, but also reduce the decoherence scaling of entangled states that are particularly fragile, from ${N}^{2}$ to $N$, resulting in a dramatic reduction of the decoherence (by orders of magnitude). Surprisingly, the conditions for the effectiveness of such decoherence control are independent of $N$.

DOI: 10.1103/physreva.83.032321

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Physical Review A

Scalability of decoherence control in entangled systems

Goren Gordon, Gershon Kurizki

Published Mar 30, 2011• 17 citations

Publisher

Abstract

We investigate the scaling of decoherence rates and their dynamical suppression with the number

N

of qubits in various entangled states. Remarkably, for sufficiently large

N

, coherence time is always in the Zeno regime. This changes the scaling to the square root of the Markov-regime scaling. We find that a simple and effective control strategy is to locally modulate the individual qubits and thereby not only suppress the decoherence rate of each qubit, but also reduce the decoherence scaling of entangled states that are particularly fragile, from

{N}^{2}

N

, resulting in a dramatic reduction of the decoherence (by orders of magnitude). Surprisingly, the conditions for the effectiveness of such decoherence control are independent of

N

DOI: 10.1103/physreva.83.032321

Related papers

Decoherence scaling transition in the dynamics of quantum information scrambling

Federico D. Domínguez, María Cristina Rodríguez, Robin Kaiser +2 more

Reliable processing of quantum information for developing quantum technologies requires precise control of out-of-equilibrium many-body systems. This is a highly challenging task because the fragility of quantum states to external perturbations increases with the system size. Here, we report on a series of experimental quantum simulations that quantify the sensitivity of a controlled Hamiltonian evolution to perturbations that drive the system away from the targeted evolution. Based on out-of-time ordered correlations, we demonstrate that the decay rate of the process fidelity increases with the effective number $K$ of correlated qubits as ${K}^{\ensuremath{\alpha}}$. As a function of the perturbation strength, we observe a decoherence scaling transition of the exponent $\ensuremath{\alpha}$ between two distinct dynamical regimes. In the limiting case below the critical perturbation strength, the exponent $\ensuremath{\alpha}$ drops sharply below 1, and there is no inherent limit to the number of qubits that can be controlled. This resilient quantum feature of the controlled dynamics of quantum information is promising for reliable control of large quantum systems.Reliable processing of quantum information for developing quantum technologies requires precise control of out-of-equilibrium many-body systems. This is a highly challenging task because the fragility of quantum states to external perturbations increases with the system size. Here, we report on a series of experimental quantum simulations that quantify the sensitivity of a controlled Hamiltonian evolution to perturbations that drive the system away from the targeted evolution. Based on out-of-time ordered correlations, we demonstrate that the decay rate of the process fidelity increases with the effective number $K$ of correlated qubits as ${K}^{\ensuremath{\alpha}}$. As a function of the perturbation strength, we observe a decoherence scaling transition of the exponent $\ensuremath{\alpha}$ between two distinct dynamical regimes. In the limiting case below the critical perturbation strength, the exponent $\ensuremath{\alpha}$ drops sharply below 1, and there is no inherent limit to the number of qubits that can be controlled. This resilient quantum feature of the controlled dynamics of quantum information is promising for reliable control of large quantum systems.

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Bryan J. Dalton

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Scaling of decoherence for a system of uncoupled spin qubits

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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.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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Markovian regime decoherence effects in quantum computers are studied in terms of the fidelity for the situation where the number of qubits N becomes large. A standard model involving three‐state lambda system ionic qubits is considered, with qubits localised around well‐separated positions via trapping potentials. The centre of mass vibrations of the qubits act as a reservoir. Coherent one and two qubit gating processes are controlled by time dependent localised classical EM fields that address specific qubits, the two qubit gating processes being facilitated by a cavity mode ancilla, which permits state interchange between qubits. With suitably chosen parameters, the decoherence time can be made essentially independent of N.Markovian regime decoherence effects in quantum computers are studied in terms of the fidelity for the situation where the number of qubits N becomes large. A standard model involving three‐state lambda system ionic qubits is considered, with qubits localised around well‐separated positions via trapping potentials. The centre of mass vibrations of the qubits act as a reservoir. Coherent one and two qubit gating processes are controlled by time dependent localised classical EM fields that address specific qubits, the two qubit gating processes being facilitated by a cavity mode ancilla, which permits state interchange between qubits. With suitably chosen parameters, the decoherence time can be made essentially independent of N.

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We analyze and compare three different strategies, all aimed at controlling and eventually halting decoherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions (``bang-bang'' pulses and their generalization, quantum dynamical decoupling), and the third uses a strong, continuous coupling. Decoherence is shown to be suppressed only if the frequency $N$ of the measurements or pulses is large enough or if the coupling $K$ is sufficiently strong. Otherwise, if $N$ or $K$ is large, but not extremely large, all these control procedures accelerate decoherence. We investigate the problem in a general setting and then consider some practical examples, relevant for quantum computation.We analyze and compare three different strategies, all aimed at controlling and eventually halting decoherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions (``bang-bang'' pulses and their generalization, quantum dynamical decoupling), and the third uses a strong, continuous coupling. Decoherence is shown to be suppressed only if the frequency $N$ of the measurements or pulses is large enough or if the coupling $K$ is sufficiently strong. Otherwise, if $N$ or $K$ is large, but not extremely large, all these control procedures accelerate decoherence. We investigate the problem in a general setting and then consider some practical examples, relevant for quantum computation.

arXiv:quant-ph/0403205Physical Review AFeb 8, 2005213 citations

We investigate the scaling of decoherence rates and their dynamical suppression with the number

N

of qubits in various entangled states. Remarkably, for sufficiently large

N

{N}^{2}

N

, resulting in a dramatic reduction of the decoherence (by orders of magnitude). Surprisingly, the conditions for the effectiveness of such decoherence control are independent of

N

K

of correlated qubits as ${K}^{\ensuremath{\alpha}}$. As a function of the perturbation strength, we observe a decoherence scaling transition of the exponent $\ensuremath{\alpha}$ between two distinct dynamical regimes. In the limiting case below the critical perturbation strength, the exponent $\ensuremath{\alpha}$ drops sharply below 1, and there is no inherent limit to the number of qubits that can be controlled. This resilient quantum feature of the controlled dynamics of quantum information is promising for reliable control of large quantum systems.

N

of the measurements or pulses is large enough or if the coupling

K

is sufficiently strong. Otherwise, if

N

K

is large, but not extremely large, all these control procedures accelerate decoherence. We investigate the problem in a general setting and then consider some practical examples, relevant for quantum computation.