Combining dynamical decoupling with fault-tolerant quantum computation

Ng, Hui Khoon; Lidar, Daniel A.; Preskill, John

doi:10.1103/physreva.84.012305

Cited by 96 publications

(144 citation statements)

References 77 publications

(161 reference statements)

Supporting

Mentioning

137

Contrasting

Unclassified

Order By: Relevance

“…DD does not require auxiliary qubits or measurements, and it may be helpful for reaching the error threshold for reliable quantum computation. Some theoretical works [76][77][78][79] proposed methods for combining DD with quantum error correction. Future research on DD will also consider applications outside QIP.…”

Section: Discussionmentioning

confidence: 99%

“…In most cases, the goal is to preserve a given input state, but it may also be combined with gate operations [76][77][78][79][80]. Decoherence effects due to the environment can in principle be reduced by shortening the cycle time t c .…”

Section: Introductionmentioning

confidence: 99%

“…Clearly, this procedure is limited by finite field strengths and associated pulse durations. Within these limitations, the goal remains to find those sequences that provide the best possible decoupling performance [45,54,55,67,[81][82][83][84]. Furthermore, the pulses do not only have finite lengths, they also do not implement perfect rotations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust dynamical decoupling

Souza

Álvarez

Suter

2012

Phil. Trans. R. Soc. A.

194

View full text Add to dashboard Cite

Quantum computers, which process information encoded in quantum mechanical systems, hold the potential to solve some of the hardest computational problems. A substantial obstacle for the further development of quantum computers is the fact that the lifetime of quantum information is usually too short to allow practical computation. A promising method for increasing the lifetime, known as dynamical decoupling (DD), consists of applying a periodic series of inversion pulses to the quantum bits. In the present review, we give an overview of this technique and compare different pulse sequences proposed earlier. We show that pulse imperfections, which are always present in experimental implementations, limit the performance of DD. The loss of coherence due to the accumulation of pulse errors can even exceed the perturbation from the environment. This effect can be largely eliminated by a judicious design of pulses and sequences. The corresponding sequences are largely immune to pulse imperfections and provide an increase of the coherence time of the system by several orders of magnitude.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust dynamical decoupling

Souza

Álvarez

Suter

2012

Phil. Trans. R. Soc. A.

194

View full text Add to dashboard Cite

show abstract

“…They increase exponentially with the DD order. Even though the exponentially increasing number of control pulses does yield significant improvement of precision (through reduction of the coefficient in front of the power of time T N+1 ) [11,35,36], implementation of CDD to high orders is challenging in experiments since errors are inevitably introduced in each control pulse.…”

Section: (T ) ≡ U(t ) and The Superscript C Denoting The Nesting Schementioning

confidence: 99%

Protection of quantum systems by nested dynamical decoupling

Wang

Liu

2011

Phys. Rev. A

View full text Add to dashboard Cite

Based on a theorem we establish on dynamical decoupling of time-dependent systems, we present a scheme of nested Uhrig dynamical decoupling (NUDD) to protect multi-qubit systems in generic quantum baths to arbitrary decoupling orders, using only single-qubit operations. The number of control pulses in NUDD increases polynomially with the decoupling order. For general multi-level systems, this scheme can preserve a set of unitary Hermitian system operators which mutually either commute or anti-commute, and hence all operators in the Lie algebra generated from this set of operators, generating an effective symmetry group for the system up to a given order of precision. NUDD can be implemented with pulses of finite amplitude, up to an error in the second order of the pulse durations.

show abstract

“…Now, the total Hamiltonian describing the control pulse sequence plus the system and environment in such a "toggling frame" [42][43][44] can be written as:…”

Section: Modified Qsd Equation For Dephasing Noisementioning

confidence: 99%

Uhrig dynamical control of a three-level system via non-Markovian quantum state diffusion

Shu

Zhao

Jing

et al. 2013

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

In this paper, we use the quantum state diffusion (QSD) equation to implement the Uhrig dynamical decoupling (UDD) to a three-level quantum system coupled to a non-Markovian reservoir comprising of infinite numbers of degrees of freedom. For this purpose, we first reformulate the nonMarkovian QSD to incorporate the effect of the external control fields. With this stochastic QSD approach, we demonstrate that an unknown state of the three-level quantum system can be universally protected against both colored phase and amplitude noises when the control-pulse sequences and control operators are properly designed. The advantage of using non-Markovian quantum state diffusion equations is that the control dynamics of open quantum systems can be treated exactly without using Trotter product formula and be efficiently simulated even when the environment comprise of infinite numbers of degrees of freedom. We also show how the control efficacy depends on the environment memory time and the designed time points of applied control pulses.

show abstract

Combining dynamical decoupling with fault-tolerant quantum computation

Cited by 96 publications

References 77 publications

Robust dynamical decoupling

Robust dynamical decoupling

Protection of quantum systems by nested dynamical decoupling

Uhrig dynamical control of a three-level system via non-Markovian quantum state diffusion

Contact Info

Product

Resources

About