Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0509157 · Physical Review A

Identifying a two-state Hamiltonian in the presence of decoherence

Jared H. Cole, Andrew D. Greentree, Daniel K. L. Oi, Sonia G. Schirmer, Cameron J. Wellard, Lloyd C. L. Hollenberg

Published Jun 27, 2006• 40 citations
arXivHTMLPDF

Abstract

Mapping the system evolution of a two-state system allows the determination of the effective system Hamiltonian directly. We show how this can be achieved even if the system is decohering appreciably over the observation time. A method to include various decoherence models is given and the limits of this technique are explored. This technique is applicable both to the problem of calibrating a control Hamiltonian for quantum computing applications and for precision experiments in two-state quantum systems. The accuracy of the results obtained with this technique are ultimately limited by the validity of the decoherence model used.

DOI
10.1103/physreva.73.062333

Related papers

Dynamical suppression of decoherence in two-state quantum systems

Lorenza Viola, Seth Lloyd

The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radio-frequency pulses that repetitively flip the state of the system, a technique that can be termed quantum ``bang-bang'' control after its classical analog. Decoherence introduced by the system's interaction with a quantum environment is shown to be washed out completely in the limit of continuous flipping and greatly suppressed provided the interval between the pulses is made comparable to the correlation time of the environment. The model suggests a strategy to fight against decoherence that complements existing quantum error-correction techniques.

arXiv:quant-ph/9803057•Physical Review A•Oct 1, 1998•1,580 citations

Identifying an experimental two-state Hamiltonian to arbitrary accuracy

Jared H. Cole, Sonia G. Schirmer, Andrew D. Greentree +3 more

Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on these parameters. This method requires only one measurement basis and the ability to initialize the system in some arbitrary state which is not an eigenstate of the Hamiltonian in question. The scaling of the uncertainty is studied for large numbers of measurements and found to be proportional to the reciprocal of the square root of the number of measurements.

arXiv:quant-ph/0501116•Physical Review A•Jun 14, 2005•84 citations

Time-averaged quantum dynamics and the validity of the effective Hamiltonian model

Omar Gamel, Daniel F. V. James

We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the general equation to harmonic Hamiltonians, we confirm a previous formula for the effective Hamiltonian together with a additional decoherence term which should, in general, be included and whose vanishing provides the criteria for validity of the effective Hamiltonian approach. Finally, we apply the theory to examples of the ac Stark shift and three-level Raman transitions, recovering a decoherence effect in the latter.

arXiv:1007.1789•Physical Review A•Nov 8, 2010•107 citations

Precision characterization of two-qubit Hamiltonians via entanglement mapping

Jared H. Cole, Simon J. Devitt, Lloyd C. L. Hollenberg

We demonstrate a method to characterize the general Heisenberg Hamiltonian with non-uniform couplings by mapping the entanglement it generates as a function of time. Identification of the Hamiltonian in this way is possible as the coefficients of each operator control the oscillation frequencies of the entanglement function. The number of measurements required to achieve a given precision in the Hamiltonian parameters is determined and an efficient measurement strategy designed. We derive the relationship between the number of measurements, the resulting precision and the ultimate discrete error probability generated by a systematic mis-characterization. This has important implications when implementing two-qubit gates for fault-tolerant quantum computation.

arXiv:quant-ph/0508229•Journal of Physics A Mathematical and General•Nov 8, 2006•19 citations

Quantum Noise Control Algorithms in Quantum Computing

Jincheng Zhang

Quantum computing holds immense promise for revolutionizing computation, yet its practical realization is severely hampered by the pervasive issue of quantum noise. This noise, arising from various sources including environmental interactions and imperfect control, introduces errors into quantum computations, degrading their fidelity. This paper explores novel control algorithms designed to mitigate the detrimental effects of quantum noise. We investigate the underlying mechanisms generating noise and propose a method based on precise qubit control and calibration to minimize its impact. The core claim is that effective noise control is crucial for achieving reliable quantum computation. The proposed algorithms leverage feedback control and adaptive calibration techniques to dynamically compensate for noise fluctuations, aiming to enhance the accuracy and robustness of quantum algorithms. The mathematical framework presented includes noise models, control equations, and performance metrics, demonstrating the feasibility and potential of this approach. Specifically, we introduce a closed-loop control system described by the equation: (Δsn+1 = K(en - sn)) + wn+1, where Δsn+1 represents the change in state, K is the gain, en is the desired state, sn is the actual state, and wn+1 is the noise term. We also examine the effect of decoherence, modeled as: ds = Hdt + Vd, where ds is the time evolution of the quantum state, H is the Hamiltonian describing the system, dt is the time step, and Vd is the damping term due to noise. The research aims to contribute towards the development of more robust and practical quantum computers.

•Aug 31, 2026•0 citations

Physics-based mathematical models for quantum devices via experimental system identification

S. G. Schirmer, Daniel K. L. Oi, Simon J. Devitt

We consider the task of intrinsic control system identification for quantum devices. The problem of experimental determination of subspace confinement is considered, and simple general strategies for full Hamiltonian identification and decoherence characterization of a controlled two-level system are presented.

arXiv:0805.2725•Journal of Physics Conference Series•Mar 1, 2008•12 citations
Mapping the system evolution of a two-state system allows the determination of the effective system Hamiltonian directly. We show how this can be achieved even if the system is decohering appreciably over the observation time. A method to include various decoherence models is given and the limits of this technique are explored. This technique is applicable both to the problem of calibrating a control Hamiltonian for quantum computing applications and for precision experiments in two-state quantum systems. The accuracy of the results obtained with this technique are ultimately limited by the validity of the decoherence model used.
The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radio-frequency pulses that repetitively flip the state of the system, a technique that can be termed quantum ``bang-bang'' control after its classical analog. Decoherence introduced by the system's interaction with a quantum environment is shown to be washed out completely in the limit of continuous flipping and greatly suppressed provided the interval between the pulses is made comparable to the correlation time of the environment. The model suggests a strategy to fight against decoherence that complements existing quantum error-correction techniques.
Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on these parameters. This method requires only one measurement basis and the ability to initialize the system in some arbitrary state which is not an eigenstate of the Hamiltonian in question. The scaling of the uncertainty is studied for large numbers of measurements and found to be proportional to the reciprocal of the square root of the number of measurements.
We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the general equation to harmonic Hamiltonians, we confirm a previous formula for the effective Hamiltonian together with a additional decoherence term which should, in general, be included and whose vanishing provides the criteria for validity of the effective Hamiltonian approach. Finally, we apply the theory to examples of the ac Stark shift and three-level Raman transitions, recovering a decoherence effect in the latter.
We demonstrate a method to characterize the general Heisenberg Hamiltonian with non-uniform couplings by mapping the entanglement it generates as a function of time. Identification of the Hamiltonian in this way is possible as the coefficients of each operator control the oscillation frequencies of the entanglement function. The number of measurements required to achieve a given precision in the Hamiltonian parameters is determined and an efficient measurement strategy designed. We derive the relationship between the number of measurements, the resulting precision and the ultimate discrete error probability generated by a systematic mis-characterization. This has important implications when implementing two-qubit gates for fault-tolerant quantum computation.
Quantum computing holds immense promise for revolutionizing computation, yet its practical realization is severely hampered by the pervasive issue of quantum noise. This noise, arising from various sources including environmental interactions and imperfect control, introduces errors into quantum computations, degrading their fidelity. This paper explores novel control algorithms designed to mitigate the detrimental effects of quantum noise. We investigate the underlying mechanisms generating noise and propose a method based on precise qubit control and calibration to minimize its impact. The core claim is that effective noise control is crucial for achieving reliable quantum computation. The proposed algorithms leverage feedback control and adaptive calibration techniques to dynamically compensate for noise fluctuations, aiming to enhance the accuracy and robustness of quantum algorithms. The mathematical framework presented includes noise models, control equations, and performance metrics, demonstrating the feasibility and potential of this approach. Specifically, we introduce a closed-loop control system described by the equation: (Δsn+1 = K(en - sn)) + wn+1, where Δsn+1 represents the change in state, K is the gain, en is the desired state, sn is the actual state, and wn+1 is the noise term. We also examine the effect of decoherence, modeled as: ds = Hdt + Vd, where ds is the time evolution of the quantum state, H is the Hamiltonian describing the system, dt is the time step, and Vd is the damping term due to noise. The research aims to contribute towards the development of more robust and practical quantum computers.