Quantum Sensing of Noisy and Complex Systems under Dynamical Control
Abstract
:1. Introduction
2. Bath-Optimized Task-Oriented Control (BOTOC)
2.1. General Formulation of BOTOC
2.2. Dynamical Control of Qubit Dephasing (Decoherence)
2.3. Modulation Forms
2.4. Optimal Decoherence Control of a Qubit
3. Control for Bath Diagnostics
4. Maximized Information on Bath’s Parameters by Dynamical Control
5. Dynamical Control of Quantum Transfer as Means of Diagnosing a Bath in Hybrid Systems
Optimized Transfer from Noisy to Quiet Qubits
6. Dynamical Control of State Transfer via Noisy Quantum Channels and the Implications for Sensing Diagnostics
6.1. Boundary Qubit Probes and State Transfer through a Quantum Channel
6.2. Optimized Filter Design for Channel Diagnostics
6.3. Diagnosing Noise Effects in Quantum Channels
- (i)
- Dynamical boundary-control can make the channel most robust against static noise, because it filters out the bath-energies that damage the transfer. In Figure 3c control is shown to be advantageous compared with the static control case , at the expense of increasing the transfer time by only a factor of 2.
- (ii)
- Modulation is not helpful against Markovian noise. Remarkably, arbitrarily high fidelities can then be achieved by slowing down the transfer time, i.e., by decreasing , because in a Markovian bath, the fast coupling fluctuations suppress disorder-localization effects that hamper the transfer fidelity.
- (iii)
- For non-Markovian fluctuating noise that randomly varies with correlation time (Figure 3b), in contrast to Markovian noise with , optimized dynamical control can strongly reduce the infidelity that lies between the static and Markovian limits, provided the bath-spectrum is gapped.
7. Dynamical Control of Multipartite Probes for Bath Diagnostics
7.1. Multipartite Decoherence Matrix
7.2. Multiqubit Probe Modulations for Reconstructing Coupling Spectra
8. Conclusions
- Local modulation can effectively decorrelate the different dephasings of the multiple qubits, i.e., eliminate their cross-decoherence, resulting in their equal dephasing rates. For two qubits, the singlet and triplet Bell-states acquire the same dynamically modified decoherence rate.
- For different couplings to a bath, one can better preserve any initial state by local modulation, which can reduce the mixing with other states, than by global modulation. Local modulation which eliminates the cross-decoherence terms, increases the fidelity more than the global modulation alternative. For two qubits, local modulation better preserves an initial Bell-state, whether a singlet or a triplet, compared to global π-phase “parity kicks.”
8.1. Comparison of Bath-Optimized Task-Oriented Control (BOTOC) to Dynamical Decoupling (DD)
- (i)
- BOTOC relaxes the DD assumption that the control fields must be either very short or very strong. In our formalism, the control fields are considered concurrently with the coupling to the bath, hence allowing a much wider variety of pulse sequences, ranging from continuous modulation all the way to DD sequences.
- (ii)
- Dynamical decoupling suggests using the same pulse sequence (be it periodic, optimized or concatenated), regardless of the shape of the bath spectrum. By contrast, BOTOC explicitly considers the bath spectrum and allows optimal tailoring of the modulation to a given bath spectrum. In many cases, the standard π-phase “bang-bang” is then found to be inadequate or non-optimal compared to dynamic control based on the optimization of the universal formula. Whereas our BOTOC approach reduces to the DD method in the particular case of proper dephasing or decay via coupling to spectrally symmetric (e.g., Lorentzian or Gaussian) noise baths with limited spectral width, phase modulation advocated for the suppression of coupling to baths with frequency cutoff or other non-monotonic spectra is, however, drastically different from the DD method which may fail for multipeak spectra.
- (iii)
- Our BOTOC universal strategy has far broader applicability than DD: It can simultaneously control, unlike DD [10,11], both decay and decoherence (proper dephasing) by either pulsed or continuous wave (CW) modulation of the system-bath coupling governed by a simple universal formula. BOTOC has been generalized by us to finite temperatures and to qubits driven by an arbitrary time-dependent field, which may cause the failure of the rotating-wave approximation [11]. It has also been extended to the analysis of multi-level systems, where quantum interference between the levels may either inhibit or accelerate the decay [19].
- (iv)
- Even if DD is adequate for independently decohering qubits, its extension to correlated multipartite systems is highly nontrivial. By contrast, BOTOC modulations with low energy decorrelate the different proper dephasings of the multiple two-level systems (TLS), resulting in equal dephasing rates for all states. For two TLS, we have shown that the singlet and triplet Bell-states acquire the same dynamically modified dephasing rate. This should be beneficial compared to standard DD based on global “bang-bang” (π-phase flips) if both the triplet and the singlet states are used (intermittently) for information transmission or storage.
8.2. Open Issues—Outlook
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Kurizki, G.; Alvarez, G.A.; Zwick, A. Quantum Sensing of Noisy and Complex Systems under Dynamical Control. Technologies 2017, 5, 1. https://doi.org/10.3390/technologies5010001
Kurizki G, Alvarez GA, Zwick A. Quantum Sensing of Noisy and Complex Systems under Dynamical Control. Technologies. 2017; 5(1):1. https://doi.org/10.3390/technologies5010001
Chicago/Turabian StyleKurizki, Gershon, Gonzalo A. Alvarez, and Analia Zwick. 2017. "Quantum Sensing of Noisy and Complex Systems under Dynamical Control" Technologies 5, no. 1: 1. https://doi.org/10.3390/technologies5010001