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Quantum systems are promising candidates for sensing of weak signals as they can provide unrivaled performance when estimating parameters of external fields. However, when trying to detect weak signals that are hidden by background noise, the signal-to-noise-ratio is a more relevant metric than raw sensitivity. We identify, under modest assumptions about the statistical properties of the signal and noise, the optimal quantum control to detect an external signal in the presence of background noise using a quantum sensor. Interestingly, for white background noise, the optimal solution is the simple and well-known spin-locking control scheme. We further generalize, using numerical techniques, these results to the background noise being a correlated Lorentzian spectrum. We show that for increasing correlation time, pulse based sequences such as CPMG are also close to the optimal control for detecting the signal, with the crossover dependent on the signal frequency. These results show that an optimal detection scheme can be easily implemented in near-term quantum sensors without the need for complicated pulse shaping.
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Quantum systems can be exquisite sensors thanks to their sensitivity to external perturbations. This same characteristic also makes them fragile to external noise. Quantum control can tackle the challenge of protecting quantum sensors from environmental noise, while leaving their strong coupling to the target field to be measured. As the compromise between these two conflicting requirements does not always have an intuitive solution, optimal control based on numerical search could prove very effective. Here we adapt optimal control theory to the quantum sensing scenario, by introducing a cost function that, unlike the usual fidelity of operation, correctly takes into account both the unknown field to be measured and the environmental noise. We experimentally implement this novel control paradigm using a Nitrogen Vacancy center in diamond, finding improved sensitivity to a broad set of time varying fields. The demonstrated robustness and efficiency of the numerical optimization, as well as the sensitivity advantaged it bestows, will prove beneficial to many quantum sensing applications.
Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of quantum revival, i.e., periodic recurrence in the time evolution, can be restored almost completely by coupling the distorted system to an external field obtained from quantum optimal control theory. We demonstrate the procedure with wave-packet calculations in both one- and two-dimensional quantum wells, and analyze the required physical characteristics of the control field. Our results generally show that the inherent dynamics of a quantum system can be idealized at an extremely low cost.
Pulses to steer the time evolution of quantum systems can be designed with optimal control theory. In most cases it is the coherent processes that can be controlled and one optimizes the time evolution towards a target unitary process, sometimes also in the presence of non-controllable incoherent processes. Here we show how to extend the GRAPE algorithm in the case where the incoherent processes are controllable and the target time evolution is a non-unitary quantum channel. We perform a gradient search on a fidelity measure based on Choi matrices. We illustrate our algorithm by optimizing a phase qubit measurement pulse. We show how this technique can lead to large measurement contrast close to 99%. We also show, within the validity of our model, that this algorithm can produce short 1.4 ns pulses with 98.2% contrast.
Quantum metrology comprises a set of techniques and protocols that utilize quantum features for parameter estimation which can in principle outperform any procedure based on classical physics. We formulate the quantum metrology in terms of an optimal control problem and apply Pontryagins Maximum Principle to determine the optimal protocol that maximizes the quantum Fisher information for a given evolution time. As the quantum Fisher information involves a derivative with respect to the parameter which one wants to estimate, we devise an augmented dynamical system that explicitly includes gradients of the quantum Fisher information. The necessary conditions derived from Pontryagins Maximum Principle are used to quantify the quality of the numerical solution. The proposed formalism is generalized to problems with control constraints, and can also be used to maximize the classical Fisher information for a chosen measurement.
We study the problem of preparing a quantum many-body system from an initial to a target state by optimizing the fidelity over the family of bang-bang protocols. We present compelling numerical evidence for a universal spin-glass-like transition controlled by the protocol time duration. The glassy critical point is marked by a proliferation of protocols with close-to-optimal fidelity and with a true optimum that appears exponentially difficult to locate. Using a machine learning (ML) inspired framework based on the manifold learning algorithm t-SNE, we are able to visualize the geometry of the high-dimensional control landscape in an effective low-dimensional representation. Across the transition, the control landscape features an exponential number of clusters separated by extensive barriers, which bears a strong resemblance with replica symmetry breaking in spin glasses and random satisfiability problems. We further show that the quantum control landscape maps onto a disorder-free classical Ising model with frustrated nonlocal, multibody interactions. Our work highlights an intricate but unexpected connection between optimal quantum control and spin glass physics, and shows how tools from ML can be used to visualize and understand glassy optimization landscapes.
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