Session R07: Quantum Measurement and Sensing II

Optimal approximate quantum error correction for quantum metrology

For a generic set of Markovian noise models, the estimation precision of a parameter associated with the Hamiltonian is limited by the 1/sqrt(t) scaling where t is the total probing time, in which case the maximal possible quantum improvement in the asymptotic limit of large t is restricted to a constant factor. However, situations arise where the constant factor improvement could be significant, yet no effective quantum strategies are known. Here we propose an optimal approximate quantum error correction (AQEC) strategy asymptotically saturating the precision lower bound in the most general adaptive parameter estimation scheme where arbitrary and frequent quantum controls are allowed. We also provide an efficient numerical algorithm finding the optimal code. Finally, we consider highly-biased noise and show that using the optimal AQEC strategy, strong noises are fully corrected, while the estimation precision depends only on the strength of weak noises in the limiting case.
  

Multi-parameter metrology with the Holevo Cramer Rao bound; an explicit 2-qubit 3-parameter bound

Quantum metrology is essential for the rigorous analysis and optimisation of all quantum-limited experiments. Since no experiment is ever truly a single parameter one what is required is multi-parameter quantum metrology. It invokes the central axiom of quantum mechanics, that of incompatible observables.

Hitherto, SLD quantum Fisher information matrix (QFIM) has largely been the Cramer-Rao bound of choice for examining multi-parameter metrology. In this work we show that the QFIM is an inadequate metric for multi-parameter problems. Further, we show that the Holevo Cramer-Rao (HCRB) bound is not only easier to calculate both numerically and analytically than previous thought but it is also essential for multi-parameter problems.

We point out new insights obtained from evaluating the HCRB for much larger Hilbert spaces than before, enabled by the convexity of the problem. We also show that previously known techniques allow us to calculate an explicit bound for 3D-magnetometry with 2 qubits, which again leads to new insight and further emphasises the pitfalls of the QFIM.   

Parametrically-enhanced quantum sensing with effective non-Hermitian lattice dynamics

Systems whose dynamics are described by a non-Hermitian effective Hamiltonian have been suggested as platforms for improved sensing. Several experiments have already demonstrated the utility of exceptional points, a uniquely non-Hermitian feature, in setups consisting of a few resonant modes [1-3]. The phenomena exhibited by coupled multi-mode non-Hermitian systems, such as the non-Hermitian skin effect [4] and the existence of abnormally large susceptibilities, are also promising sensing resources. Here, we show how to harness the unusual lattice physics to build quantum sensing platforms with remarkable properties. In particular, the quantum Fisher information of our measurement scheme grows exponentially with system size, even when bounding the number of photons used for the measurement. This is achieved without coupling to dissipative baths or postselection. Our setup is realizable in a number of experimental platforms, including superconducting quantum circuits and quantum optical setups.

[1] Hodaei, H. et al,. Nature 548, 187–191 (2017)
[2] Chen, W., Kaya Özdemir, S., Zhao, G., Wiersig, J. & Yang, L. Nature 548, 192–196 (2017)
[3] Naghiloo, M., Abbasi, M., Joglekar, Y. N. & Murch, K. W. Nat. Phys. (2019)
[4] S. Yao and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018).
  

Metrology near exceptional points from superconducting circuits with loss

The underlying mechanism of sensors, amplifiers, and metrological devices is a strong response to small perturbations. Such strong responses are expected for classical systems governed by non-Hermitian Hamiltonians. We use post-selection to create an effective non-Hermitian Hamiltonian for a superconducting quantum circuit and measure the sensitivity of the circuit to a coherent drive for different system parameters. We find that the quantum Fischer information about the drive amplitude diverges at the exceptional point, indicating enhanced sensitivity. However, enhanced sensitivity is achieved at the cost of additional experimental data due to post-selection statistics. With this experiment, we highlight the interplay of dissipation, dephasing, and loss near exceptional points of non-Hermitian open quantum systems and, we observe the role of quantum measurement backaction for quantum sensing.   

Macroscopic Quantum Tunneling Devices for Nanoscale Attonewton Force Sensing

The precision enabled by ultra-high vacuum, low temperature scanning tunneling microscopy for atomic manipulation has allowed the design of nanostructures that exhibit quantifiable quantum dynamics. This work presents a novel nanoscale probe of atomic-scale forces and enables new detection methods of the energy landscape in a Fermi gas. In a two-dimensional electron gas, the geometry of the boundaries on the surface will produce uniquely non-local alterations in the electronic wave function. By creating a device in which a single atom or molecule can macroscopically tunnel between degenerate states in a double potential well, we are able to detect quantum forces that break the degeneracy by measuring an asymmetry in the tunneling rates between each side. Our new method of two-dimensional nanoscale force measurement is able to detect forces with attonewton sensitivity, and the device’s design permits the probing of quantum forces due to proximal nanostructures with atomic resolution. Designer boundary conditions can amplify the measured forces and further illustrate the non-local nature of quantum force fields. We will discuss ways to extend device sensitivity even further, below the attonewton level.   

Dissipation-based quantum sensing of magnons

Magnons are the quanta of collective spin excitations. We introduce a novel technique for quantum sensing of magnons by leveraging the quantum coherence of a superconducting qubit which interacts with a magnetostatic mode. This is enabled by the realization of a strong dispersive coupling between the uniformly precessing magnetostatic mode in a ferromagnetic sphere and a superconducting qubit in a hybrid system [1,2]. A finite magnon population induces additional dephasing in the qubit, and can thus be inferred by probing the qubit coherence via Ramsey interferometry. A magnon detection sensitivitiy of around 10^-3 magnons/√Hz is demonstrated, in good agreement with numerical simulations. The dissipation-based nature of our quantum sensor is confirmed by the dependence of the sensitivity on the detuning used in the Ramsey interferometry. The use of quantum sensing techniques in magnonics could find applications in fields such as magnon spintronics and magnetic field sensing.
[1] D. Lachance-Quirion et al., Science Advances 3, e1603150 (2017).
[2] D. Lachance-Quirion et al., arXiv:1910.09096.   

Quantum sensing with superconducting microwave circuits

Quantum mechanics offers intriguing opportunities for sensing applications with accuracies beyond the classically obtainable limits. An especially interesting approach is based on using entangled microwave photons for radar applications [Las Heras et al., Sci. Rep., 7, 9333 (2017)]. Here, we discuss a novel frequency-degenerate scheme for quantum sensing with superconducting microwave circuits. Our method is based on continuous variables that provide a convenient platform for quantum communication [Pogorzalek et al., Nat. Commun., 10, 2604 (2019)]. The same microwave regime is utilized in conventional radars owing to the transparency window of the atmosphere. Hence, our scheme suffers no conversion losses and, therefore, is promising for future real-world applications.   

Quantum-Enhanced Noise Radar

Quantum Illumination (QI) promises improvement in the sensitivity of target detection technologies. The approach takes advantage of strong correlations that can be created in electromagnetic beams using quantum processes, through a form of entanglement. Notably, QI has proven to be very robust to the presence of noise and loss, suggesting that it may have practical applications. We have made a proof-of-principle demonstration of a novel QI protocol: quantum-enhanced noise radar (QENR). In QENR, we use a parametric amplifier to produce a two-mode squeezed (TMS) state, which exhibits continuous-variable entanglement between signal and idler beams. This state is the input to the radar system. Compared to existing proposals for QI, our protocol does not require joint measurement of the signal and idler. This greatly enhances the practicality of the system by eliminating the need for a quantum memory to store the idler. We compare the performance of a TMS source to an ideal classical source that saturates the classical bound for correlation, finding a quantum enhancement approaching a factor of 10. One of the main challenges to making QENR practical is bringing the quantum microwaves out of the cryostat. We will discuss progress towards overcoming this challenge.   

Mitigating back-action in parametric quantum amplifiers

Parametric quantum amplifiers are of paramount importance for quantum information processing with superconducting circuits. A promising route to design quantum amplifiers is based on parametric modulation of coupled modes, where the required mode-mixing processes are realized by utilizing Josephson junction-based tunable couplers. All designs face the challenge of higher-order nonlinearities, resulting in a limitation of the dynamical range of the amplifier. However, even without any higher-order nonlinearities, the amplification process is itself nonlinear, e.g., it involves the mixing of three waves: the pump, the idler and the signal. Only for weak enough signal intensity the pump can be considered stiff and the amplification process becomes linear. Once the signal strength grows this approximation does not hold true anymore. The nonlinear nature of the mixing process leads to back-action, limiting the dynamical range of the amplifier.
Here we present possible ways to face these challenges, and how to avoid unwanted back-action effects in engineered quantum systems. Furthermore, we discuss routes for optimizing the design of quantum-limited parametric amplifiers that one can avoid pump-depletion effects completely.   

Near quantum limited Josephson traveling wave amplifiers I, Fabrication and characterization

Efficient low noise amplification is a crucial component for any system dealing with low amplitude signals. Currently, Josephson parametric amplifiers(JPAs) can attain quantum limited amplification for microwave signals. However, JPAs based on resonant structures are limited to low bandwidth and saturation power. These limitations can be overcome using Josephson meta-materials forming traveling wave parametric amplifiers(TWPAs).

In part I, we will present in detail, our simplified aluminum-based two-step fabrication technique for TWPAs with low footprint[1], and discuss their linear characterization[2]. This technique paves the way for on-chip integration of broadband amplifiers with quantum devices.

In part II, we will present the performance of these amplifiers, exhibiting a large and near quantum limited gain over bandwidth larger than 2GHz; and conclude with a discussion on techniques for mitigating some of the limitations.


[1] L. Planat et al., arXiv:1907.10162
[2] L. Planat et al., arXiv:1907.10158   

Near quantum limited Josephson traveling wave amplifiers II Performance and further development

Efficient low noise amplification is a crucial component for any system dealing with low amplitude signals. Currently, Josephson parametric amplifiers(JPAs) can attain quantum limited amplification for microwave signals. However, JPAs based on resonant structures are limited to low bandwidth and saturation power. These limitations can be overcome using Josephson meta-materials forming traveling wave parametric amplifiers(TWPAs).

In part I, we will present in detail, our simplified aluminum-based two-step fabrication technique for TWPAs with low footprint[1], and discuss their linear characterization[2]. This technique paves the way for on-chip integration of broadband amplifiers with quantum devices.

In part II, we will present the performance of these amplifiers, exhibiting a large and near quantum limited gain over bandwidth larger than 2GHz; and conclude with a discussion on techniques for mitigating some of the limitations.


[1] L. Planat et al., arXiv:1907.10162
[2] L. Planat et al., arXiv:1907.10158   

Heisenberg-limited single-mode quantum metrology in a superconducting circuit

Quantum metrology is one of the most promising near-term applications of quantum technology. Reaching a quantum advantage in metrology usually requires hard-to-prepare two-mode entangled states such as NOON states. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. In this talk, we demonstrate such a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally in a superconducting circuit by preparing the superpositions of Fock states (|0>+|N>) up to N=12. We realize a 9.1 dB improvement over the SNL at N=12, which is only 1.7 dB away from the HL. Our experimental architecture can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications.
  

Quantum Metrology in the Era of Quantum Information

A comprehensive overview of the most recent advances in theoretical methods of quantum metrology will be presented, that in particular benefit from the quantum information related concepts such as quantum error-correction or matrix product states formalism. The theory developed allows to determine whether the Heisenberg scaling of precision is possible for a quantum sensor subject to a general Markovian noise. The theory takes into account all the possible quantum strategies, including entangling the sensor with ancillary systems, adaptive strategies such as e.g. quantum error correction protocols. Moreover, effective algorithms, based on the matrix product states/matrix product operator formalism, are developed that allow to identify the optimal metrological protocols in presence of noise (also correlated noise) in the limit of large number of probes, inaccessible by the state-of-the-art methods. These results are highly relevant for modern developments of quantum enhanced sensing protocols, including NV-center magnetometry, squeezed states enhanced optical and atomic interferometry or stabilization protocols for atomic clocks.

References:
[1] R. Demkowicz-Dobrzanski, J. Czajkowski, P. Sekatski, Adaptive quantum metrology under general Markovian noise, Phys. Rev. X 7, 041009 (2017)
[2] K. Chabuda, J. Dziarmaga, T. Osborne, R. Demkowicz-Dobrzanski, Tensor Networks for Quantum Metrology, arXiv:1906.02761 (2019)