Quantum Sensing

Many sensing applications are concerned with the continuous monitoring of time-dependent phenomena such as a varying electromagnetic field, temperature, or inertial effects through their influence on a quantum meter system. When a state or an observable of a single quantum system is probed continuously in time, the measurement results take the form of a time dependent measurement record, where the measurement at each instant of time is governed by Born’s rule, and the quantum meter system, in turn, evolves due to the back action of the measurements themselves. The measurement back action may benefit sensing by conditionally squeezing the measured observable and hence improving the sensitivity, and by continuously quenching the system and launching a transient response with stronger dependence on the imposed perturbations than displayed in the steady state. We review the use of quantum trajectories for optimal Bayesian estimation of imposed perturbations, the possibility to retrodict past values of a perturbation from later measurement, and theories to compute the classical and quantum Fisher information, which provide deterministic results for the sensing capabilities of a given quantum meter system.

The Heisenberg limit (HL, with estimation error, scales as 1/n) and the standard quantum limit (SQL, 1/sqrt(n)) are two fundamental limits in estimating an unknown parameter in n copies of quantum channels and are achievable with full quantum controls, e.g., quantum error correction (QEC). It is unknown whether these limits are still achievable in restricted quantum devices when QEC is unavailable, e.g., with only unitary controls or bounded system sizes. In this talk, I will discuss various new limits for estimating qubit channels under restrictive controls. The HL is proven to be unachievable in various cases, indicating the necessity of QEC in achieving the HL. Furthermore, a necessary and sufficient condition to achieve the SQL is determined, where a novel unitary control protocol is identified to achieve the SQL for certain types of noisy channels, and a constant floor on the estimation error is proven for other cases.

An efficient and scalable means of entangling atoms is to couple them to a single mode of light in an optical cavity.  Such collective atom-light coupling naturally produces a single globally entangled state, such as a squeezed spin state, which can serve as a resource for enhancing clocks or sensors.  However, many practical sensing tasks involve estimating more than a single parameter, and therefore benefit from advances in controlling the spatial structure of entanglement.  I will report on experiments in which we program the network of entanglement within an array of atomic ensembles by combining global cavity-mediated interactions with local addressing.  We demonstrate the flexibility of this approach for entanglement-enhanced sensing of spatially patterned fields and for engineering continuous-variable graph states.  The minimal instance of such a graph state — an EPR entangled state — enables simultaneous sensitivity to perturbations in non-commuting observables for applications including ac and vector magnetometry.  Benefiting from this sensitivity requires measuring nonlocal quantities, which we achieve via a cavity-enabled interaction-based readout scheme.  I will also touch on applications of interaction-based readout in quantum simulation, which we illustrate by probing topological edge states with a cavity-based nonlocal interferometer.

Bosonic two-mode squeezed states are paradigmatic entangled Gaussian states that have wide utility in quantum information and metrology. We show that the basic structure of these states can be generalized to arbitrary bipartite quantum systems in a manner that allows simultaneous, Heisenberg-limited estimation of two independent parameters for finite-dimensional systems. Further, we show that these general states can always be stabilized by a relatively simple Markovian dissipative process. In the specific case where the two subsystems are ensembles of two-level atoms or spins, our generalized states define a notion of two-mode spin squeezing that is valid beyond the Gaussian limit and that enables true multi-parameter estimation. We discuss how generalized Ramsey measurements allow one to reach the two-parameter quantum Cramer-Rao bound, and how the dissipative preparation scheme is compatible with current experiments.

Noise sensing in microwave cavities has implications in important tasks such as dark matter search. In this talk, we introduce the fundamental limits and design protocols on achieving the limits. We begin with assuming noiseless ancilla, where ultimate limit is derived and protocols to achieve them are found. When all modes are lossy, it is found that a Rayleigh limit exists on the sensitivity. We discuss transient state sensing to mitigate the Rayleigh limit.

This talk will start with gravitational wave detectors, which can be viewed as measuring weak gravitational forces.  I will discuss the application of Quantum Fisher information of waveform estimation and how the injection of squeezed vacuum, the application of quantum parametric amplification, and the detection of frequency-dependent field quadratures allow us to saturate the QFI, increase the level of QFI, and eventually improve sensitivity. As we turn to estimate the spectral density of a noisy signal, I will show that injecting non-Gaussian optical states and measurement via photon counting (instead of homodyne detection) can be more advantageous.  I will finally discuss estimating the quantum state of test masses and how that can allow us to test quantum mechanics in the macroscopic regime.

As fully fault-tolerant quantum computers capable of solving useful problems remain a future goal, we anticipate an era of ``early fault tolerance'' allowing for limited error correction. We propose a framework for designing early fault-tolerant algorithms by trading between error correction overhead and residual logical noise, and apply it to quantum phase estimation (QPE). We develop a quantum-Fourier-transform (QFT)-based QPE technique that is robust to global depolarising noise and outperforms the previous state of the art at low and moderate noise rates. We further develop a data processing technique, Explicitly Unbiased Maximum Likelihood Estimation (EUMLE), allowing us to mitigate arbitrary error on QFT-based QPE schemes in a consistent, asymptotically normal way. This extends quantum error mitigation techniques beyond expectation value estimation, which was labeled an open problem for the field. Applying this scheme to the ground state problem of the two-dimensional Hubbard model and various molecular Hamiltonians, we find we can roughly halve the number of physical qubits with a ~10x wall-clock time overhead, but further reduction causes a steep runtime increase. This work provides an end-to-end analysis of early fault-tolerance cost reductions and space-time trade-offs, and identifies which areas can be improved in the future.

I will review advances to beat standard metrological limits when the quantum system is explicitly time-dependent.  In general both coherent control and adaptive strategies are required to unlock these advantages. Examples will be given in qubit systems and experiments discussed.  Recent advanced using variational methods and applications to many-body systems will also be discussed.

Optimal storage and transmission of data is a fundamental task of information processing. For quantum sensing, the outputs of quantum sensors are $N$ ($gg 1$) copies of a quantum state that contains some unknown information to estimate. In this talk, I will show compression protocols that compresses the outputs of quantum sensors into a memory of size $O(log N)$ (qu)bits, with an optimal asymptotic compression rate and a small error vanishing in $N$, and I will prove that this task cannot be achieved by quantum state tomography. The compression covers not only states of fixed dimensions, but also states generated by a large but shallow quantum circuit. Besides the fundamental interest, it also leads to new sensing protocols, such as a quantum stopwatch, that achieves quantum advantage in new regimes of sensing.

Optical atomic clocks based on transitions in atoms and ions continue to be at the frontier of time and frequency metrology. The precision of such a clock depends on the number of atoms that can be interrogated in parallel, as well as the relative coherence time of the atoms with the oscillator that is being stabilized to the atoms. When using many atoms, multi-particle entanglement can also be used to improve the precision of the clock. I will describe our work in this area, using an array of strontium atoms that are controlled with single-particle resolution via a tweezer array and entangled using Rydberg interactions. I will focus on one example where we demonstrate a new multi-qubit gate protocol to create so-called “cascaded GHZ states” for enhanced sensing with a large dynamic range.  

Josephson junction-based quantum circuits have enabled broad exploration into open quantum systems in the microwave frequency domain. The combination of coherent quantum bits, robust single qubit control, entangling gates, and quantum noise-limited parametric amplifiers has yielded an unprecedented view into the physics of quantum measurement and dissipation. I will discuss our recent experimental work that focuses on harnessing entangled states to perform measurements beyond the capabilities of unentangled sensors. Key topics will include discussion of an entanglement-enabled probe of non-Markovian dynamics and time-travel-inspired metrology protocols.

Detection of weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. I will introduce and study a fundamental trade-off which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. The trade-off is quantified in terms of the quantum Fisher information, which is a standard measure of sensitivity in quantum estimation theory. I will then connect our results to the notion of quantum error correction. Indeed, a weaker variant of the standard conditions for quantum error correction turn out to be necessary and sufficient conditions for a state's sensitivity to be unaffected by the noise. I will discuss how such states, which we call "metrological codes," enrich the broader picture of developing schemes in metrology based on quantum error correction.

Joint work with: Mischa P. Woods, Victor V. Albert, Joseph M. Renes, Jens Eisert, and John Preskill.

Reference: https://arxiv.org/abs/2207.13707

Quantum sensing is one of the most promising applications of near-term quantum systems. In this talk, I will introduce a new form of exponential entanglement advantage in the context of sensing correlated noise. Specifically, we focus on the problem of estimating parameters associated with Lindblad dephasing dynamics and show that entanglement can lead to an exponential enhancement in the sensitivity (as quantified via quantum Fisher information of the sensor state), for estimating a small parameter characterizing the deviation of system Lindbladian from a class of maximally correlated dephasing dynamics. This result stands in stark contrast to previously studied scenarios of sensing uncorrelated dephasing noise, where one can prove that entanglement does not lead to an advantage in the signal-to-noise ratio. Our work thus opens a novel pathway towards achieving entanglement-based sensing advantage, which may find applications in characterizing decoherence dynamics of current quantum devices. Further, our approach provides a potential quantum-enhanced probe of many-body correlated phases by measuring noise generated by a sensing target. We also discuss the realization of our protocol using near-term quantum hardware.

Spatially correlated dephasing noise remains a leading source of decoherence in state-of-the-art platforms for quantum-enhanced sensing. In this talk, I will focus on quantum frequency estimation in the presence of fully correlated (“collective”) classical dephasing noise, in both the Markovian and non-Markovian (temporally correlated) regime.  In standard Ramsey interferometry settings where the target parameter couples linearly to an observable of N non-interacting qubit probes, a no-go for asymptotic superclassical precision scaling can be established, even if the estimation protocol is augmented with the use of time-dependent dephasing-preserving control. I will outline two strategies for possibly evading such a no-go result. First, I will consider generalized metrological protocols with quadratic signal encoding, and show how, for non-Markovian dephasing, a scaling advantage over the linear 1/N Heisenberg scaling may be reached with initial unentangled spin-coherent states, with further improvement from initial spin-squeezed states. Returning to linear quantum metrology, I will then argue that, for non-Markovian dephasing, the use of time-dependent quadratic control may provide a mechanism for separating the noise from the signal and for achieving a scaling advantage over the no-control case.