Quantum feedback and control
One can continuously monitor partial information about a quantum system in order to control experimental parameters in real time for a variety of purposes, such as state purification and initialization, coherence stabilization, and error correction.

Correlated multi-qubit measurement
The expected advantages of quantum computing are rooted in multi-qubit coherence and entanglement effects, with information extracted through uncorrelated high-fidelity projective measurements. A less-explored possibility is exploiting the spatio-temporal correlations between generalized (e.g. weaker) measurements to extract useful information.

Quantum Parameter Estimation
Determining how well one is modeling the physical system in the lab is not a trivial matter. Modern tomographic methods under development use compressive sensing and adaptive estimation techniques to reduce the amount of data that one needs to collect, and reduce the computational resources required to reconstruct the estimates.

Machine Learning for Device Characterization
As chips become more complex in the laboratory, calibration and tune-up becomes an increasingly daunting task. Modern machine learning methods offer novel solutions for auto-calibrating device parameters and tracking dynamics occuring during a computational run.

Monitoring fast superconducting qubit dynamics using a neural network

Gerwin Koolstra, Noah Stevenson, Shiva L. Barzili, Lucas Burns, Karthik Siva, Sacha Greenfield, William Livingston, Akel Hashim, Ravi K Naik, John M Kreikebaum, Kevin P O'Brien, David I Santiago, Justin Dressel, Irfan Siddiqi

Physical Review X 12, 031017(2022).

PDF Cite DOI arXiv URL

Weak measurements of a quantum system allow us to monitor a quantum state in real time with only a small disturbance. Finding the quantum state from a series of weak measurements typically involves a “quantum filter” derived from basic laws of quantum mechanics. This traditional weak measurement approach works well if the quantum state changes slowly compared with the detector response time. However, if the qubit changes rapidly, traditional methods that reconstruct the quantum state fail because the detector affects our best estimate of the quantum state. In our experiment, we use weak measurements to monitor fast dynamics of a superconducting qubit coupled to a readout resonator.

Instead of using a traditional method to monitor the qubit state, we develop a new method with a long short-term memory neural network, which learns the quantum mechanics responsible for the state trajectories by itself. The long short-term memory neural network also learns an unexpected correction to the standard quantum filter, which is most clearly visible in the stochastic measurement disturbance of the fast qubit trajectories. Our newly developed theory shows that this correction can be well explained by the memory effect of the detector.

With our ability to accurately track fast qubit dynamics, we expect to see new applications of weak measurements such as diagnosing qubit gates in quantum processors and continuous measurements for quantum error correction.

PDF Cite DOI arXiv URL

Quantum instruments
Measurements are a dynamical process in quantum mechanics, best represented as a collection of transformations that are in one-to-one correspondence with the distinguishable results of a physical detector. The information collected by the detector updates the quantum state according to these transformations, which generalize Bayes’ rule from classical probability theory. Unlike textbook quantum measurements, the quantum state only partially “collapses” when partial information is collected.

Weak Measurements
When almost no information is gathered by a detector making a measurement, the quantum state is almost entirely preserved. Nevertheless, taking a sufficiently large sample of data still permits the same average infomation to be extracted as textbook projective measurements that fully collapses the state.

Preserving entanglement during weak measurement demonstrated with a violation of the Bell--Leggett--Garg inequality

Theodore C White, Josh Y Mutus, Justin Dressel, Julian Kelly, Rami Barends, Evan Jeffrey, Daniel Sank, Anthony Megrant, B Campbell, Yu Chen, Zijun Chen, Ben Chiaro, A Dunsworth, Io-Chun Hoi, Charles Neill, Peter J J O'Malley, Pedram Roushan, Amit Vainsencher, Jim Wenner, Alexander N Korotkov, John M Martinis

npj Quantum Information 2, 15022(2016).

PDF Cite DOI Supplement arXiv URL

Scientists in the US have developed a method to evaluate the properties of complex quantum states without causing their destruction. A team at the University of California Santa Barbara led by John Martinis verified that the properties of entangled quantum states can be probed using weak measurements. By extracting only small parts of quantum information in a single measurement, weak measurements avoid the problem whereby quantum states are destroyed when the information contained in them is measured. Although this has been successfully demonstrated for single quantum states, it remained unclear if weak measurements were compatible with more complicated entangled systems. By implementing an experimental test that verifies with high accuracy the preservation of those entangled states in measurements, the researchers have made it possible to probe the properties of qubits in complex quantum computing schemes.

PDF Cite DOI Supplement arXiv URL

Quantum trajectories
Discretizing time into small pieces and applying both natural state evolution and measurement-induced state updates at each time step yields a quantum trajectory. Generally these state trajectories show a competition between the natural evolution from the Schroedinger equation and the stochastic evolution from the measurement itself. Stronger measurements per unit time rapidly collapse the state and pin it near the measurement eigenstates, between which quantum jumps can then be tracked. Weaker measurements per unit time minimally perturb the natural evolution, allowing temporal correlations of this coherent evolution to be faithfully extracted.

Conditioned Statistics
Many strange features of quantum mechanics only manifest when several measurements are correlated. Examples include quantum erasure, violations of local realism via Bell inequalities, violations of macrorealism via Leggett-Garg inequalities, anomalously large conditioned averages (including weak values), and even the bunching and anti-bunching behavior of particle statistics.

Mapping the optimal route between two quantum states

Steven J Weber, Areeya Chantasri, Justin Dressel, Andrew N. Jordan, Kater W Murch, Irfan Siddiqi

Nature 511, 570-573(2014).

PDF Cite DOI arXiv URL

Classical systems are unmoved when a measurement is performed. Not so quantum systems, where continuous monitoring can direct the quantum state along a random path. Steve Weber et al. have tracked the quantum trajectories in a qubit, consisting of two aluminum paddles connected by a tunable Josephson junction deposited on silicon. The authors manage to determine which of the possible paths between an initial and a final quantum state is the most probable and show that these ‘optimal paths’ are in agreement with the route predicted by theory, a quantum relative of the principle of least action that defines the correct path linking two points in space and time in classical mechanics. As well as giving insights into the interplay between measurement dynamics and evolution of a system, this work opens up new possibilities for first-principles synthesis of control sequences for complex quantum systems and in information processing.

PDF Cite DOI arXiv URL

Quantum Weak Values
Averaging weak measurements of a pre- and post-selected ensemble consistently produces an average described by a curious quantity known as a weak value, rather than the usual expectation value. These quantities appear througohut the quantum formalism in surprising ways and are closely related to quasiprobabilistic descriptions of joint observable statistics.

Colloquium: Understanding quantum weak values: Basics and applications

Justin Dressel, Mehul Malik, Filippo M Miatto, Andrew N. Jordan, Robert W Boyd

Reviews of Modern Physics 86, 307(2014).

PDF Cite DOI arXiv URL

Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical …

PDF Cite DOI arXiv URL

Contextuality, Locality, and Macrorealism
While most agree that quantum mechanics is weird, it is more difficult to quantify that weirdness in a satisfying (and experimentally accessible) way. The arguably most successful efforts have isolated specific axioms that are aligned with our macroscopic intuition of the physical world (e.g., noncontextual value assignment, locality, and realism), and have constructed rigorous tests to show exactly where quantum mechanics violates these seemingly safe assumptions.

Noncommutative Probability Theory
The infamous “state collapse” in the quantum theory can be understood as a straightforward generalization of Bayes’ theorem in classical probability theory. This observation places probability distributions and quantum states on analogous footing, making the study of noncommutative probability theory a promising route toward reformulating the quantum theory.

Applications of Clifford Algebras
Through an accident of historical development, the practical application of Clifford algebras has been left largely undeveloped in favor of less expressive mathematical formalisms (e.g., the vector calculus of Gibbs/Heaviside). More careful scrutiny reveals that Clifford algebras greatly simplify the mathematical expression of physical law in highly suggestive ways. One example is the unification of Maxwell’s equations into a single equation: ∇F = j, where F = E+BI is the proper (frame-independent) generalization of the Riemann-Silberstein complex electromagnetic field vector, j is the 4-vector current density, ∇ is the same Dirac differential operator as for the relativistic quantum electron, and I is the intrinsic pseudoscalar (volume element) of spacetime.

Spacetime algebra as a powerful tool for electromagnetism

Justin Dressel, Konstantin Y Bliokh, Franco Nori

Physics Reports 589, 1-71(2015).

PDF Cite DOI arXiv URL

We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of …

PDF Cite DOI arXiv URL

Relativistic Fields
Even before introducing second quantization, relativistic fields have remarkably rich structure that is important for practical applications. Notably, modern experimental research in classical optics has forced the reinvestigation of troublesome topics, such as the local momentum of optical vortex singularities, and the proper theoretical separation of orbital and spin parts of the angular momentum density (which can be separately measured with probe particles).