Events

Lindbladians Obeying Local Conservation Laws and Showing Thermalization

This talk will investigate the possibility of a Markovian quantum master equation (QME) that consistently describes a finite-dimensional system, a part of which is weakly coupled to a thermal bath. For physical consistency, we will demand that the QME should preserve local conservation laws and be able to show thermalization. After providing some background on QMEs, I will present our three main results: 

1. The microscopically derived Redfield equation (RE), which is known to preserve local conservation laws and show thermalization, necessarily violates complete positivity except in extremely special cases. These special cases can be easily identified.
2. I will then turn to Lindblad QMEs and show that imposing complete positivity and demanding preservation of local conservation laws enforces the Lindblad operators and the lamb-shift Hamiltonian to be `local', i.e. to be supported only on the part of the system directly coupled to the bath.
3. Finally, I will show how the problem of finding 'local' Lindblad QME, which can show thermalization, can be turned into a semidefinite program (SDP). This SDP can be solved numerically for any specific example, and its solution conclusively shows whether the desired type of QME is possible up to a given precision. Whenever a QME is possible, it also outputs a form for such a QME.

Taken together, our results indicate that the possibility of a Markovian QME with the desired properties must be taken on a case-by-case basis, since there are setups where such a QME is impossible.

This talk is based on https://arxiv.org/abs/2301.02146.

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Driving-enhanced Qudit-Oscillator Interactions

Classical drives on a qudit have been extensively used to create, control and read out quantum states. We consider a qudit-oscillator system where the qudit is continuously driven. We show that strong driving allows for qudit-conditional operations on the oscillator such as displacement, squeezing and higher order effects. We discuss the case of a driven qubit with linear or quadratic coupling to the oscillator, and we generalize the scheme to multi-qubit and qudit (d>2) systems. We discuss the use of driven qudit-oscillator systems for encoding and performing operations on bosonic codes.

Optimal Bounds for Quantum Learning via Information Theory

I will discuss our recent work on finding lower bounds to solve three problems in Quantum Learning Theory: Quantum PAC learning, Quantum Agnostic Learning and Quantum Coupon Collector. Our main goal was to use tools from Quantum Information Theory, specifically the data processing inequality, to obtain these results, instead of going for more exotic ones. We succeed in doing so for the first two problems, and we show concretely that it doesn't work for the last problem, due to an inherent loss of information that is possible even for valid learning algorithms, for which we give a bound using an alternate method that utilizes the analysis we went through previously. We hope that these tools are broadly applicable to other quantum learning problems.

Some Learning Bounds and Guarantees for Testing (Quantum) Hypotheses

Machine learning is a powerful tool, yet we often do not know how well a learning algorithm might perform on any given task. One standard approach to bound the accuracy of a learning algorithm is to reduce the learning task to hypothesis testing. Fano's inequality then states that a large amount of mutual information between the learner's observations and the set of unknown parameters is a necessary condition for success.

In this talk, I will describe how such a condition is also sufficient for succeeding at some learning task, thereby providing a purely information-theoretic guarantee for learning. Noting that this guarantee has an immediate extension to quantum information theory, I will then introduce the task of "testing quantum hypotheses", in which the unknown parameters of the learning task are prepared in a quantum register in superposition (rather than being sampled stochastically) and the learner's success at this task is measured by their ability to establish quantum correlations with that register. I will discuss ongoing attempts to characterize this scenario.

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Positivity and Sum-of-Squares in Quantum Information

A multivariate polynomial is said to be positive if it takes only non-negative values over reals. Hilbert's 17th problem concerns whether every positive polynomial can be expressed as a sum of squares of other polynomials. In general, we say a noncommutative polynomial is positive (resp. matrix positive) if plugging operators (resp. matrices) always yields a positive operator. Many problems in math and computer science are closely connected to deciding whether a given polynomial is positive and finding certificates (e.g., sum-of-squares) of positivity.

In the study of nonlocal games in quantum information, we are interested in tensor product of free algebras. Such an algebra models a physical system with two spatially separated subsystems, where in each subsystem we can make different quantum measurements. The recent and remarkable MIP*=RE result shows that it is undecidable to determine whether a polynomial in a tensor product of free algebras is matrix positive. In this talk, I'll present joint work with Arthur Mehta and William Slofstra, in which we show that it is undecidable to determine positivity in tensor product of free algebras. As a consequence, there is no sum-of-square certificate for positivity in such algebras.

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Critical Phase and Spin Sharpening in SU(2)-Symmetric Monitored Quantum Circuits

Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we identify a “spin-sharpening transition.” Across the transition, the rate at which measurements reveal information about the total spin quantum number changes parametrically with system size.

Reference https://journals.aps.org/prb/abstract/10.1103/PhysRevB.108.054307

Programmable Individual Optical Addressing for Trapped-ion Quantum Information Processors

Trapped ions are among the most advanced platforms for quantum computation and simulation. Programmable, arbitrary, and precise control—usually through laser-induced light-matter interaction—is required to tune ion-ion interactions. These interactions translate into diverse parameters of the system under study. Current technologies grapple with scalability issues in large ion chains and with "crosstalk" due to micron-level inter-ion separation.

In this talk, we present our development of two optical addressing systems optimized for non-coherent and coherent quantum controls, respectively.

The first addressing system employs a reprogrammable hologram to modulate the wavefront of the addressing beam, thereby engineering the amplitude and phase profile of light across the ion chain. Our implementation compensates for optical aberrations in the system down to λ/20 RMS and exhibits less than 10⁻⁴ intensity cross-talk error. This results in more than 99.9% fidelity when resetting the state or 99.66% when reading out the state of an individual ion without influencing adjacent ions. This scheme can be readily extended to over a hundred ions and adapted to other platforms, such as neutral atom arrays.

Additionally, we introduce another addressing design, tailored for coherent quantum operations through Raman transitions. This design uses a mirrored acoustic-optical deflector (AOD) setup to optimize optical power scaling and sidestep the undesired site-dependent frequency shift commonly observed in AOD-based setups.

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Using Symmetries to Improve Quantum de Finetti Reductions

Quantum Nano Centre, 200 University Ave W, Room QNC 1201
Waterloo, ON, CA N2L 3G1