Events

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.

IQC Colloquium - Nir Bar-Gill, Applied Physics and Physics, The Hebrew University

In this talk I will address these topics through the platform of nitrogen-vacancy (NV) spins in diamond, in the context of purification (or cooling) of a spin bath as a quantum resource and for enhanced metrology and sensing.

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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Developing a Large-Scale, Programmable Trapped Ion Quantum Simulator with In Situ Mid-Circuit Measurement and Reset

Quantum simulators are a valuable resource for studying complex many-body systems. With their ability to provide near-term advantages, analog quantum simulators show great promise. During the course of my PhD, my aim was to construct a large-scale trapped-ion based analog quantum simulator with several objectives in mind: controllability, minimal external decoherence, an expandable toolkit for quantum simulations, enhanced stability through robust design practices, and pushing the boundaries of error correction.

One of my key achievements is the demonstration of high-fidelity preservation of an “asset” ion qubit while simultaneously resetting or measuring a neighboring “process” qubit located a few microns away. My results show that I achieve a probability of accidental measurement of the asset qubit below 1×10−3 while resetting the process qubit. Similarly, when applying a detection beam on the same neighboring qubit to achieve fast detection times, the probability remains below 4 × 10−3 at a distance of 6 μm. These low probabilities correspond to the preservation of the quantum state of the asset qubit with fidelities above 99.9% for state reset and 99.6% for state measurement.

Additionally, I successfully conduct a dissipative many-body cooling experiment based on reservoir engineering by leveraging site-selective mid-circuit resets. I propose and optimize a protocol utilizing reservoir engineering to efficiently cool the spin state of a subsystem coupled to a reservoir with controlled dissipation. Through analog quantum simulation of this protocol, I am able to demonstrate the lowering of energy within the subsystem.

Furthermore, I thoroughly discuss the design, fabrication, and assembly of a large-scale trapped ion quantum simulator called the Blade trap as part of my PhD work. I highlight the specific design considerations taken to isolate the trapped ions from external disturbances that could introduce errors. Comprehensive testing procedures are presented to evaluate the performance and stability of the Blade trap, which are crucial for assessing the effectiveness of the design. An important milestone I achieve is reaching a base pressure below 9E-13 mbar, demonstrating the successful implementation of techniques to maintain an extremely low-pressure environment ideal for quantum simulation.

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