Events

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

Quantum Nano Centre (QNC) Room 0101, 200 University Avenue West, Waterloo, ON

IQC Colloquium, Harry Buhrman - QuSoft

One of the major challenges in computer science is to establish lower bounds on the resources, usually time, that are needed to solve computational problems. This holds in particular for computational problems that appear in practise. One way towards dealing with this situation is the study of fine- grained complexity where we use special reductions to prove time lower bounds for many diverse problems based on the conjectured hardness of some key problems.

Impromptu Whiteboard Poster Session

Quantum Nano Centre (QNC) Room 1201, 200 University Avenue West, Waterloo, ON

This week’s student seminar will take place in the form of an impromptu whiteboard poster session, where attendees will be divided into groups and will discuss each other's current work using the whiteboard. This is to encourage students to talk about their work in progress, and practice communication skills by talking to non-experts (quantum is a big field!). As always, pizza will be provided for attendees after the seminar.

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IQC Colloquium - Alex May, Perimeter Institute

Quantum Nano Centre (QNC) Room 0101 200 University Ave West, Waterloo Ontario

The subject of quantum gravity seeks to understand gravitational physics within the framework of quantum mechanics. Increasingly, tools from quantum information, complexity, and cryptography have been brought into this challenging area. Here, I describe a set of connections between quantum gravity, specifically the AdS/CFT correspondence, and a set of cryptographic primitives studied in information theoretic cryptography and position-verification. The cryptographic perspective provides new insights into how gravitational physics can be recorded into quantum mechanics, and led to new gravitational conjectures in AdS space. These conjectures were then proven gravitationally. Conversely, the gravitational perspective has suggested new relationships among these cryptographic primitives, and these relationships were then proven within quantum cryptography. I comment on some directions this cryptography-gravity relationship may lead in the future.  

IQC Colloquium - Mio Murao, The University of Tokyo

Quantum Nano Centre (QNC) Room 0101 200 University Ave West, Waterloo Ontario

Please note start time 3:00 PM

Efficiently learning properties of unknown quantum objects is a fundamental task in quantum mechanics and quantum information. When there are two unknown quantum objects, and if we want to learn just the relationship between the objects, a method to directly compare the two objects without identifying their descriptions is preferable, especially when the number of available copies of each target object is limited. In this work, we investigate the comparison of unknown unitary channels with multiple uses of the unitary channels based on the quantum tester formalism.  We obtain the optimal minimum-error strategy and the optimal unambiguous strategy of unitary comparison of two unknown d-dimensional unitary channels when the number of uses of the channels satisfies a certain condition. These optimal strategies are implemented by parallel uses of the unitary channels, even though all sequential and adaptive strategies implementable by the quantum circuit model are considered. When the number of the smaller uses of the unitary channels is fixed, the optimal averaged success probability is achieved by a certain number of uses of the other channel. This feature contrasts with the case of pure-state comparison, where adding more copies of the unknown pure states always improves the optimal averaged success probability. It highlights the difference between corresponding tasks for states and channels, which has been previously shown for quantum discrimination tasks.  

Reference: Y. Hashimoto, A. Soeda and M. Murao, Comparison of unknown unitary channels with multiple uses, arXiv:2208.12519

IQC Seminar - Johannes Prell, Institute of Communication and Navigation, OSL German Aerospace Center (DLR) Oberpfaffenhofen, Germany

Quantum Nano Centre (QNC) Room 0101 200 University Ave West, Waterloo Ontario

Satellite based laser communication technology both classical and QKD (Q uantum K ey D istribution is gaining popularity and being increasingly commercial i zed . Optical ground stations serve as the receiv ing station in satellite to ground scenarios. The DLR institute of Communications and Navigation hosts an experimental optical ground station for research and demonstration purpose. Supporting increasingly demanding technical requirements from current and futu re missions and technology demonstrations, it was decided to replace the 40cm Cassegrain telescope an equip the new one with Nasmyth Ports for direct experiments, a Coudé Path to the lab and an Adaptive Optics System . This new 80cm (31.5inch) main apertur e diameter i nstrument is a Nasmyth Design Ritchey Chretien telescope The special feature is the C oudé P ath which is guiding the received light onto an optical table in a lab oratory room below the telescope mount (see figure 1 The usage of the Coudé Path is new implemented at DLR and offers a wide possibility for several different experiments with the same setup The optical propaga tion through a custom designed lens system inside the coudé path is optimized for wavelength s used for optical communication, like 589nm, 850nm, 1064nm and 1550nm. It is possible to use the setup as a receiving station and also as a transmitting facility f or beacon lasers . The transmitt ing system ca n be installed either beside the telescope as a side installation or even launched from the optical table through coudé path and telescope directly

The optical Experiment table in the lab is equipped with an Adaptive Optics ( System including fibe r coupling. This system uses a Shack Hartmann Wave front sensor, designed to match a deformable mirror in the “ f ried g eometry”. The system couples the light into a single mode fibe r , which can be con nected to a coherent or Quantum encrypted communications system. [ The telescope itself has four usable Nasmyth ports The first one is reserved for the coudé pa th, t wo others are equipped with optical benches directly on the telescope, and on the last one has a fixed classical laser communication receiving setup including two cameras one visible light and one infra red and a signal receiving united is installed References

[1] Andrew Paul Reeves, Ilija R. Hristovski, Alexandru Octavian Duliu, Stefanie H äu sler, Hela Friew Kelemu, Pia Lützen, Florian Moll, Eltimir Peev, Juraj Poliak, Amita Shrestha, Joana Sul Torres; Adaptive Optics Corrected Bi Directional Links with a Geo Stationary Satellite from the DLR KN Optical Ground Station Figure 1 OGSOP System Overvi ew