Events

CS/Math Seminar - Rajesh Pereira, the University of Guelph

We explore two convex subsets of the sets of quantum channels. The set of mixed unitary channels and the set of entanglement breaking channels. We study the geometry of these sets, and show how certain geometric and spectral properties of these sets can be studied using positive definite functions, stochastic matrices and other mathematical tools.

Control and Readout of High-Dimensional Trapped Ion Qudits

The trapped ion platform is one of the quantum computing platforms that is at the forefront for realizing large-scale quantum information processing, which is crucial for practically actualizing the advantages of quantum algorithms. Scaling up the trapped ion quantum computing architecture remains a challenge. We explore an alternative avenue in a trapped ion system for increasing the computational Hilbert space other than trapping more ions, which is by increasing the qudit dimension of an ion. Our ion of choice is 137Ba+, which has a rich energy level structure for high-dimensional qudit encoding. Utilizing the additional energy states found in 137Ba+ also comes with non-trivial complexities that require careful considerations, which we have solved and report in this work. We report on a single-shot state measurement protocol which allows qudit encoding in 137Ba+ of up to 25 levels, and demonstrate state preparation and measurement of up to 13 levels, which is unprecedented in a trapped ion system. This PhD defense presentation also covers some other interesting topics within the thesis, which include our experimental setup, barium ion loading via laser ablation, and detailed studies of some experimental observations that may not be intuitively clear.

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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Ablation Loading and Qudit Measurements with Barium Ions

Barium is one of the best ions for performing quantum information in a trapped-ion system. Its long-lived metastable D5/2 state allows for some interesting quantum operations, including the current best state preparation and measurement fidelity in qubits. This metastable state also opens up the possibility of implementing higher dimensional qudits instead of qubits. However, installing a barium metal source in a vacuum chamber has shown to be somewhat of a challenge. Here, we present a loading technique which uses a barium chloride source instead, making it much easier to install. Laser ablation with a high-energy pulsed laser is used to generate neutral atoms, and a two-step photoionization technique is used to selectively load different isotopes of barium in our ion trap. The process of laser ablation and the plume of atoms it generates are characterized, informing us on how to best load ions. Loading is achieved, and selectivity of our method is demonstrated, giving us a reliable way to load ba138 and ba137 ions. The quadrupole transition into the metastable D5/2 state is investigated, with all of the individual transitions successfully found and characterized for ba138 and ba137. Coherent operations are performed on these transitions, allowing us to use them to define a 13-level qudit, on which we perform a state preparation and measurement experiment. The main error source in operations using this transition is identified to be magnetic field noise, and so we present attempts at mitigating this noise. An ac-line noise compensation method is used, which marginally improved the coherence time of the quadrupole transitions, and an additional method of using permanent magnets is proposed for future work. These efforts will help to make trapping barium more reliable, making it an even more attractive option for trapped ion systems. The state preparation and measurement results using the quadrupole transition to the long-lived metastable D52 state establish barium as an interesting platform for performing high-dimensional qudit quantum computing.

IQC Seminar - Sahel Ashhab, National Institute of Information and Communications, Japan

Superconducting qubits are based on nonlinear electric circuits that support multiple quantum states. Although only two states are used to realize a qubit, it is possible to utilize more states and realize qudits (d-level quantum systems). We have proposed and experimentally demonstrated optimized implementations of qutrit gates. We have also investigated the time-optimal implementation of two-qubit gates in weakly anharmonic superconducting circuits.

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.

Measuring Quantum Correlations of Polarization, Spatial Mode, and Energy-Time Entangled Photon Pairs

Optical quantum technologies have found applications in all facets of quantum information. Single photons are actively being researched for quantum computation, communication, and sensing, due to their robustness against decoherence stemming from their minimal interaction with the environment. For communication and networking applications, specifically, photons are lauded for their speed and coherence over long distances. While clear benefits arise from the lack of photon-environment interaction, measurement and control of all photonic degrees of freedom is made challenging. Each degree of freedom, be it polarization, space, time, or frequency, comes with its own advantages and drawbacks. The potential that single photons bring to future quantum technologies may only be realized by full control over each of these properties of light.

CS/Math Seminar - Yaroslav Herasymenko, TU Delft (whiteboard presentation)

Fermionic optimization is a quantum extension of constraint satisfaction that is a distinct alternative to the qubit Hamiltonian problem. Extremal eigenvalues of fermionic Hamiltonians can sometimes be approximated via so-called Gaussian states, which are classically simulable. The accuracy of such an approximation depends on the structure of the Hamiltonian. From the mathematical perspective, this dependence is not very well understood.

Analog Quantum Simulation via Parametric Interactions in Superconducting Circuits

While universal quantum computers are still years away from being used for simulating complicated quantum systems, analog quantum simulators have become an increasingly attractive approach to studying classically intractable quantum systems in condensed matter physics, chemistry, and high-energy physics. In this dissertation, we utilize superconducting cavities and qubits to establish analog quantum simulation (AQS) platforms to study systems of interest. 

An approach of AQS that has gained interest lately is the use of photonic lattices to simulate popular lattice models. These systems consist of an array of cavities or resonators arranged on a lattice with some couplings graph between modes. We propose an in situ programmable platform based on a superconducting multimode cavity. The unique design of the cavity allows us to program arbitrarily connected lattices where the coupling strength and phase of each individual coupling are highly programmable via parametrically activated interactions. Virtually any quadratic bosonic Hamiltonian can be realized in our platform with a straightforward pumping scheme.

The effectiveness of the cavity-based AQS platform was demonstrated by the experimental simulation of two interesting models. First, we simulated the effect of a fictitious magnetic field on a 4-site plaquette of a bosonic Creutz ladder, a paradigmatic topological model from high-energy physics.  Under the right magnetic field conditions, we observed topological features such as emergent edge states and localized soliton states. The platform's ability is further explored by introducing pairing (downconversion) terms to simulate the Bosonic Kitaev chain (BKC), the bosonic version of the famous Fermionic Kitaev chain that hosts Majorana fermions. We observe interesting properties of BKC, such as chiral transport and sensitivity to boundary conditions.  

In the final part of the dissertation, we propose and implement a parametrically activated 3-qubit interaction in a circuit QED architecture as the simplest building block to simulate lattice gauge theories (LGT). LGT is a framework for studying gauge theories in discretized space-time, often used when perturbative methods fail.   The gauge symmetries lead to conservation laws, such as Gauss's law in electrodynamics, which impose constraints tying the configuration of the gauge field to the configuration of ''matter'' sites.  Therefore, any quantum simulation approach for LGTs must maintain these conservation laws, with one strategy in AQS being to build them in at the hardware level.  Here, the gauge constraints are explicitly included using a higher-order parametric process between three qubits. The simplest 2-site U(1) LGT building block is realized with two qubits as matter sites and a third qubit as the gauge field mediating the matter-matter interaction, which is crucial to maintain the symmetry of U(1) LGTs.