Seminar

The thermodynamic limit is foundational to statistical mechanics, underlying our understanding of many-body phases. It assumes that, as the system size grows infinitely at fixed density of particles, unambiguous macroscopic phases emerge that are independent of the system's boundary shape. We present explicit quantum spin and dimer Hamiltonians whose ground states violate this principle.

The title and abstract for this talk are forthcoming.

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Due to the fragility of quantum states, quantum error correction is a necessary ingredient for scalable, beneficial quantum computation. In order not to lose the corrective power of an error correcting code, logical operations as well as the decoding need to be performed in a fault-tolerant way. In this context, I will present recent results on the modelling of lattice surgery for performing a logical state teleportation between surface codes, as well as recent experimental demonstration of fault-tolerant lattice surgery with quantum repetition codes [1].

The quantum capacity is a fundamental bound on the rate of a quantum error correcting code: it gives the maximal number of logical qubits k that can be encoded in n noisy physical qubits, subject to random depolarizing or erasure errors. A major achievement of classical coding theory is the construction of LDPC error correcting codes approaching the classical capacity of symmetric binary channels.

Quantum error-correcting codes are essential in the realization of a scalable fault-tolerant quantum computation. Traditionally, these codes encodes logical information in a fixed subspace of a many-body quantum system which allow correction of errors by performing commuting measurements to determine appropriate corrections. By allowing non-commuting measurements, one obtain the so called "subsystem’’ code which allow for simpler measurements and the ability to perform universal fault-tolerant computation by switching across logical subspaces.

Quantum information science is a promising, interdisciplinary field focusing on both understanding and utilizing quantum systems. Two major paradigms of quantum mechanics are discrete variable (finite dimensional) systems, such as qubits and qudits, and continuous variable (infinite dimensional) systems,  such as bosonic modes. In this dissertation, we explore the properties, protocols, and applications of both discrete and continuous variable systems.

Robust storage and manipulation of quantum information in realistic quantum devices remains one of the central challenges in realizing practical quantum computation. To resolve this problem, the quantum error correction (QEC) is proposed as a technique to perform robust encoding and operations in noisy and realistic quantum devices. In the quantum realm, two fundamentally different types of particles—fermions and bosons—exhibit distinct behaviors.

Quantum computers have the theoretical potential to solve problems intractable for classical computers. However, realizing this potential requires dealing with the noise inherent in near and far-term devices. One way of doing this is to redundantly encode the quantum information in a quantum error-correcting code and manipulate the encoded states to do computation. Protecting quantum information in this way incurs additional space overhead in the form of extra qubits; this is problematic since qubits are a scarce resource, especially for near-term quantum computers.

Locality constrains the flow of information between different parts of many-body quantum systems. In quantum computers, this affects the ability to perform arbitrary interactions for quantum information processing tasks. A crucial challenge for scalable quantum architectures is thus to minimize the overheads due to locality constraints. Additionally, locality constraints affect the way information and entanglement can be spread in many body quantum systems, and our ability to make predictions about such systems.

Instabilities, where initially small fluctuations seed the formation of large-scale structures, govern the dynamics in wide variety of fluid flows. The Rayleigh-Taylor instability (RTI) is an iconic example that leads to the development of mushroom-shaped incursions when immiscible fluids are accelerated into each other. RTI drives structure formation throughout science and engineering including table-top oil and water mixtures; supernova explosions; and inertial confinement fusion.  Despite its ubiquity, controlled laboratory RTI experiments are technically challenging.