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Transformers, while powerful, suffer from quadratic computational complexity and the ever-growing Key-Value (KV) cache of the attention mechanism. This paper introduces Trellis, a novel Transformer architecture with bounded memory that…
Here we investigate the effect lattice geometry has on the lifetime of two-dimensional topological quantum memories. Initially, we introduce various lattice patterns and show how the error-tolerance against bit-flips and phase-flips depends…
Reliable quantum computation requires systematic identification and correction of errors that occur and accumulate in quantum hardware. To diagnose and correct such errors, standard quantum error-correcting protocols utilize…
Recently, it has become apparent that the thermal stability of topologically ordered systems at finite temperature, as discussed in condensed matter physics, can be studied by addressing the feasibility of self-correcting quantum memory, as…
This thesis develops a decision-theoretic framework for extracting thermodynamic work from temporal correlations in quantum systems. We model a classical agent -- lacking quantum memory -- performing adaptive work extraction through…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
Topological degeneracy is the degeneracy of the ground states in a many-body system in the large-system-size limit. Topological degeneracy cannot be lifted by any local perturbation of the Hamiltonian. The topological degeneracies on closed…
We can encode a qubit in the energy levels of a quantum system. Relaxation and other dissipation processes lead to decay of the fidelity of this stored information. Is it possible to preserve the quantum information for a longer time by…
Many proposals for quantum information processing are subject to detectable loss errors. In this paper, we give a detailed account of recent results in which we showed that topological quantum memories can simultaneously tolerate both loss…
A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with…
We examine two proposals for marginally self-correcting quantum memory, the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their…
In a number of natural and social systems, the response to an exogenous shock relaxes back to the average level according to a long-memory kernel $\sim 1/t^{1+\theta}$ with $0 \leq \theta <1$. In the presence of an epidemic-like process of…
We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is, in principle, possible to store quantum information for macroscopic times without the…
We refine an old idea for performing fault-tolerant error correction in topological codes by simulating confining interactions between excitations. We implement confinement using an array of local classical processors that measure…
Quantum memory is a central component for quantum information processing devices, and will be required to provide high-fidelity storage of arbitrary states, long storage times and small access latencies. Despite growing interest in applying…
We construct simulation-secure one-time memories (OTM) in the random oracle model, and present a plausible argument for their security against quantum adversaries with bounded and adaptive depth. Our contributions include: (1) A simple…
We propose a new method to autonomously correct for errors of a logical qubit induced by energy relaxation. This scheme encodes the logical qubit as a multi-component superposition of coherent states in a harmonic oscillator, more…
Transformer networks, driven by self-attention, are central to Large Language Models. In generative Transformers, self-attention uses cache memory to store token projections, avoiding recomputation at each time step. However, GPU-stored…
Memory replay based techniques have shown great success for continual learning with incrementally accumulated Euclidean data. Directly applying them to continually expanding networks, however, leads to the potential memory explosion problem…
Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In…