This presentation will report on a number of studies conducted in my laboratory, mainly on the ability of large language models to solve analogies between sentences. We show that the task does not necessarily require a large number of parameters for fairly formal analogies. By defining constraints and introducing a measure of analogy quality, we are able to collect a large number of more or less robust analogies between sentences. We show that analogy quality prevails over quantity in fine-tuning and demonstrate this in machine translation tasks with low-resource languages. We also mention experiments on solving arithmetic problems by answer verification (binary classification), multiple-choice questions (selection from candidate answers), and generation of answer. The results clearly show that binary classification is the easiest task, and that there is little correlation between the three tasks.

Quantum Singular Value Transformation (QSVT) is a unified framework that describes most quantum algorithms discovered thus far. This method implements polynomial transformations to any matrix embedded in the top-left block of a unitary, known as a block encoding. Given such a block-encoding U as an input, QSVT leads to optimal complexities in terms of the number of queries to U. However, the reliance on block encoding is a serious bottleneck for this framework. For instance, consider any Hamiltonian H that is a sum of L local operators. Constructing a block encoding of H itself requires O(log L) ancilla qubits and several sophisticated multi-qubit controlled gates which detrimentally affects the applicability of QSVT.

In my talk, I will discuss our recent work where we develop new quantum algorithms for implementing QSVT without relying on block encodings. Surprisingly, our methods make use of only basic Hamiltonian simulation techniques such as Trotterization to achieve near-optimal complexities while needing only a single ancilla qubit. Central to our method is a novel use of Richardson extrapolation, enabling systematic error cancellation in any interleaved sequences of arbitrary unitaries and Hamiltonian evolution operators, establishing a broadly applicable framework beyond QSVT. As applications, we develop new quantum algorithms for solving quantum linear systems and ground state property estimation, both achieving near optimal complexities without oracular access or sophisticated quantum subroutines, and consuming very few ancilla qubits. This represents a major simplification over existing algorithms for solving these problems.

We also develop two randomized quantum algorithms for QSVT in a setting where there is only sampling access to the terms of the Hamitonian. We prove concrete lower bounds for the complexity of QSVT within this access model which extends to other randomized quantum linear algebra-based techniques. Overall, our results provide a new framework for quantum algorithms, reducing hardware overhead while maintaining near-optimal performance, with implications for both near-term and fault-tolerant quantum computing.

In this talk, I will briefly introduce Quantinuum and the quantum computers we develop. I will then present our recent advances in device-independent (DI) quantum cryptography, in which devices are treated as untrusted black boxes. Specifically, I will discuss two new protocols: the first generates DI randomness from a quantum computational advantage — and was demonstrated for the first time on our 56-qubits quantum computer H2; the second amplifies weak randomness using Bell inequality violations. Along the way, I will also address some of the key challenges faced when implementing quantum cryptography protocols in the real-world. The talk is a mix of foundations and pragmatism.