Post, February 25, 2021 • We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving. Prove-It uses a highly-flexible Jupyter notebook-based user interface that documents interactions and proof steps using LaTeX. Prove-It is a theorem-proving assistant that is designed...

# Uncategorized

## Quantum Computing 2022

Post, July 22, 2022 • We provide a tour of quantum computing and quantum technology that is aimed to be comprehensible to scientists and engineers without becoming a popular account. There is high need for sober assessments of quantum of the promise of quantum technology appropriate for the quantum interested. We have aimed to cite...

## Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers

Post, April 22, 2021 • We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting...

## Quantum proportional-integral feedback control

Post, August 8, 2020 • We develop a theory of proportional-integral (PI) feedback control for quantum systems, and demonstrate its utility in two canonical state stabilization problems in quantum information. Feedback control is a general approach to engineering reliability and stability in many modern technologies. PI feedback is the most common and useful type of...

## Quantum simulation of the qubit-regularized O(3)-sigma model

Post, July 6, 2020 • We demonstrate how to prepare the ground state of the O(3)-sigma model and measure the O(3) Noether charge, on a quantum computer. We present and analyze a quantum simulation algorithm that is suitable for near-term noisy quantum devices. We consider a crucial step in simulating field theories, which is a...

## Quantum simulation of weak-field light-matter interactions

Post, July 22, 2022 • We develop a quantum simulation approach that enable platforms with controllable bosonic degrees of freedom, such as the trapped ions and circuit-QED, to simulate the dynamics of matter in response to illumination by extremely weak light fields. The dynamics of matter under weak-field illumination dictates the behavior of photodetectors, photovoltaics,...

## Quantum state verification in the quantum linear systems problem

Post, September 19, 2020 • We analyze the complexity of quantum state verification (QSV) in the context of solving systems of linear equations and provide complexity bounds that show that any verification procedure for this problem is "expensive". Our results are an important contribution to quantum complexity and, among other implications, show that checking that...

## Qubit-efficient exponential suppression of errors

Post, April 22, 2021 • We propose a novel error mitigation method that exponentially suppresses errors with a fixed number of qubits. Our method is feasible for the quantum advantage regime. Error mitigation will be necessary for practical quantum advantage. Most error mitigation methods do not provide exponential suppression of errors. An exception is virtual...

## Surrogate-based optimization for variational quantum algorithms

Post, July 22, 2022 • The most useful potential applications of quantum computers will require programs containing millions of operations, but current state-of-the-art devices are able to run programs that are only a small fraction of that length. To accommodate this limitation, procedures known as “variational quantum algorithms” (VQAs) have been developed, which attempt to...

## The battle of clean and dirty qubits in the era of partial error correction

Post, July 22, 2022 • When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between...

## Unified approach to data-driven quantum error mitigation

Post, February 25, 2021 • Data-driven approaches to error mitigation are the current state-of-the-art. We unify two such approaches. One approach involves circuits with variable noise, and the other involves Clifford circuits. Our approach uses both types of data (Clifford circuits with variable noise), resulting in a method more powerful than the previous ones. Our...

## Unifying and benchmarking state-of-the-art quantum error mitigation techniques

Post, August 30, 2021 • Error mitigation is an essential component of achieving practical quantum advantage in the near term, and a number of different approaches have been proposed. In this work we unify three recently proposed error mitigation methods: zero-noise extrapolation (ZNE), Clifford-data regression (CDR), and virtual distillation (VD). We unify these three methods under a...

## Variational quantum state eigensolver

Post, July 6, 2020 • We introduce a near-term algorithm for extracting the eigenvalues and eigenvalues of a density matrix, with application to error mitigation, entanglement spectroscopy, and principal component analysis (PCA). PCA is an important primitive in big-data analysis. Previous quantum algorithms for PCA are difficult to implement on NISQ computers. Here, we propose...

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