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Symmetry plays a crucial role in the design and analysis of quantum protocols. This result shows a canonical circuit decomposition of a $(G \times H)$-invariant quantum comb for compact groups $G$ and $H$ using the corresponding…
We have taken significant steps towards the realization of a practical quantum computer: using nuclear spins and magnetic resonance techniques at room temperature, we provided proof of principle of quantum computing in a series of…
A goal of quantum information technology is to control the quantum state of a system, including its preparation, manipulation, and measurement. However, scalability to many qubits and controlled connectivity between any selected qubits are…
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…
The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons, which are otherwise difficult to…
The requirement of performing both single-qubit and two-qubit operations in the implementation of universal quantum logic often leads to very demanding constraints on quantum computer design. We show here how to eliminate the need for…
The Esscher Transform is a tool of broad utility in various domains of applied probability. It provides the solution to a constrained minimum relative entropy optimization problem. In this work, we study the generalization of the Esscher…
This thesis focuses on quantum information processing using the superconducting device, especially, on realizing quantum gates and algorithms in open quantum systems. Such a device is constructed by transmon-type superconducting qubits…
We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan…
We discuss a new approach to simulate quantum algorithms using classical probabilistic bits and circuits. Each qubit (a two-level quantum system) is initially mapped to a vector in an eight dimensional probability space (equivalently, to a…
This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of generic algorithms -- that is, algorithms that do not exploit any properties of the group…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
The performance of quantum algorithms for eigenvalue problems, such as computing Hamiltonian spectra, depends strongly on the overlap of the initial wavefunction and the target eigenvector. In a basis of Slater determinants, the…
The spin states of single electrons in gate-defined quantum dots satisfy crucial requirements for a practical quantum computer. These include extremely long coherence times, high-fidelity quantum operation, and the ability to shuttle…
Quantum computers, besides offering substantial computational speedups, are also expected to provide the possibility of preserving the privacy of a computation. Here we show the first such experimental demonstration of blind quantum…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
This dissertation explores quantum computation using qudits encoded into large spins, emphasizing the concept of quantum co-design to harness the unique capabilities of physical platforms for enhanced quantum information processing. First,…
Quantum computing promises to exploit the laws of quantum mechanics for processing information in ways fundamentally different from today's classical computers, leading to unprecedented efficiency. One-way quantum computation, sometimes…
Recently, Yamaguchi and Kempf [Phys. Rev. Lett. 136:010801, arXiv:2501.02757] proved that encrypted qubits can be cloned. In this work, we generalize the encrypted cloning protocol and prove that it also applies to higher-order quantum…
This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…