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Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_2(3)$…
Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…
Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an…
The Heisenberg representation of quantum operators provides a powerful technique for reasoning about quantum circuits, albeit those restricted to the common (non-universal) Clifford set H, S and CNOT. The Gottesman-Knill theorem showed that…
Fault-tolerant quantum computing requires extremely precise knowledge and control of qubit dynamics during the application of a gate. We develop a data-driven learning protocol for characterizing quantum gates that builds off previous work…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
We study the non-singlet sectors of Matrix Quantum Mechanics in application to two-dimensional string theory. We use the chiral formalism, which operates directly with incoming and outgoing asymptotic states, related by a scattering…
Scaling up quantum computing hardware is hindered by the narrow operating margins of current quantum components. Here, we introduce a composite qubit and gate scheme that achieves wide margins by use of transistor-like nonlinearities to…
Quantum holonomic gates hold built-in resilience to local noises and provide a promising approach for implementing fault-tolerant quantum computation. We propose to realize high-fidelity holonomic $(N+1)$-qubit controlled gates using…
We develop randomized quantum algorithms to simulate quantum collision models, also known as repeated interaction schemes, which provide a rich framework to model various open-system dynamics. The underlying technique involves composing…
Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them suitable to express resource-sensitive systems, in which variables cannot be copied or discarded at will. In SMTs, traditional tree-like terms are…
Executing quantum algorithms over distributed quantum systems requires quantum circuits to be divided into sub-circuits which communicate via entanglement-based teleportation. Naively mapping circuits to qubits over multiple quantum…
Design of a large-scale quantum computer has paramount importance for science and technologies. We investigate a scheme for realization of quantum algorithms using noncomposite quantum systems, i.e., systems without subsystems. In this…
We introduce a quantum neural network, QNN, that can represent labeled data, classical or quantum, and be trained by supervised learning. The quantum circuit consists of a sequence of parameter dependent unitary transformations which acts…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
Matrix geometric means between two positive definite matrices can be defined from distinct perspectives - as solutions to certain nonlinear systems of equations, as points along geodesics in Riemannian geometry, and as solutions to certain…
Quantum algorithms claim significant speedup over their classical counterparts for solving many problems. An important aspect of many of these algorithms is the existence of a quantum oracle, which needs to be implemented efficiently in…
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…
We present a new graphical calculus that is sound and complete for a universal family of quantum circuits, which can be seen as the natural string-diagrammatic extension of the approximately (real-valued) universal family of Hadamard+CCZ…