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Quantum computing has recently emerged as a promising computing paradigm for many application domains. However, the size of quantum circuits that can be run with high fidelity is constrained by the limited quantity and quality of physical…

Many of the envisioned use-cases for quantum computers involve optimisation processes. While there are many algorithmic primitives to perform the required calculations, all eventually lead to quantum gates operating on quantum bits, with an…

Active subspaces are an emerging set of tools for identifying and exploiting the most important directions in the space of a computer simulation's input parameters; these directions depend on the simulation's quantity of interest, which we…

Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…

As quantum computing technology advances, the need for optimized arithmetic circuits continues to grow. This paper presents the implementation and resource estimation of a library of quantum arithmetic algorithms, including addition,…

We are faced with convex quadratic programing in many contexts related to control theory, economy and robotics. In this paper, we introduce a new active set algorithm for solving such problems and analyze its possible advantages. The…

Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…

In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling…

We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…

The current state of quantum computing is commonly described as the Noisy Intermediate-Scale Quantum era. Available computers contain a few dozens of qubits and can perform a few dozens of operations before the inevitable noise erases all…

Quantum Phase Estimation (QPE) routines are known to fail probabilistically even with perfect gates and input states. This effect stems from an incompatibility of finite-sized quantum registers to capture a phase within QPE with phase…

Quantum computing could impact various industries, with the automotive industry with many computational challenges, from optimizing supply chains and manufacturing to vehicle engineering, being particularly promising. This chapter…

Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…

Qubit reuse offers a promising way to reduce the hardware demands of quantum circuits, but current approaches are largely restricted to reordering measurements and applying qubit resets. In this work, we present an approach to further…

Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…

A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…

Performing large calculations with a quantum computer will likely require a fault-tolerant architecture based on quantum error-correcting codes. The challenge is to design practical quantum error-correcting codes that perform well against…

The network paradigm for quantum computing involves interconnecting many modules to form a scalable machine. Typically it is assumed that the links between modules are prone to noise while operations within modules have significantly higher…

We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the…

Existing quantum systems provide very limited physical qubit counts, trying to execute a quantum algorithm/circuit on them that have a higher number of logical qubits than physically available lead to a compile-time error. Given that it is…