Related papers: Enhanced CAD-Based Quantifier Elimination With Mul…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built through a process of projection and lifting to move the problem…
Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
The solution of physical problems discretized using the finite element methods using quantum computers remains relatively unexplored. Here, we present a unified formulation (FEqa) to solve such problems using quantum annealers. FEqa is a…
Quantization has been applied to multiple domains in Deep Neural Networks (DNNs). We propose Depthwise Quantization (DQ) where $\textit{quantization}$ is applied to a decomposed sub-tensor along the $\textit{feature axis}$ of weak…
There is growing interest in solving computer vision problems such as mesh or point set alignment using Adiabatic Quantum Computing (AQC). Unfortunately, modern experimental AQC devices such as D-Wave only support Quadratic Unconstrained…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a…
Quantum algorithms based on parameterized quantum circuits (PQCs) have enabled a wide range of applications on near-term quantum devices. However, existing PQC architectures face several challenges, among which the ``barren plateaus"…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…
Although only two quantum states of a physical system are often used to encode quantum information in the form of qubits, many levels can in principle be used to obtain qudits and increase the information capacity of the system. To take…
Algorithms and hardware for solving quadratic unconstrained binary optimization (QUBO) problems have made significant recent progress. This advancement has focused attention on formulating combinatorial optimization problems as quadratic…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
In density-based topology optimization, design variables associated to the boundaries of the design domain require unique treatment to negate boundary effects arising from the filtering technique. An effective approach to deal with…
Combinatorial optimization problems are typically formulated using Quadratic Unconstrained Binary Optimization (QUBO), where constraints are enforced through penalty terms that introduce auxiliary variables and rapidly increase Hamiltonian…
We develop numerical methods for elliptic systems governed by partial segregation constraints, in which three nonnegative components are required to have a vanishing pointwise product throughout the domain. This constraint enforces that at…
Scaling the size of monolithic quantum computer systems is a difficult task. As the number of qubits within a device increases, a number of factors contribute to decreases in yield and performance. To meet this challenge, distributed…