Related papers: Qubit Complexity of Continuous Problems
Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in…
Scalable modern-time fault-tolerant quantum computation and quantum communication in a network employ a large number of physical qubits. For example, IBM is reported to have made a 127-qubit quantum computer. Unlike classical computation,…
In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of…
The power of quantum computers is still somewhat speculative. While they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical…
The paradigm behind digital quantum computing inherits the idea of using binary information processing. Nature in fact gives much more rich structures of physical objects that can be used for encoding information, which is especially…
This paper proposes a hybrid quantum-classical algorithm to solve a fundamental power system problem called unit commitment (UC). The UC problem is decomposed into a quadratic subproblem, a quadratic unconstrained binary optimization (QUBO)…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
Topological invariants of a dataset, such as the number of holes that survive from one length scale to another (persistent Betti numbers) can be used to analyze and classify data in machine learning applications. We present an improved…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
Complexity of a quantum analogue of the satisfiability problem is studied. Quantum k-SAT is a problem of verifying whether there exists n-qubit pure state such that its k-qubit reduced density matrices have support on prescribed subspaces.…
We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum…
Developing high-performance materials is critical for diverse energy applications to increase efficiency, improve sustainability and reduce costs. Classical computational methods have enabled important breakthroughs in energy materials…
We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity…
An essential component of many sophisticated metaheuristics for solving combinatorial optimization problems is some variation of a local search routine that iteratively searches for a better solution within a chosen set of immediate…
We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP. 1. BQP is low for PP, i.e.,…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
Suppose we have a small quantum computer with only M qubits. Can such a device genuinely speed up certain algorithms, even when the problem size is much larger than M? Here we answer this question to the affirmative. We present a hybrid…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…