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Optimization of circuits is an essential task for both quantum and classical computers to improve their efficiency. In contrast, classical logic optimization is known to be difficult, and a lot of heuristic approaches have been developed so…
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
Parallelization is a major challenge in quantum algorithms due to physical constraints like no-cloning. This is vividly illustrated by the conjecture of Moore and Nilsson from their seminal work on quantum circuit complexity [MN01,…
We prove that the computation of the Kronecker coefficients of the symmetric group is contained in the complexity class #BQP. This improves a recent result of Bravyi, Chowdhury, Gosset, Havlicek, and Zhu. We use only the quantum computing…
In the geometric approach to define complexity, operator complexity is defined as the distance on the operator space. In this paper, based on the analogy with the circuit complexity, the operator size is adopted as the metric of the…
The Polynomial-Time Hierarchy ($\mathsf{PH}$) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to ''quantum advantage'' analyses for near-term quantum computers.…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
In this work, we propose a generalization of the current most widely used quantum computing hardware metric known as the quantum volume. The quantum volume specifies a family of random test circuits defined such that the logical circuit…
The quantum equivalence principle says that, for any given point, it is possible to find a quantum coordinate system with respect to which we have definite causal structure in the vicinity of that point. It is conjectured that this…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
We announce two breakthrough results concerning important questions in the Theory of Computational Complexity. In this expository paper, a systematic and comprehensive geometric characterization of the Subset Sum Problem is presented. We…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
The complexity class NP is quintessential and ubiquitous in theoretical computer science. Two different approaches have been made to define "Quantum NP," the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA by Knill,…
We introduce a systematic study of "symmetric quantum circuits", a new restricted model of quantum computation that preserves the symmetries of the problems it solves. This model is well-adapted for studying the role of symmetry in quantum…
Some representation-theoretic multiplicities, such as the Kostka and the Littlewood-Richardson coefficients, admit a combinatorial interpretation that places their computation in the complexity class #P. Whether this holds more generally is…
Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit…
We study the conditions under which, given a generic quantum system, complexity metrics provide actual lower bounds to the circuit complexity associated to a set of quantum gates. Inhomogeneous cost functions ---many examples of which have…
We introduce a novel software-oriented model of quantum computation motivated by the practical constraints of near-term quantum hardware. In this model, gates are specified by constraints expressed in terms of Pauli observables, with each…
Quantum neural networks (QNNs) based on parametrized quantum circuits are promising candidates for machine learning applications, yet many architectures lack clear connections to classical models, potentially limiting their ability to…