Related papers: Continuous structures of quantum circuits
Unitary designs are unitary ensembles that emulate Haar-random unitary statistics. They provide a vital tool for studying quantum randomness and have found broad applications in quantum technologies. However, existing research has focused…
In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation,…
Generalizing the notion of continuous Hilbert space representations of compact topological groups we define unitary continuous correpresentations of $C^*$-completions of compact quantum group Hopf algebras on arbitrary Hilbert spaces. It is…
Quantum gauge theories with finite-dimensional representation spaces are constructed that can have canonical gauge field theories as singular limits. They describe nature as a recursive quantum assembly by iterating Fermi-Dirac…
One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions…
Hybrid quantum-classical systems make it possible to utilize existing quantum computers to their fullest extent. Within this framework, parameterized quantum circuits can be regarded as machine learning models with remarkable expressive…
We show that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements and "small" coherent superposition resource states.
We show that quantum computation circuits with coherent states as the logical qubits can be constructed using very simple linear networks, conditional measurements and coherent superposition resource states.
We present a quantum computational framework for SU(2) lattice gauge theory, leveraging continuous variables instead of discrete qubits to represent the infinite-dimensional Hilbert space of the gauge fields. We consider a ladder as well as…
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad…
We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection…
An essential element of classical computation is the "if-then" construct, that accepts a control bit and an arbitrary gate, and provides conditional execution of the gate depending on the value of the controlling bit. On the other hand,…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide.…
In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard Hilbert space model of quantum…
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey…