相关论文: Quantum NP and a Quantum Hierarchy

In this work we argue against the interpretation that underlies the "Standard" account of Quantum Mechanics (SQM) that was established during the 1930s by Niels Bohr and Paul Dirac. Ever since, following this orthodox narrative, physicists…

We consider the problem of mapping digital data encoded on a quantum register to analog amplitudes in parallel. It is shown to be unlikely that a fully unitary polynomial-time quantum algorithm exists for this problem; NP becomes a subset…

We propose solutions of the quantum Q-systems of types $B_N,C_N,D_N$ in terms of $q$-difference operators, generalizing our previous construction for the Q-system of type $A$. The difference operators are interpreted as $q$-Whittaker limits…

Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data…

We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…

The rapid development of quantum computer hardware has laid the hardware foundation for the realization of QNN. Due to quantum properties, QNN shows higher storage capacity and computational efficiency compared to its classical…

One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if [P,Q]=const. If a pair of difference operators (K,L) obey the relation KL=const LK we say that they specify a discrete quantum curve. This terminology…

We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…

It is suggested that a quantum neural network (QNN), a type of artificial neural network, can be built using the principles of quantum information processing. The input and output qubits in the QNN can be implemented by optical modes with…

We consider the power of various quantum complexity classes with the restriction that states and operators are defined over a real, rather than complex, Hilbert space. It is well know that a quantum circuit over the complex numbers can be…

Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…

Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…

Aaronson, Bouland, Fitzsimons and Lee introduced the complexity class PDQP (which was original labeled naCQP), an alteration of BQP enhanced with the ability to obtain non-collapsing measurements, samples of quantum states without…

The P=?NP problem is philosophically solved by showing P is equal to NP in the random access with unit multiply (MRAM) model. It is shown that the MRAM model empirically best models computation hardness. The P=?NP problem is shown to be a…

Quantum Martin-L\"of randomness (q-MLR) for infinite qubit sequences was introduced by Nies and Scholz. We define a notion of quantum Solovay randomness which is equivalent to q-MLR. The proof of this goes through a purely linear algebraic…

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…

Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain…

Quantum Neuromorphic Computing (QNC) merges quantum computation with neural computation to create scalable, noise-resilient algorithms for quantum machine learning (QML). At the core of QNC is the quantum perceptron (QP), which leverages…

Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…

The necessity of complex numbers in quantum mechanics has long been debated. This paper develops a real Kahler space formulation of quantum mechanics [19], asserting equivalence to the standard complex Hilbert space framework. By mapping…