Related papers: Models of quantum complexity growth
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
We study a generic model of quantum computer, composed of many qubits coupled by short-range interaction. Above a critical interqubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of the computer eigenstates. In…
Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schr\"odinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately…
Proponents of Complexity Science believe that the huge variety of emergent phenomena observed throughout nature, are generated by relatively few microscopic mechanisms. Skeptics however point to the lack of concrete examples in which a…
We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that…
Quantum circuit complexity-a measure of the minimum number of gates needed to implement a given unitary transformation-is a fundamental concept in quantum computation, with widespread applications ranging from determining the running time…
In quantum mechanics, a state is an element of a Hilbert space whose dimension exponentially grows with the increase of the number of particles (or qubits, in quantum computing). The vague question "is this huge Hilbert space really there?"…
We enhance our quantitative comprehension of the complexity associated with both time-optimal and time sub-optimal quantum Hamiltonian evolutions that connect arbitrary source and target states on the Bloch sphere, as recently presented in…
The speed limit provides an upper bound for the dynamical evolution time of a quantum system. Here, we introduce the notion of quantum acceleration limit for unitary time evolution of quantum systems under time-dependent Hamiltonian. We…
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
In quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere…
Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical…
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…
One of the core questions of quantum physics is how to reconcile the unitary evolution of quantum states, which is information-preserving and time-reversible, with evolution following the second law of thermodynamics, which, in general, is…
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…
We calculate the frame potential for Brownian clusters of $N$ spins or fermions with time-dependent all-to-all interactions. In both cases the problem can be mapped to an effective statistical mechanics problem which we study using a path…
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…
We present a scalable, robust approach to creating quantum programs of arbitrary size and complexity. The approach is based on the true abstraction of the problem. The quantum program is expressed in terms of a high-level model together…
Determining the quantum circuit complexity of a unitary operation is closely related to the problem of finding minimal length paths in a particular curved geometry [Nielsen et al, Science 311, 1133-1135 (2006)]. This paper investigates many…