Related papers: Circuit complexity in quantum field theory
Characterizing the quantum complexity of local random quantum circuits is a very deep problem with implications to the seemingly disparate fields of quantum information theory, quantum many-body physics and high energy physics. While our…
The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which…
Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of…
In this article, we investigate various physical implications of quantum circuit complexity using squeezed state formalism of Primordial Gravitational Waves (PGW). Recently quantum information theoretic concepts, such as entanglement…
Holographic principle states that the maximum entropy of a system is its boundary area in Planck units. However, such a holographic entropy cannot be realized by the conventional quantum field theory. We need a new microscopic theory which…
We survey various recent results that rigorously study the complexity of learning quantum states. These include progress on quantum tomography, learning physical quantum states, alternate learning models to tomography and learning classical…
We derive a holographic description of the simplest quantum mechanical system, a 1d free particle. The dual formulation uses a couple of two-dimensional topological abelian BF theories with appropriate boundary conditions, interactions and…
We consider a strongly coupled field theory with a critical point and nonzero chemical potential at finite temperature, which is dual to an asymptotically AdS charged black hole. We study the evolution of the rescaled holographic subregion…
By using a recent approach proposed by Hackl $et\, al.$ to evaluate the complexity of the free fermionic Gaussian state, we compute the complexity of the Dirac vacuum state as well as the excited state of the Fermi system with a mass…
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…
The paper investigates relations between the phase space structure of a quantum field theory ("nuclearity") and the concept of pointlike localized fields. Given a net of local observable algebras, a phase space condition is introduced that…
Nielsen \cite{Nielsen05} recently asked the following question: "What is the minimal size quantum circuit required to exactly implement a specified $% \mathit{n}$-qubit unitary operation $U$, without the use of ancilla qubits?" Nielsen was…
We define circuits given by unitary representations of Lorentzian conformal field theory in 3 and 4 dimensions. Our circuits start from a spinning primary state, allowing us to generalize formulas for the circuit complexity obtained from…
A fundamental motif in frustrated magnetism is the fully mutually coupled cluster of $N$ spins, with each spin coupled to every other spin. Clusters with $N=2$ and $3$ have been extensively studied as building blocks of square and…
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…
We make comments on some shortcomings of the non-unitary-invariant and non-bi-invariant complexity in quantum mechanics/field theory and argue that the unitary-invariant and bi-invariant complexity is still a competitive candidate in…
We argue that the model of a quantum computer with N qubits on a quantum space background, which is a fuzzy sphere with n=2^N elementary cells, can be viewed as the minimal model for Quantum Gravity. In fact, it is discrete, has no free…
Quantum circuits are time dependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable and heuristic methods must…
..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational…
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…