Related papers: Towards Complexity for Quantum Field Theory States
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
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…
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…
Consanguinity of entropy and complexity is pointed out through the example of coherent states of the group $SL(d+1,\C)$. Both are obtained from the K\"ahler potential of the underlying geometry of the sphere corresponding to the…
Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the…
This work is originally a Cambridge Part III essay paper. Quantum complexity arises as an alternative measure to the Fubini metric between two quantum states. Given two states and a set of allowed gates, it is defined as the least complex…
An extension to computational mechanics complexity measure is proposed in order to tackle quantum states complexity quantification. The method is applicable to any $n-$partite state of qudits through some simple modifications. A Werner…
The achievement of quantum supremacy boosted the need for a robust medium of quantum information. In this task, higher-dimensional qudits show remarkable noise tolerance and enhanced security for quantum key distribution applications.…
We introduce "binding complexity", a new notion of circuit complexity which quantifies the difficulty of distributing entanglement among multiple parties, each consisting of many local degrees of freedom. We define binding complexity of a…
The area law for entanglement entropy fundamentally reflects the complexity of quantum many-body systems, demonstrating ground states of local Hamiltonians to be represented with low computational complexity. While this principle is…
We develop a general framework to calculate the many-body density of states (DOS) of isolated and interacting quantum systems. Based on the generalized coherent state formalism and the Simon-Lieb bounds for a quantum partition function, our…
The Fubini-Study metric of quantum state manifold generated by the operators which satisfy the Heisenberg Lie algebra is calculated. The similar problem is studied for the manifold generated by the so(3) Lie algebra operators. Using these…
The measurement based, or one-way, model of quantum computation for continuous variables uses a highly entangled state called a cluster state to accomplish the task of computing. Cluster states that are universal for computation are a…
The notion of complexity of quantum states is quite different from uncertainty or information contents, and involves the tradeoff between its classical and quantum features. In this work, we we introduce a quantifier of complexity of…
We present a general construction of a geometric notion of circuit complexity for Gaussian states (both bosonic and fermionic) in terms of Riemannian geometry. We lay out general conditions that a Riemannian metric function on the space of…
The operator approach is applied to investigate the complexity of Bose-Hubbard model. We present a systematic method to expand the quantum complexity in series of coupling constant. We first study 2-sites system. For the ground state we can…
Beyond computer science, quantum complexity theory can potentially revolutionize multiple branches of physics, ranging from quantum many-body systems to quantum field theory. In this paper, we investigate the relationship between the sample…
Adaptive quantum circuits, leveraging measurements and classical feedback, significantly expand the landscape of realizable quantum states compared to their non-adaptive counterparts, enabling the preparation of long-range entangled states…
In this study, we explore a form of quantum circuit complexity that extends to open systems. To illustrate our methodology, we focus on a basic model where the projective Hilbert space of states is depicted by the set of orientations in the…
The statistical complexity of continuous-variable quantum states can be characterized with a quantifier defined in terms of information-theoretic quantities derived from the Husimi Q-function. In this work, we utilize this complexity…