Related papers: Complexity measures in QFT and constrained geometr…
There are at least a number of ways to formally define complexity. Most of them relate to some kind of minimal description of the studied object. Being this one in form of minimal resources of minimal effort needed to generate the object…
In this note we investigate the role of Lloyd's computational bound in holographic complexity. Our goal is to translate the assumptions behind Lloyd's proof into the bulk language. In particular, we discuss the distinction between…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
We show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times, independent of any choices of the fundamental gates or cost metric. Deviations…
Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian…
In Nielsen's geometric approach to quantum complexity, the introduction of a suitable geometrical space, based on the Lie group formed by fundamental operators, facilitates the identification of complexity through geodesic distance in the…
For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated…
We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…
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…
Complexity plays a very important part in quantum computing and simulation where it acts as a measure of the minimal number of gates that are required to implement a unitary circuit. We study the lower bound of the complexity [Eisert, Phys.…
In quantum computation, optimizing depth and number of ancillary qubits in quantum circuits is crucial due to constraints imposed by current quantum devices. This paper presents an innovative approach to implementing arbitrary symmetric…
Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity…
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…
We formulate and investigate the simplest version of time-optimal quantum computation theory (t-QCT), where the computation time is defined by the physical one and the Hamiltonian contains only one- and two-qubit interactions. This version…
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…
Computation of circuit complexity has gained much attention in the Theoretical Physics community in recent times to gain insights into the chaotic features and random fluctuations of fields in the quantum regime. Recent studies of circuit…
Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present…
Excited bound states are often understood within scattering based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert…
This paper considers the realizability of quantum gates from the perspective of information complexity. Since the gate is a physical device that must be controlled classically, it is subject to random error. We define the complexity of gate…
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…