Related papers: Circuit complexity and functionality: a thermodyna…
The minimum number of NOT gates in a Boolean circuit computing a Boolean function is called the inversion complexity of the function. In 1957, A. A. Markov determined the inversion complexity of every Boolean function and proved that…
The evaluation of a query over a probabilistic database boils down to computing the probability of a suitable Boolean function, the lineage of the query over the database. The method of query compilation approaches the task in two stages:…
Black hole thermodynamics has recently witnessed three distinct classification schemes: based on local geometric properties of the temperature function, global topological invariants, and Riemann surface foliations in the complex plane. We…
The presumption that Hawking radiations are thermally distributed can be considered to result from their entanglement with the internal degrees of freedom for a black hole. This leads to the "firewall" paradox if unitary evolution continues…
To derive black hole thermodynamics in any quantum theory of gravity, one must introduce constraints that ensure that a black hole is actually present. For a large class of black holes, the imposition of such ``horizon constraints'' allows…
By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with…
Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
Thermodynamic depth is an appealing but flawed structural complexity measure. It depends on a set of macroscopic states for a system, but neither its original introduction by Lloyd and Pagels nor any follow-up work has considered how to…
Given at PiTP 2018 summer program entitled "From Qubits to Spacetime." The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. Lecture two reviews the…
Reduce and control complexity is an essential practice in software design. Cyclomatic complexity (CC) is one of the most popular software metrics, applied for more than 40 years. Despite CC is an interesting metric to highlight the number…
We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using…
In this article, we investigate the physical implications of the causality constraint via effective sound speed $c_s(\leq 1)$ on Quantum Circuit Complexity(QCC) in the framework of Cosmological Effective Field Theory (COSMOEFT) using the…
Noise is one of the main obstacles to realizing quantum devices that achieve a quantum computational advantage. A possible approach to minimize the noise effect is to employ shallow-depth quantum circuits since noise typically accumulates…
Here we show that to quantize any lumped element circuit, the circuit geometry must be included in a mathematical model of either the circuit fluxes or the circuit charges. By geometry of the circuit, we refer to the so-called parasitic…
The circuit diameter of a polyhedron is the maximum length (number of steps) of a shortest circuit walk between any two vertices of the polyhedron. Introduced by Borgwardt, Finhold and Hemmecke (SIDMA 2015), it is a relaxation of the…
Recently a certain conceptual puzzle in the AdS/CFT correspondence, concerning the growth of quantum circuit complexity and the wormhole volume, has been identified by Bouland-Fefferman-Vazirani and Susskind. In this note, we propose a…
We revisit the minimum-link path problem: Given a polyhedral domain and two points in it, connect the points by a polygonal path with minimum number of edges. We consider settings where the vertices and/or the edges of the path are…
We refine the complexity landscape for enumeration problems by introducing very low classes defined by using Boolean circuits as enumerators. We locate well-known enumeration problems, e.g., from graph theory, Gray code enumeration, and…
The fission process is a fascinating phenomenon in which the atomic nucleus, a compact self-bound mesoscopic system, undergoes a spontaneous or induced quantum transition into two or more fragments. A predictive, accurate and precise…