Related papers: Circuit complexity and functionality: a thermodyna…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
Proving that there are problems in $\mathsf{P}^\mathsf{NP}$ that require boolean circuits of super-linear size is a major frontier in complexity theory. While such lower bounds are known for larger complexity classes, existing results only…
We say that a circuit $C$ over a field $F$ functionally computes an $n$-variate polynomial $P$ if for every $x \in \{0,1\}^n$ we have that $C(x) = P(x)$. This is in contrast to syntactically computing $P$, when $C \equiv P$ as formal…
Quantum circuit complexity quantifies the minimal number of gates needed to realize a unitary transformation and plays a central role in quantum computation. In this work, we investigate the complexity of quantum circuits through coherence…
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…
We study the holographic complexity conjectures for rotating black holes, uncovering a relationship between the complexity of formation and the thermodynamic volume of the black hole. We suggest that it is the thermodynamic volume and not…
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…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
Motivated by holographic complexity proposals as novel probes of black hole spacetimes, we explore circuit complexity for thermofield double (TFD) states in free scalar quantum field theories using the Nielsen approach. For TFD states at t…
Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…
Embezzlement of entanglement is the counterintuitive process in which entanglement is extracted from a resource system using local unitary operations, with almost no detectable change in the resource's state. It has recently been argued…
Classical complexity theory measures the cost of computing a function, but many computational tasks require committing to one valid output among several. We introduce determination depth -- the minimum number of sequential layers of…
This paper provides a precise and scientific definition of complexity and coupling, grounded in the functional domain, particularly within industrial control and automation systems (iCAS). We highlight the widespread ambiguity in defining…
Modern understanding of symmetry in quantum field theory includes both invertible and non-invertible operations. Motivated by this, we extend Nielsen's geometric approach to quantum circuit complexity to incorporate non-invertible gates.…
We propose a duality between thermodynamics and computational complexity, elevating the difficulty of a computational task to the status of a thermodynamic variable. By introducing a complexity measure C as a novel coordinate, we formulate…
The singularities prevalent in classical thermodynamics largely stem from the "postulate of equal a priori probabilities" neglecting the physical constraints imposed by computational complexity. This paper introduces Complexity Window…
Boolean matching is an important problem in logic synthesis and verification. Despite being well-studied for conventional Boolean circuits, its treatment for reversible logic circuits remains largely, if not completely, missing. This work…
In the rapidly evolving field of quantum computing, quantifying circuit complexity remains a critical challenge. This paper introduces Character Complexity, a novel measure that bridges Group-theoretic concepts with practical quantum…
We reduce the problem of proving deterministic and nondeterministic Boolean circuit size lower bounds to the analysis of certain two-dimensional combinatorial cover problems. This is obtained by combining results of Razborov (1989),…