Related papers: Weighting gates in circuit complexity and holograp…
In the canonical approach of loop quantum gravity, arguably the most important outstanding problem is finding and interpreting solutions to the Hamiltonian constraint. In this work, we demonstrate that methods of machine learning are in…
Obtaining a good load balance is a significant challenge in scaling up lattice-Boltzmann simulations of realistic sparse problems to the exascale. Here we analyze the effect of weighted decomposition on the performance of the HemeLB…
Recent advancements in Quantum Computing and Machine Learning have increased attention to Quantum Machine Learning (QML), which aims to develop machine learning models by exploiting the quantum computing paradigm. One of the widely used…
This work develops measures for quantifying the effects of field noise upon targeted unitary transformations. Robustness to noise is assessed in the framework of the quantum control landscape, which is the mapping from the control to the…
Coherent errors in quantum operations are ubiquitous. Whether arising from spurious environmental couplings or errors in control fields, such errors can accumulate rapidly and degrade the performance of a quantum circuit significantly more…
We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…
One of the hardest problems to tackle in the dynamics of canonical approaches to quantum gravity is that of the Hamiltonian constraint. We investigate said problem in the context of formal geometric quantization. We study the implications…
This thesis develops recent work on the so called Volume-Complexity and Action-Complexity conjectures. According to this family of proposals, geometric quantities can be defined in some holographic gravitational theories that can be mapped…
Fibonacci gate problems have severed as computation primitives to solve other problems by holographic algorithm and play an important role in the dichotomy of exact counting for Holant and CSP frameworks. We generalize them to weighted…
Despite using a novel model of computation, quantum computers break down programs into elementary gates. Among such gates, entangling gates are the most expensive. In the context of fermionic simulations, we develop a suite of compilation…
A quantum computing simulation provides the opportunity to explore the behaviors of quantum circuits, study the properties of quantum gates, and develop quantum computing algorithms. Simulating quantum circuits requires geometric time and…
Complex quantum simulation workflows are often hindered by incompatible wavefunction representations adopted across different algorithmic frameworks. In particular, the mismatch between the first- and second-quantization formalisms prevents…
Non Abelian geometric phases are attracting increasing interest because of possible experimental application in quantum computation. We study the effects of the environment (modelled as an ensemble of harmonic oscillators) on a holonomic…
In this paper, we consider the effect of electromagnetic field to the definition of complexity in the context of $f(G,T)$ gravity, where $G$ and $T$ express the Gauss-Bonnet term and energy-momentum tensor, respectively. The physical…
When a quantum system is divided into subsystems, their entanglement entropies are subject to an inequality known as "strong subadditivity". For a field theory this inequality can be stated as follows: given any two regions of space $A$ and…
Quadratic unconstrained binary optimization (QUBO) provides problem formulations for various computational problems that can be solved with dedicated QUBO solvers, which can be based on classical or quantum computation. A common approach to…
We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the $\phi^4$ theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled…
Variational quantum algorithms use non-convex optimization methods to find the optimal parameters for a parametrized quantum circuit in order to solve a computational problem. The choice of the circuit ansatz, which consists of…