Related papers: Quantum geometry and quantum algorithms
We present a formal but simple calculational scheme to relate the expectation value of Wilson loops in Chern-Simons theory to the Jones polynomial. We consider the exponential of the generator of homotopy transformations which produces the…
Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…
Quantum computers are expected to give major speed-ups for the simulation of quantum systems. In these conference proceedings, we discuss quantum algorithms for the simulation of perturbative Quantum Chromodynamics (QCD) processes. In…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
We consider the task of estimating the expectation value of an $n$-qubit tensor product observable $O_1\otimes O_2\otimes \cdots \otimes O_n$ in the output state of a shallow quantum circuit. This task is a cornerstone of variational…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…
Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups…
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…
Topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions. Chern-Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…
We construct 3D $\mathcal{N}=2$ abelian gauge theories on $\mathbb{S}^2 \times \mathbb{S}^1$ labeled by knot diagrams whose K-theoretic vortex partition functions, each of which is a building block of twisted indices, give the colored Jones…
Only a few classes of quantum algorithms are known which provide a speed-up over classical algorithms. However, these and any new quantum algorithms provide important motivation for the development of quantum computers. In this article new…
Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the…
We propose an experimentally feasible scheme to achieve quantum computation based solely on geometric manipulations of a quantum system. The desired geometric operations are obtained by driving the quantum system to undergo appropriate…
Quantum algorithms are conventionally formulated for implementation on a single system of qubits amenable to projective measurements. However, in expectation value quantum computation, such as nuclear magnetic resonance realizations, the…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum simulation of strongly correlated fermionic…
Conformal field theory, describing systems with scaling symmetry, plays a crucial role throughout physics. We describe a quantum algorithm to simulate the dynamics of conformal field theories, including the action of local conformal…