Related papers: From Fermions to Qubits: A ZX-Calculus Perspective
For half a century, Feynman diagrams have provided an enlightening way of representing many-body effects between elementary fermions and bosons. They however are quite inappropriate to visualize fermion exchanges taking place between a…
Quantum computers are believed to have the ability to process huge data sizes which can be seen in machine learning applications. In these applications, the data in general is classical. Therefore, to process them on a quantum computer,…
We propose a solvable model of Quantum Darwinism to encoding transitions -- abrupt changes in how quantum information spreads in a many-body system under unitary dynamics. We consider a random Clifford circuit on an expanding tree, whose…
Loop quantum gravity (LQG) attempts to unify general relativity with quantum physics to offer a complete description of the universe by quantising spacetime geometry, but the numerical calculations we encounter are extraordinarily…
Quantum computation requires the precise control of the evolution of a quantum system, typically through application of discrete quantum logic gates on a set of qubits. Here, we use the cross-resonance interaction to implement a gate…
Majorana zero modes (MZMs) promise a platform for topologically protected fermionic quantum computation. However, creating multiple MZMs and generating (directly or via measurements) the requisite transformations (e.g., braids) pose…
The ZX-calculus is a universal graphical language for qubit quantum computation, meaning that every linear map between qubits can be expressed in the ZX-calculus. Furthermore, it is a complete graphical rewrite system: any equation…
In this paper, an algorithm for Quantum Inverse Fast Fourier Transform (QIFFT) is developed to work for quantum data. Analogous to a classical discrete signal, a quantum signal can be represented in Dirac notation, application of QIFFT is a…
This article presents a novel algorithmic methodology for performing automated diagrammatic deductions over combinatorial structures, using a combination of modified equational theorem-proving techniques and the extended Wolfram model…
Finite-dimensional quantum theory serves as the theoretical foundation for quantum information and computation. Mathematically, it is formalized in the category FHilb, comprising all finite-dimensional Hilbert spaces and linear maps between…
In this research paper, our primary focus revolves around the domain-specific hardware mapping strategy tailored for Quantum Fourier Transformation (QFT) circuits. While previous approaches have heavily relied on SAT solvers or heuristic…
We provide an algorithm that factorizes one-dimensional quantum walks into a protocol of two basic operations: A fixed conditional shift that transports particles between cells and suitable coin operators that act locally in each cell. This…
Four-fermion operators have been utilized in the past to link the quark-exchange processes in the interaction of hadrons with the effective meson-exchange amplitudes. In this paper, we apply the similar idea of a Fierz rearrangement to the…
A numerical method is presented for reproducing fermionic quantum gas microscope experiments in equilibrium. By employing nested componentwise direct sampling of fermion pseudo-density matrices, as they arise naturally in determinantal…
After reviewing the theory of "causal fermion systems" (CFS theory) and the "Events, Trees, and Histories Approach" to quantum theory (ETH approach), we compare some of the mathematical structures underlying these two general frameworks and…
Many-body fermionic systems can be simulated in a hardware-efficient manner using a fermionic quantum processor. Neutral atoms trapped in optical potentials can realize such processors, where non-local fermionic statistics are guaranteed at…
We present, in the context of dimensional regularization, a prescription to renormalize Feynman diagrams with an arbitrary number of external fermions. This prescription, which is based on the original t'Hooft-Veltman proposal to keep…
Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude…
Quantum fermionic computations on occupation numbers proposed in quant-ph/0003137 are studied. It is shown that a control over external field and tunneling would suffice to fulfill all quantum computations without valuable slowdown in the…
We show that the computational effort for the numerical solution of fermionic quantum systems, occurring e.g., in quantum chemistry, solid state physics, field theory in principle grows with less than the square of the particle number for…