Related papers: Fermion determinants on a quantum computer
Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most…
Powerful generative artificial intelligence from large language models (LLMs) harnesses extensive computational resources for inference. In this work, we investigate the transformer architecture, a key component of these models, under the…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
We present a quantum algorithm for computing the Ramsey numbers whose computational complexity grows super-exponentially with the number of vertices of a graph on a classical computer. The problem is mapped to a decision problem on a…
We present an algorithm computing the determinant of an integer matrix A. The algorithm is introspective in the sense that it uses several distinct algorithms that run in a concurrent manner. During the course of the algorithm partial…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
The Wilson fermion determinant can be written in the form of a series expansion in fugacity $\xi=\exp(\mu/T)$, provided that the eigenmodes of the temporally reduced operator are obtained. Since the calculation of all eigenmodes rapidly…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
We present a method for encoding second-quantized fermionic systems in qubits when the number of fermions is conserved, as in the electronic structure problem. When the number $F$ of fermions is much smaller than the number $M$ of modes,…
The increase with time of computer resources devoted to simulations of full QCD is spectacular. Yet the reduction of systematic errors is comparatively slow. This is due to the algorithmic complexity of the problem. I review, in elementary…
We present in details a numerical approach for solving supersymmetric quantum mechanical systems with a gauge symmetry valid in all fermionic sectors. The method uses a recursive algorithm to calculate matrix elements of any gauge invariant…
Solving Hamiltonian matrix is a central task in quantum many-body physics and quantum chemistry. Here we propose a novel quantum algorithm named as a quantum Heaviside eigen solver to calculate both the eigen values and eigen states of the…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
We report on a program to compute the electromagnetic form factors of mesons. We discuss the techniques used to compute the pion form factor and present results computed with domain wall valence fermions on MILC asqtad lattices, as well as…
Recent developments in quantum technology mean that is it now possible to manipulate systems and measure fermion fields (e.g. reservoirs of electrons) at the quantum level. This progress has motivated some recent work on filtering theory…
The lattice formulation provides a way to regularize, define and compute the Path Integral in a Quantum Field Theory. In this paper we review the theoretical foundations and the most basic algorithms required to implement a typical lattice…
The path-integral of the fermionic oscillator with a time-dependent frequency is analyzed. We give the exact relation between the boundary condition to define the domain in which the path-integral is performed and the transition amplitude…
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…
Quantum Phase Estimation is one of the most useful quantum computing algorithms for quantum chemistry and as such, significant effort has been devoted to designing efficient implementations. In this article, we introduce TFermion, a library…
Simulating fermionic systems on a quantum computer requires representing fermionic states using qubits. The complexity of many simulation algorithms depends on the complexity of implementing rotations generated by fermionic…