Lowering qubit requirements for quantum simulations of fermionic systems

The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. One challenge in realizing simulations on near-term quantum devices is the large number of qubits required by such mappings. In this work, we develop methods that allow us to trade-off qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a non-linear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with only a very modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.Comment: 11+13 pages, 5 figures, 2 tables, see ArXiv files for Mathematica code (text file) and documentation (pdf); fixed typos in this new versio

The Future of Computation

``The purpose of life is to obtain knowledge, use it to live with as much satisfaction as possible, and pass it on with improvements and modifications to the next generation.'' This may sound philosophical, and the interpretation of words may be subjective, yet it is fairly clear that this is what all living organisms--from bacteria to human beings--do in their life time. Indeed, this can be adopted as the information theoretic definition of life. Over billions of years, biological evolution has experimented with a wide range of physical systems for acquiring, processing and communicating information. We are now in a position to make the principles behind these systems mathematically precise, and then extend them as far as laws of physics permit. Therein lies the future of computation, of ourselves, and of life.Comment: 7 pages, Revtex. Invited lecture at the Workshop on Quantum Information, Computation and Communication (QICC-2005), IIT Kharagpur, India, February 200

BOOL-AN: A method for comparative sequence analysis and phylogenetic reconstruction

A novel discrete mathematical approach is proposed as an additional tool for molecular systematics which does not require prior statistical assumptions concerning the evolutionary process. The method is based on algorithms generating mathematical representations directly from DNA/RNA or protein sequences, followed by the output of numerical (scalar or vector) and visual characteristics (graphs). The binary encoded sequence information is transformed into a compact analytical form, called the Iterative Canonical Form (or ICF) of Boolean functions, which can then be used as a generalized molecular descriptor. The method provides raw vector data for calculating different distance matrices, which in turn can be analyzed by neighbor-joining or UPGMA to derive a phylogenetic tree, or by principal coordinates analysis to get an ordination scattergram. The new method and the associated software for inferring phylogenetic trees are called the Boolean analysis or BOOL-AN

Rapid prediction of NMR spectral properties with quantified uncertainty

open access articleAccurate calculation of specific spectral properties for NMR is an important step for molecular structure elucidation. Here we report the development of a novel machine learning technique for accurately predicting chemical shifts of both 1H and 13C nuclei which exceeds DFT-accessible accuracy for 13C and 1H for a subset of nuclei, while being orders of magnitude more performant. Our method produces estimates of uncertainty, allowing for robust and confident predictions, and suggests future avenues for improved performance

Approximate Two-Party Privacy-Preserving String Matching with Linear Complexity

Consider two parties who want to compare their strings, e.g., genomes, but do not want to reveal them to each other. We present a system for privacy-preserving matching of strings, which differs from existing systems by providing a deterministic approximation instead of an exact distance. It is efficient (linear complexity), non-interactive and does not involve a third party which makes it particularly suitable for cloud computing. We extend our protocol, such that it mitigates iterated differential attacks proposed by Goodrich. Further an implementation of the system is evaluated and compared against current privacy-preserving string matching algorithms.Comment: 6 pages, 4 figure