Noise Decoherence and Errors from Entanglement-function Theory for Quantum Computing
A significant problem in quantum computing is the development of physical realizations of algorithms that are robust against noise. One way to examine and mitigate noise would be to simulate large sets of qubits coupling to the external environment on classical computers. This is extremely challenging as quantum information processing is in some sense tied to computing resources that scale exponentially with the number of computing elements (qubits). In this LDRD, we set the foundation for a computational framework potentially allowing simulations of 1000s of qubits vs. 10s now possible. Exact wave-function-based methods demand exponentially increasing resources with system size. The method proposed, entanglement-functional theory (EFT), requires vastly fewer resources. The crucial step is to map the information contained in the wave-functions into a simpler object with associated 1.) auxiliary gate operations and 2.) entanglement functionals of this object. This is similar to the Time-dependent Density Functional Theory (TDDFT) approach that has revolutionized chemistry and materials science. Instead of dealing with the exponentially large wave-function, EFT works with a polynomially large set of projections (the density) that are easily manipulated through unitary operations. For a given set of quantum gates, an isomorphism exists that relates the sequence of events to the time-dependent density. A system of entangled qubits can be simulated at drastically reduced cost relative to existing state-of-the-art vector-state simulation codes.