A key step in many quantum algorithms is setting everything up: you need all your dominoes in place before you can do much else. This is called “state preparation”, and it’s a trickier problem than it might seem.
Our team has developed new protocols that can help – and in a big way. Specifically, the team worked on preparing “multivariate” functions, which just means functions that are used to explore problems with more than one variable, or in more than 1 dimension. One-dimensional problems do exist (think of a path that only goes forwards or backwards – we can call the variable “x”) but in the real world it’s much more common to have problems with many dimensions, or variables (think instead of a landscape where you can go forwards, backwards, left, right, up, and down – we can call the variables “x”, ”y”, and “z”).
Our new multivariate function quantum state preparation protocols don’t rely on some commonly-used and computationally expensive subroutines - instead they expand the desired multivariate function into well-known mathematical basis functions, called Fourier and Chebyshev functions. This makes our protocols simpler and more effective than previous options.
Generally, state preparation is a hard problem, and costs exponentially many resources to prepare an arbitrary state. By expanding the functions in a Fourier or Chebyshev series, one can truncate the series to create good approximations, which instead uses only polynomially many resources – meaning that this method has better asymptotic scaling than many other non-heuristic methods (which are often designed to work in only one dimension anyways).
Our team used their protocol to prepare a commonly used initial state on our H2 trapped-ion quantum processor, the bivariate Gaussian. Bivariate Gaussians are used everywhere from physics to finance, underscoring the practicality of these new protocols. They also analyzed examples potentially useful for quantum chemistry and partial differential equations.
A very nice feature of this work is that it is broadly applicable, generic, and entirely modular – meaning it can be plugged in to the beginning of almost any quantum algorithm, giving our customers and users even more flexibility and power.