Abstract
This paper studies methods for numerical simulations of many-body quantum systems, useful for simulating photonic networks and some quantum computers. The authors show that different phase-space methods have an exponentially large range of efficiency and speed for computing high-order correlations. The results can be either exponentially faster or slower than experimental measurement.
Highlights
For simulations of large dynamical quantum systems, one must have scalability as the mode number increases [1], since the number of dimensions in the Hilbert space is exponentially complex in the number of modes
Scalability is an issue even when there are exact solutions, because representing an arbitrary initial quantum state may require a superposition of exponentially many eigenstates
The sampling error eS is directly proportional to 1/ S for S computed or experimentally measured random samples. Both the computational and experimental time scales as 1/e2S. This exponential reduction in sampling errors we find in these complex weighted approaches leads to exponentially faster simulation times for high-order correlations at large mode numbers
Summary
For simulations of large dynamical quantum systems, one must have scalability as the mode number increases [1], since the number of dimensions in the Hilbert space is exponentially complex in the number of modes. These methods have already been used to treat very large Hilbert spaces, up to millions of qubit equivalents in BEC dynamics [13,14,15], and thousands of qubit equivalents [16,17,18] in the simulation of optical quantum computers, including the coherent Ising machine used to solve NP-hard optimization problems [19,20,21] Both types of system can be experimentally scaled to large sizes, with measured higher-order correlations [22,23,24]. Both the computational and experimental time scales as 1/e2S This exponential reduction in sampling errors we find in these complex weighted approaches leads to exponentially faster simulation times for high-order correlations at large mode numbers
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