It is believed that random quantum circuits are difficult to simulate classically. These have been used to demonstrate quantum supremacy: the execution of a computational task on a quantum computer that is infeasible for any classical computer. The task underlying the assertion of quantum supremacy by Arute et al. (Nature, 574, 505-510 (2019)) was initially estimated to require Summit, the world's most powerful supercomputer today, approximately 10,000 years. The same task was performed on the Sycamore quantum processor in only 200 seconds.In this work, we present a tensor network-based classical simulation algorithm. Using a Summit-comparable cluster, we estimate that our simulator can perform this task in less than 20 days. On moderately-sized instances, we reduce the runtime from years to minutes, running several times faster than Sycamore itself. These estimates are based on explicit simulations of parallel subtasks, and leave no room for hidden costs. The simulator's key ingredient is identifying and optimizing the "stem" of the computation: a sequence of pairwise tensor contractions that dominates the computational cost. This orders-of-magnitude
We develop an algorithmic framework for contracting tensor networks and demonstrate its power by classically simulating quantum computation of sizes previously deemed out of reach. Our main contribution, index slicing, is a method that efficiently parallelizes the contraction by breaking it down into much smaller and identically structured subtasks, which can then be executed in parallel without dependencies. We benchmark our algorithm on a class of random quantum circuits, achieving greater than 105 times acceleration over the original estimate of the simulation cost. We then demonstrate applications of the simulation framework for aiding the development of quantum algorithms and quantum error correction. As tensor networks are widely used in computational science, our simulation framework may find further applications.
In the present work, we generalize the setting of dimers with potential gain and loss which have been extensively considered recently in PT -symmetric contexts. We consider a pair of waveguides which are evanescently coupled but may also be actively coupled and may possess onsite gain and loss, as well as (possibly non-uniform) nonlinearity. We identify (and where appropriate review from earlier work) a plethora of interesting dynamical scenaria ranging from the existence of stable and unstable fixed points and integrable dynamics, to the emergence of pitchfork or Hopf bifurcations and the generation of additional fixed points and limit cycles, respectively, as well as the potential deviation of trajectories to infinity. Thus, a catalogue of a large number of possible cases is given and their respective settings physically justified (where appropriate).
The reflectionless coherent light transport in the coupled resonator array is investigated in the presence of intraresonator intermodal coupling between the clockwise and counterclockwise modes, which plays a constructive role for modulating the light flow rather than inducing the unwanted backscattering. The interplay between the intra-resonator intermodal coupling and the inter-resonator couplings enables the coherent resonant transmission (CRT) of the properly superposed injection constituted by the clockwise and counterclockwise modes. The superposition coefficients of the initial excitation determine the mode chirality of the resonant transmission. Sequentially experiencing the time-reversal process of CRT and the CRT realizes the perfect mode conversion that the mode chirality of the injection wave switches into the opposite after resonant transmission. Our findings on the coherent light transport provide insights for the control and manipulation of light field in the integrated photonics, nanophotonics, chiral optics, and beyond.
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