Efficient parallelization of tensor network contraction for simulating quantum computation

Abstract

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.

Solving the sampling problem of the Sycamore quantum supremacy circuits

“…3 indicates that our distribution fits very well to the Porter-Thomas distribution [1,11]. The 2 20 26 bitstrings obtained from the Sycamore supremacy circuits with n = 53 qubits and m = 20 cycles. N = 2 n is the dimension of the Hilbert space.…”

“…For each group we assign 2 6 = 64 correlated bitstrings, corresponding to 6 open qubits. So finally we have computed 2 26 bitstrings amplitudes by contracting G by summing over 2 16 paths. As a sanity check, we compute the squared norm N = 2 20 i=1 64 µ=1 | ψ µ i | 2 of the sparse-state by summing only a fraction of total paths, and compare to the expected fidelity with partial summation (i.e.…”

“…II D. Analogous to the sampling procedure we performed for the circuits with n = 53 qubits and m = 20 cycles. On the circuit with n = 30 qubits and m = 14 cycles we also computed approximate probabilities { P(s i )} for 2 26 bitstrings {s i } which are grouped into 2 20 groups. Then we sample one bitstring from each group using the rejection sampling with Markov chains and finally produce 2 20…”

“…II B) is L = 2 20 groups of amplitudes, each group contains l = 2 6 = 64 bitstring amplitudes. That is, we have computed approximate amplitudes for 2 26 = 67, 108, 864 bitstrings and finally sampled 2 20 uncorrelated bitstrings from them.…”

“…To increase the GPU efficiency, the branch merge strategy [16,26] was adopted during the contraction. After branch merging, the GPU efficiency is 31.76% for G head and 14.27% for G tail , the overall efficiency is 18.85%.…”