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General-purpose quantum circuit simulator with Projected Entangled-Pair States and the quantum supremacy frontier
Chu Guo, Yong Liu, Min Xiong, Shichuan Xue, Xiang Fu, Anqi Huang, Xiaogang Qiang, Ping Xu, Junhua Liu, Shenggen Zheng, He-Liang Huang, Mingtang Deng, Dario Poletti, Wan-Su Bao, Junjie Wu
TL;DR
The paper examines the quantum-supremacy frontier for random quantum circuits. It uses PEPS-based tensor-network contraction to quantify simulation costs and demonstrates a 7 × 7, depth 1 + 40 + 1 simulation in 31 minutes using 92.51 TB of memory.
Problem
The paper investigates the quantum-supremacy frontier for random quantum circuits.
Method
The paper uses PEPS tensor-network contraction to compute circuit amplitudes and quantify memory and time complexity.
Results
31 minutes and 92.51 TB memory were required to measure an amplitude for a 7 × 7 circuit with depth 1 + 40 + 1.
Takeaways & Limitations
The simulator identifies the reachable frontier for random quantum circuits and can be combined with fast sampling to measure many amplitudes.
Takeaways & Limitations
An optimized implementation reported in [38] is faster when mapped to unit fidelity than this proof-of-principle calculation.
Abstract
from arXiv · showhide
Recent advances on quantum computing hardware have pushed quantum computing to the verge of quantum supremacy. Random quantum circuits are outstanding candidates to demonstrate quantum supremacy, which could be implemented on a quantum device that supports nearest-neighbour gate operations on a two-dimensional configuration. Here we show that using the Projected Entangled-Pair States algorithm, a tool to study two-dimensional strongly interacting many-body quantum systems, we can realize an effective general-purpose simulator of quantum algorithms. This technique allows to quantify precisely the memory usage and the time requirements of random quantum circuits, thus showing the frontier of quantum supremacy. With this approach we can compute the full wave-function of the system, from which single amplitudes can be sampled with unit fidelity. Applying this general quantum circuit simulator we measured amplitudes for a $7\times 7$ lattice of qubits with depth $1+40+1$ and double-precision numbers in 31 minutes using less than $93$ TB memory on the Tianhe-2 supercomputer.
Supplementary Materials General-purpose quantum circuit simulator with Projected Entangled-Pair States and
The supplementary materials accompany a general-purpose quantum simulator based on Projected Entangled-Pair States.
- The supplementary materials concern a general-purpose quantum circuit simulator using Projected Entangled-Pair States.
INTRODUCTION TO RANDOM QUANTUM CIRCUITS
Random quantum circuits use layered Hadamard, controlled-phase, and single-qubit gates on a two-dimensional lattice. Their average-case hardness and anti-concentration make them benchmarks for quantum supremacy.
- Random quantum circuits begin and end with Hadamard gates, with intermediate layers of controlled-phase and randomly chosen single-qubit gates.The intermediate operations are repeated to increase circuit depth.
- Controlled-phase gates alternate among eight configurations to entangle neighboring qubits on the lattice.
- The circuits satisfy average-case hardness and anti-concentration conditions, so they cannot be efficiently simulated classically.These properties motivate their use in quantum-supremacy demonstrations.
ALGORITHM FOR EXACT COMPUTATION OF THE OVERLAP
The overlap algorithm contracts the PEPS tensor network using lattice-dependent strategies, with complexity determined by the largest intermediate tensor. Specialized partitioning for square lattices improves parallelism and identifies the classical simulation frontier.
- Square-lattice strategies: The square-lattice strategies allow easier parallelism while preserving an exact contraction route to the amplitude.
- Generic contraction: The generic contraction strategy processes tensors row by row or column by column, requiring a largest tensor of rank min(Lh, Lv) + 1.The direction is chosen according to the lattice shape.
- Generic contraction: The resulting space and time estimates have clear prefactors and can be reduced through advanced matrix multiplication and parallelization.
- Square-lattice strategies: For square lattices, partitioning the network into four sublattices supports alternative contractions for even and odd side lengths.The four-part contractions ultimately produce the probability amplitude.
- Complexity and frontier: For depth 1 + 40 + 1, 8 × l circuits are within reach of state-of-the-art supercomputers, defining the frontier for this simulator and random quantum circuits.The method can also combine with fast sampling to measure many amplitudes, reusing results from other partitions.
COMPLEXITY ANALYSIS OF GOOGLE BRISTLECONE QPU
The PEPS simulator’s space and time costs are analyzed for random circuits on the Google Bristlecone lattice, including the memory required by its contraction strategy.
- COMPLEXITY ANALYSIS OF GOOGLE BRISTLECONE QPU: The simulator contracts the rotated Bristlecone tensor network with tensors having at most 11 legs, determining the space cost of the calculation.
- COMPLEXITY ANALYSIS OF GOOGLE BRISTLECONE QPU: Figure S3 reports time and space complexity as functions of vertical lattice size for both rectangular and square circuit geometries.The plots distinguish Lv > Lh from Lv = Lh and mark memory limits of 2.17 PB for Tianhe-2 and 2.67 PB for Summit.
- COMPLEXITY ANALYSIS OF GOOGLE BRISTLECONE QPU: Less than 0.6 PB memory is required to simulate the Google Bristlecone circuit to depth (1 + 32 + 1) with the described simulator.The reported scaling is 2^32/8×11+1 = 2^45, corresponding to less than 0.6 PB.
MASSIVE PARALLEL BENCHMARKING ON SUPERCOMPUTER
Massive parallel benchmarking evaluates the PEPS simulator on Tianhe-2, using distributed tensor contraction to measure amplitudes for large random circuits.
- MASSIVE PARALLEL BENCHMARKING ON SUPERCOMPUTER: The largest-depth benchmark simulated a 7 × 7 circuit at depth (1 + 40 + 1) in 31 minutes using 92.51 TB across 4,096 fat nodes.Each fat node used 23.13 GB; duplicated data increased memory beyond the 16 TB theoretical prediction.
- MASSIVE PARALLEL BENCHMARKING ON SUPERCOMPUTER: The largest-qubit benchmark simulated a 10 × 10 circuit at depth (1 + 26 + 1), measuring one amplitude in 6 minutes on 1,024 normal nodes.
- MASSIVE PARALLEL BENCHMARKING ON SUPERCOMPUTER: The Bristlecone contraction strategy partitions the 12 × 6 lattice into four 6 × 3 sub-lattices, producing tensors of ranks 11, 10, 10, and 11.Contracting the four resulting tensors requires storing at least two rank-11 tensors.
- MASSIVE PARALLEL BENCHMARKING ON SUPERCOMPUTER: A prior Summit implementation computed 10^6 amplitudes for the same 7 × 7 depth-(1 + 40 + 1) circuit in 2.4 hours using 2.67 PB and single-precision numbers.The passage states that its optimized implementation is faster when mapped to unit fidelity than this proof-of-principle calculation.