Source-linked AI summary
Quantum Teleportation-Inspired Algorithm for Sampling Large Random Quantum Circuits
Ming-Cheng Chen, Riling Li, Lin Gan, Xiaobo Zhu, Guangwen Yang, Chao-Yang Lu, Jian-Wei Pan
TL;DR
The paper addresses efficient simulation of low-depth random quantum circuits by replacing large physical-qubit circuits with smaller logical-qubit circuits. Its supplementary methods define logical gates and threshold-rejection sampling, with cross-entropy fidelity used to characterize the resulting samples. The approach provides a memory-efficient simulation framework with a clear circuit-transformation picture.
Problem
Efficiently simulating low-depth random quantum circuits requires circuit transformations and sampling procedures that can operate on reduced representations.
Source: Supplementary Information · p. 5Method
The method defines logical qubits along circuit topology, translates residual circuits into logical gates, and uses threshold-rejection sampling to generate samples.
Source: Supplementary Information · p. 5Results
The supplementary procedure characterizes generated samples using cross-entropy fidelity and sampling efficiency.
Source: Supplementary Information · p. 5Takeaways & Limitations
The framework combines circuit renormalization through logical gates with sampling-quality characterization for low-depth random-circuit simulation.
Source: Supplementary Information · p. 5
Abstract
from arXiv · showhide
We show that low-depth random quantum circuits can be efficiently simulated by a quantum teleportation-inspired algorithm. By using logical qubits to redirect and teleport the quantum information in quantum circuits, the original circuits can be renormalized to new circuits with a smaller number of logical qubits. We demonstrate the algorithm to simulate several random quantum circuits, including 1D-chain 1000-qubit 42-depth, 2D-grid 125*8-qubit 42-depth and 2D-Bristlecone 72-qubit 32-depth circuits. Our results present a memory-efficient method with a clear physical picture to simulate low-depth random quantum circuits.
Supplementary Information
The supplementary information specifies how transversal computation constructs logical gates, models sampling efficiency and fidelity, and lays out circuit-specific transformation patterns.
Logical gates for logical qubits
- Transversal computation first defines logical qubits along circuit topology, then translates residual circuits between them into logical gates.For 1D, 2D-grid, and 2D-Bristlecone circuits, the supplementary figures provide circuit-specific logical-qubit layouts and representative gate-construction widgets.Source: Supplementary Information · p. 5
Sampling efficiency and sample fidelity
- Threshold-rejection sampling truncates the ideal sorted probability distribution at p_th, then accepts or rejects proposed samples according to the resulting areas.Its efficiency is defined by the accepted-area fraction, while cross-entropy fidelity characterizes the effective samples.Source: Supplementary Information · p. 5
- Cross-entropy fidelity is used to characterize samples generated by the threshold-rejection sampler.The supplementary text relates this measure to the fidelity of a noisy quantum state model.Source: Supplementary Information · p. 5
Basic transformation widgets
- The basic transformation widgets include logical-qubit passage through CZ gates, translation into single- and two-qubit logical gates, virtual-state initialization and projection, and circuit-node rearrangement.The widgets also connect disconnected nodes using an appropriate single-qubit gate.Source: Figure S1 · p. 6
Circuit layouts
- The 2D-grid layout repeats eight CZ-gate patterns every eight circuit depths, while the 2D-Bristlecone layout uses the same eight-depth repetition principle.These layouts define the entangling-gate structures used by the corresponding transversal circuits.Source: Figure S2 · p. 6, Figure S3 · p. 7
2D-grid logical-qubit layout
- For the 2D-grid 125 × 8-qubit, 42-depth circuit, 125 repeated slices define 40 logical qubits whose information flows between neighboring slices.Residual circuits within slices act as multi-qubit logical gates, and computational complexity is determined by the number of logical qubits.Source: Figure S4 · p. 7