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.
Method
The method defines logical qubits along circuit topology, translates residual circuits into logical gates, and uses threshold-rejection sampling to generate samples.
Results
The supplementary procedure characterizes generated samples using cross-entropy fidelity and sampling efficiency.
Takeaways & Limitations
The framework combines circuit renormalization through logical gates with sampling-quality characterization for low-depth random-circuit simulation.
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.
- 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.
- Sampling efficiency and sample fidelity: 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.
- 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.
- 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.
- 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.