Sketching the Best Approximate Quantum Compiling Problem

Abstract

This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and consider algorithmic tools to scale it to higher numbers of qubits. We investigate stochastic gradient descent and two sketch-and-solve algorithms. For all three algorithms, we compute the gradient efficiently using matrix-vector instead of matrix-matrix computations. Allowing for a runtime on the order of one hour, our implementation using either sketch-and-solve algorithm is able to compile 9 qubit, 27 CNOT circuits; 12 qubit, 24 CNOT circuits; and 15 qubit, 15 CNOT circuits. Without our algorithmic tools, standard optimization does not scale beyond 9 qubit, 9 CNOT circuits, and, beyond that, is theoretically dominated by barren plateaus.

arXiv comment10 pages, 4 figures, 1 table

References in corpus (21)

• Barren plateaus in quantum neural network training landscapes
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• t$|$ket$⟩$ : A Retargetable Compiler for NISQ Devices
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• Quantum-assisted quantum compiling
• Layerwise learning for quantum neural networks
• Quantum Circuit Simplification and Level Compaction
• Learning the quantum algorithm for state overlap
• Large gradients via correlation in random parameterized quantum circuits
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• Quantum Circuit Placement
• Optimal Layout Synthesis for Quantum Computing
• Symbolic integration with respect to the Haar measure on the unitary group
• Approaching the theoretical limit in quantum gate decomposition
• Generators and relations for n-qubit Clifford operators
• QFAST: Quantum Synthesis Using a Hierarchical Continuous Circuit Space

Cited by in corpus (2)

• Energy risk analysis with Dynamic Amplitude Estimation and Piecewise Approximate Quantum Compiling
• A Novel Single-Layer Quantum Neural Network for Approximate SRBB-Based Unitary Synthesis