Entanglement geometry separates circuit cutting, classical hardness, and trainability
2026-07-20 • Distributed, Parallel, and Cluster Computing
Distributed, Parallel, and Cluster ComputingEmerging TechnologiesMachine Learning
AI summaryⓘ
The authors investigate how breaking quantum circuits into smaller parts (circuit cutting) affects their usefulness for quantum advantage and training. They find that simple circuit types with limited entanglement can be cut cheaply but are still easy to simulate on classical computers, meaning no big quantum speedup is possible there. They design more complex circuits that are still easy to cut but hard to simulate, though these are difficult to train due to conflicting requirements on circuit depth. They also show using quantum 'magic' states instead of just entanglement can avoid this problem, allowing circuits that are easy to cut and train yet hard to simulate classically.
circuit cuttingquantum advantageentanglementmatrix product statestree tensor networksclassical simulationtrainabilityquantum depthClifford+T circuitsmagic states
Authors
Maria Gragera Garces, Sabina Drăgoi, Lirandë Pira
Abstract
Circuit cutting promises to scale quantum computations beyond current hardware, but variational quantum advantage also requires low cutting overhead, classical hardness, and trainability. We show that these properties are strongly constrained by entanglement geometry. Matrix product state (MPS) and tree tensor network (TTN) circuits with constant seam bond dimension can be cut with \(O(1/\varepsilon^2)\) sampling overhead, but remain efficiently classically simulable, ruling out asymptotic quantum advantage within these families. By independently controlling seam and intra-block entanglement, we construct a two-block circuit family that remains cheaply cuttable while requiring a super-polynomial global MPS bond dimension, as supported numerically up to \(n=100\). However, MPS hardness and trainability require incompatible depth regimes, \(d=ω(\log n)\) and \(d=O(\log n)\), respectively. Using magic rather than entanglement as the hardness resource avoids this conflict: shallow Clifford+\(T\) circuits remain cuttable and trainable while their stabiliser-simulation cost grows exponentially with the \(T\)-count.