Suguru Endo

Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, or other domains. Quantum computing provides an alternative to the perturbation paradigm, yet current quantum processors with few noisy qubits are of limited practical utility. In this talk, we introduce perturbative quantum simulation, which combines the complementary strengths of the two approaches, enabling the solution of large quantum problems using limited intermediate-scale quantum hardware. The use of a quantum processor alleviates the need to identify a solvable unperturbed Hamiltonian, while the introduction of perturbative coupling permits a quantum processor to simulate systems with larger sizes. We present an explicit perturbative expansion that mimics the Dyson series expansion and involves only local unitary operations. We then discuss its optimality over other expansions under certain conditions. This perturbative approach is benchmarked by simulating the interacting dynamics of representative quantum systems.

Circuit knitting/cutting is a family of techniques that enables large quantum computations on limited-size quantum devices by decomposing a target circuit into smaller subcircuits. However, it typically incurs a measurement overhead exponential in the number of cut locations, and this scaling has long been believed to be fundamentally unavoidable. In this work, we show that such an exponential scaling is not universal: it can be circumvented for tree-structured quantum circuits via concatenated quantum tomography protocols. We first consider the task of estimating the expectation value of an observable within additive error $\epsilon$ for a tree-structured circuit with tree depth 1, maximum branching factor $R$, and bond dimension at most $d$ on each edge. Our approach uses quantum tomography to construct, for each cut edge, a local decomposition that eliminates the rescaling factors in conventional QPD, instead introducing a controllable bias set by the tomography sample size. As a result, we show that $\mathcal{O}(d^3R^3\ln(dR)/\epsilon^2)$ total measurements suffice, including tomography measurements. Next, we extend the tree-depth-1 case to general trees of depth $L\geq2$, and give an algorithm whose total measurement cost $\mathrm{poly}(d,K,1/\epsilon)$ scales polynomially with the number of cuts $K$ for complete multi-ary trees. Finally, we perform an information-theoretic analysis to show that, in a comparable tree-depth-1 setting, conventional circuit-cutting methods require at least $\Omega((d+1)^R/\epsilon^2)$ measurements. This exponential separation in the number of cuts suggests that the improvement is not solely due to the tree restriction, highlighting the essential role of tomography-based construction in reducing measurement overhead in hybrid quantum–classical computations.