Armando Angrisani

Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that any noise `truncates' most quantum circuits to effectively logarithmic depth, in the task of computing Pauli expectation values. We then prove that quantum circuits under any non-unital noise exhibit lack of barren plateaus for cost functions composed of local observables. But, by leveraging the effective shallowness, we also design a classical algorithm to estimate Pauli expectation values within inverse-polynomial additive error with high probability over the ensemble. Its runtime is independent of circuit depth and it operates in polynomial time in the number of qubits for one-dimensional architectures and quasi-polynomial time for higher-dimensional ones. Taken together, our results showcase that, unless we carefully engineer the circuits to take advantage of the noise, it is unlikely that noisy quantum circuits are preferable over shallow quantum circuits for algorithms that output Pauli expectation value estimates, like many variational quantum machine learning proposals. Moreover, we anticipate that our work could provide valuable insights into the fundamental open question about the complexity of sampling from (possibly non-unital) noisy random circuits.

A central challenge in quantum many-body physics is to understand how operators evolve in time. Key phenomena like operator growth, transport, and scrambling are most naturally framed in the Heisenberg picture, but classical approaches (e.g., tensor networks or Pauli propagation) run into limits set by entanglement or magic. In the first paper of this joint submission, we develop a general Heisenberg-picture simulation framework for quantum computers based on vectorization and transfer-matrix ideas. This lets us represent time-evolved Heisenberg operators as quantum states in a structure-preserving way, so a wide range of Heisenberg-native tasks can be recast as standard state-based procedures. As a result, we obtain new quantum algorithms for computing many operator diagnostics, including Pauli statistics, OTOCs, superoperator moments, two-point correlators, and operator entanglement/stabilizer entanglement measures. In the second paper, we target the problem of learning many correlators simultaneously. We introduce “shadows of Heisenberg operators,” obtained via randomized measurements with local or global Clifford schemes, enabling simultaneous estimation of broad families of OTOCs or two-point correlators from shared data. We also prove information-theoretic lower bounds for multi-OTOC estimation across different learning models, yielding exponential separations that formalize when and why the vectorized approach provides genuine measurement-efficiency advantages.

Analyzing the impact of noise is of fundamental importance to understand the advantages provided by quantum systems. While the classical simulability of noisy discrete-variable systems is increasingly well understood, noisy bosonic circuits are more challenging to simulate and analyze. Here, we address this gap by introducing the displacement propagation algorithm, a continuous-variable analogue of Pauli propagation for simulating noisy bosonic circuits. By exploring the interplay of noise and quantum resources, we identify several computational phase transitions, revealing regimes where even modest noise levels render bosonic circuits efficiently classically simulable. In particular, our analysis reveals a surprising phenomenon: computational resources usually associated with bosonic quantum advantage, namely non-Gaussianity and symplectic coherence, can make the system easier to classically simulate in presence of noise.