Related papers: Characterizing Pauli Propagation via Operator Comp…
We study real-time operator evolution using sparse Pauli dynamics, a recently developed method for simulating expectation values of quantum circuits. On the examples of energy and charge diffusion in 1D spin chains and sudden quench…
The complexity of simulating quantum many-body dynamics, or quantum computations, in the Heisenberg picture is governed by the scrambling of initially simple operators into superpositions of exponentially many Pauli strings. The…
We introduce a symmetry-adapted framework for simulating quantum dynamics based on Pauli propagation. When a quantum circuit possesses a symmetry, many Pauli strings evolve redundantly under actions of the symmetry group. We exploit this by…
Simulating noiseless quantum dynamics classically faces a fundamental dilemma: tensor-network methods become inefficient as entanglement saturates, while Pauli-truncation approaches typically rely on noise or randomness. To close the gap,…
Local-operator entanglement (LOE) dictates the complexity of simulating Heisenberg evolution using tensor network methods, {and bears witness to many-body chaos for local dynamics}. We show that LOE is also sensitive to how non-Clifford a…
Understanding the spreading of the operator space entanglement entropy ($OSEE$) is key in order to explore out-of-equilibrium quantum many-body systems. Here we argue that for integrable models the dynamics of the $OSEE$ is related to the…
The complexity of representation of operators in quantum mechanics can be characterized by the operator space entanglement entropy (OSEE). We show that in the homogeneous Heisenberg XY spin 1/2 chains the OSEE for initial local operators…
The complexity of simulating the out-of-equilibrium evolution of local operators in the Heisenberg picture is governed by the operator entanglement, which grows linearly in time for generic non-integrable systems, leading to an exponential…
Quantum Machine Learning models typically require expensive on-chip training procedures and often lack efficient gradient estimation methods. By employing Pauli propagation, it is possible to derive a symbolic representation of observables…
We extend the Pauli Propagation framework to simulate imaginary-time evolution. By deriving explicit update rules for the propagation of Pauli operators under imaginary-time evolution generated by Pauli strings, we introduce an…
Classical methods to simulate quantum systems are not only a key element of the physicist's toolkit for studying many-body models but are also increasingly important for verifying and challenging upcoming quantum computers. Pauli…
Electron spin s in semiconductor quantum dot s have been intensively studied for implementing quantum computation and high fidelity single and two qubit operation s have recently been achieved . Quantum teleportation is a three qubit…
A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli…
Analysis of quantum processes, especially in the context of noise, errors, and decoherence is essential for the improvement of quantum devices. An intuitive representation of those processes modeled by quantum channels are Pauli transfer…
Variational quantum algorithms are often hindered by rugged optimization landscapes. In this Letter, we investigate the low-weight Pauli propagation (LWPP) algorithm and find that it serves as an unreliable energy estimator for variational…
The study of out-of-equilibrium quantum many-body dynamics remains one of the most exciting research frontiers of physics, standing at the crossroads of our understanding of complex quantum phenomena and the realization of quantum…
We present a polynomial-time classical algorithm for estimating expectation values of arbitrary observables on typical quantum circuits under any incoherent local noise, including non-unital or dephasing. Although previous research…
Local-operator entanglement (LOE) quantifies the nonlocal structure of Heisenberg operators and serves as a diagnostic of many-body chaos. We provide rigorous bounds showing when an operator can be well-approximated by a matrix-product…
The fusion rules and operator product expansion (OPE) serve as crucial tools in the study of operator algebras within conformal field theory (CFT). Building upon the vision of using entanglement to explore the connections between fusion…
Stabilizer Entropy (SE) quantifies the spread of a state in the basis of Pauli operators. It is a computationally tractable measure of non-stabilizerness and thus a useful resource for quantum computation. SE can be moved around a quantum…