This paper presents ``Stim", a fast simulator for quantum stabilizer circuits. The paper explains how Stim works and compares it to existing tools. With no foreknowledge, Stim can analyze a distance 100 surface code circuit (20 thousand qubits, 8 million gates, 1 million measurements) in 15 seconds and then begin sampling full circuit shots at a rate of 1 kHz. Stim uses a stabilizer tableau representation, similar to Aaronson and Gottesman's CHP simulator, but with three main improvements. First, Stim improves the asymptotic complexity of deterministic measurement from quadratic to linear by tracking the {\em inverse} of the circuit's stabilizer tableau. Second, Stim improves the constant factors of the algorithm by using a cache-friendly data layout and 256 bit wide SIMD instructions. Third, Stim only uses expensive stabilizer tableau simulation to create an initial reference sample. Further samples are collected in bulk by using that sample as a reference for batches of Pauli frames propagating through the circuit.
MPStab: an hybrid stabilizers tensor-network quantum circuit simulator
University of Trieste（的里雅斯特大学）；Istituto Nazionale di Fisica Nucleare, Trieste Section（意大利国家核物理研究所的里雅斯特分部）；University of Helsinki（赫尔辛基大学）；European Organization for Nuclear Research (CERN)（欧洲核子研究组织（日内瓦））；Chalmers University of Technology（查尔姆斯理工大学）
According to the Gottesman-Knill theorem, a class of quantum circuits, namely the so-called stabilizer circuits, can be simulated efficiently on a classical computer. We introduce a new algorithm for this task, which is based on the graph-state formalism. It shows significant improvement in comparison to an existing algorithm, given by Gottesman and Aaronson, in terms of speed and of the number of qubits the simulator can handle. We also present an implementation.
SymFT: Universal Fault-Tolerant Quantum Circuit Simulation via Symbolic Clifford--Pauli Frames and Stabilizer Coordinates
University of Edinburgh（爱丁堡大学）；Arclight Quantum Computing Inc.（Arclight量子计算公司）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）
Clifford Manipulations of Stabilizer States: A graphical rule book for Clifford unitaries and measurements on cluster states, and application to photonic quantum computing
NSF-ERC Center for Quantum Networks, Wyant College of Optical Sciences, The University of Arizona（亚利桑那大学怀特光学科学学院量子网络 NSF-ERC 中心）
Non-stabilizerness or magic resource characterizes the amount of non-Clifford operations needed to prepare quantum states. It is a crucial resource for quantum computing and a necessary condition for quantum advantage. However, quantifying magic resource beyond a few qubits has been a major challenge. Here, we introduce efficient measures of magic resource for pure quantum states with a sampling cost that is independent of the number of qubits. Our method uses Bell measurements over two copies of a state, which we implement in experiment together with a cost-free error mitigation scheme. We sh…
Generic quantum-circuit simulation appears intractable for conventional computers and may be unnecessary because useful quantum circuits exhibit significant structure that can be exploited during simulation. For example, Gottesman and Knill identified an important subclass, called stabilizer circuits, which can be simulated efficiently using group-theory techniques and insights from quantum physics. Realistic circuits enriched with quantum error-correcting codes and fault-tolerant procedures are dominated by stabilizer subcircuits and contain a relatively small number of non-Clifford component…
Bounding the cost of classically simulating the outcomes of universal quantum circuits to additive error $δ$ is often called weak simulation and is a direct way to determine when they confer a quantum advantage. Weak simulation of the $T$+Clifford gateset is $BQP$-complete and is expected to scale exponentially with the number $t$ of $T$ gates. We constructively tighten the upper bound on the worst-case $L_1$ norm sampling cost to next order in $t$ from $\mathcal O(ξ^t δ^{-2})$ if $δ^2 \gg ξ^{-t}$ to $\mathcal O((ξ^t{-}t) δ^{-2} )$ if $δ^2 \gg (ξ^t -t)^{-1}$, where $ξ^t = 2^{\sim 0.228 t}$ is …
