Corpus ID: 236777035

LIMDD A Decision Diagram for Simulation of Quantum Computing Including Stabilizer States

  title={LIMDD A Decision Diagram for Simulation of Quantum Computing Including Stabilizer States},
  author={Lieuwe Vinkhuijzen and Tim Coopmans and David Elkouss and Vedran Dunjko and Alfons W. Laarman},
Efficient methods for the representation of relevant quantum states and quantum operations are crucial for the simulation and optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent Boolean functions, have proven capable of capturing interesting aspects of quantum systems, but their limits are not well understood. In this work, we investigate and bridge the gap between existing DD-based structures and the stabilizer formalism, a well… Expand
Tools for Quantum Computing Based on Decision Diagrams
With quantum computers promising advantages even in the near-term NISQ era, there is a lively community that develops software and toolkits for the design of corresponding quantum circuits. AlthoughExpand


Simulation of quantum circuits by low-rank stabilizer decompositions
A comprehensive mathematical theory of the stabilizerRank and the related approximate stabilizer rank is developed and a suite of classical simulation algorithms with broader applicability and significantly improved performance over the previous state-of-the-art are presented. Expand
Efficient Inner-product Algorithm for Stabilizer States
It is proved that each n-qubit stabilizer state has exactly 4(2^n - 1) nearest-neighbor stabilizer states, and is generalized to compute the inner product between two such frames. Expand
Improving Gate-Level Simulation of Quantum Circuits
The results demonstrate that QuIDDs asymptotically outperform all other known simulation techniques and show that well-known worst-case instances of classical searching can be circumvented in many specific cases by data compression techniques. Expand
Improved Simulation of Stabilizer Circuits
The Gottesman-Knill theorem, which says that a stabilizer circuit, a quantum circuit consisting solely of controlled-NOT, Hadamard, and phase gates can be simulated efficiently on a classical computer, is improved in several directions. Expand
Advanced Simulation of Quantum Computations
  • Alwin Zulehner, R. Wille
  • Computer Science, Mathematics
  • IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
  • 2019
The basics of quantum computation are revisited, how corresponding quantum states and quantum operations can be represented even more compactly, and, eventually, simulated in a more efficient fashion are investigated, leading to a new graph-based simulation approach which outperforms state-of-the-art simulators. Expand
Exploring Quantum Computation Through the Lens of Classical Simulation
This project looks at the problem of classically simulating quantum circuits through decompositions into stabilizer circuits, a restricted class of quantum computation which can be efficiently simulated classically. Expand
Quantum Multiple-Valued Decision Diagrams in Graphical Calculi
This paper shows how to turn a quantum multiple-valued decision diagrams into an equivalent ZHdiagram, and vice-versa, and shows how reducing a QMDD translates in the ZH-Calculus, hence allowing tools from one formalism to be used into the other. Expand
A Tensor Network based Decision Diagram for Representation of Quantum Circuits
It is shown that the operations of tensor networks essential in their applications, can also be implemented efficiently in TDDs, and it is expected that TDDs will play an important role in various design automation tasks related to quantum circuits. Expand
High-performance QuIDD-based simulation of quantum circuits
An improved implementation of QuIDDs is presented which can simulate Grover's algorithm for quantum search with the asymptotic runtime complexity of an ideal quantum computer up to negligible overhead. Expand
QMDD: A Decision Diagram Structure for Reversible and Quantum Circuits
  • D. M. Miller, M. Thornton
  • Mathematics, Computer Science
  • 36th International Symposium on Multiple-Valued Logic (ISMVL'06)
  • 2006
A novel structure specifically designed to represent and manipulate the matrices encountered in the specification of reversible and quantum gates and circuits, both binary and multiple-valued is presented. Expand