# Checking equivalence of quantum circuits and states

@article{Viamontes2007CheckingEO, title={Checking equivalence of quantum circuits and states}, author={George F. Viamontes and Igor L. Markov and John P. Hayes}, journal={2007 IEEE/ACM International Conference on Computer-Aided Design}, year={2007}, pages={69-74} }

Among the post-CMOS technologies currently under investigation, quantum computing (QC) holds a special place. QC offers not only extremely small size and low power, but also exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to. but more challenging, than the related problems in classical (non-quantum) CAD. such as determining if two states or circuits are functionally equivalent. While differences in classical states are…

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## References

SHOWING 1-10 OF 36 REFERENCES

Improving Gate-Level Simulation of Quantum Circuits

- Computer ScienceQuantum Inf. Process.
- 2003

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.

Quantum circuits for incompletely specified two-qubit operators

- Mathematics, PhysicsQuantum Inf. Comput.
- 2005

This work identifies cases in which unitary operators can be implemented using fewer quantum gates than are required for generic completely specified operators, and takes up the practical challenge of satisfying a given specification with the smallest possible circuit.

Elementary gates for quantum computation.

- MathematicsPhysical review. A, Atomic, molecular, and optical physics
- 1995

U(2) gates are derived, which derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number of unitary operations on arbitrarily many bits.

Graph-based simulation of quantum computation in the density matrix representation

- Computer ScienceSPIE Defense + Commercial Sensing
- 2004

This work proposes a new technique aimed at efficiently simulating quantum circuits that are subject to errors, and describes new graph-based algorithms implemented in the simulator QuIDDPro/D that use the density matrix representation.

Improved Simulation of Stabilizer Circuits

- Computer ScienceArXiv
- 2004

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.

Quantum Circuit Placement: Optimizing Qubit-to-qubit Interactions through Mapping Quantum Circuits into a Physical Experiment

- Physics2007 44th ACM/IEEE Design Automation Conference
- 2007

This work studies the theoretical aspects of the problem of the practical realization of an abstract quantum circuit when executed on quantum hardware and presents empirical results that match the best known solutions that have been developed by experimentalists.

The Heisenberg Representation of Quantum Computers

- Physics
- 1998

Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features…

Fast quantum modular exponentiation

- Computer Science
- 2005

It is found that to exponentia te an n-bit number, for storage space 100n, the authors can execute modular exponentiation two hundred to seven hundred times faster than optimized versions of the basic algorithms, depending on architecture, for n = 128.

Synthesis of quantum-logic circuits

- Computer ScienceIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
- 2006

Efficient quantum-logic circuits that perform two tasks are discussed: 1) implementing generic quantum computations, and 2) initializing quantum registers that are asymptotically optimal for respective tasks.

Quantum computation and quantum information

- PhysicsMathematical Structures in Computer Science
- 2007

This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal…