Xin Hong
Yuan Feng
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Abstract
Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This article proposes a decision diagram style data structure, called Tensor Decision Diagram (TDD), for more principled and convenient applications of tensor networks. This new data structure provides a compact and canonical representation for quantum circuits. By exploiting circuit partition, the TDD of a quantum circuit can be computed efficiently. Furthermore, we show that the operations of tensor networks essential in their applications (e.g., addition and contraction) can also be implemented efficiently in TDDs. A proof-of-concept implementation of TDDs is presented and its efficiency is evaluated on a set of benchmark quantum circuits. It is expected that TDDs will play an important role in various design automation tasks related to quantum circuits, including but not limited to equivalence checking, error detection, synthesis, simulation, and verification.
- [1] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G. S. L. Brandao, David A. Buell, Brian Burkett, Yu Chen, Zijun Chen, Ben Chiaro, Roberto Collins, William Courtney, Andrew Dunsworth, Edward Farhi, Brooks Foxen, Austin Fowler, Craig Gidney, Marissa Giustina, Rob Graff, Keith Guerin, Steve Habegger, Matthew P. Harrigan, Michael J. Hartmann, Alan Ho, Markus Hoffmann, Trent Huang, Travis S. Humble, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Paul V. Klimov, Sergey Knysh, Alexander Korotkov, Fedor Kostritsa, David Landhuis, Mike Lindmark, Erik Lucero, Dmitry Lyakh, Salvatore Mandrà, Jarrod R. McClean, Matthew McEwen, Anthony Megrant, Xiao Mi, Kristel Michielsen, Masoud Mohseni, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Murphy Yuezhen Niu, Eric Ostby, Andre Petukhov, John C. Platt, Chris Quintana, Eleanor G. Rieffel, Pedram Roushan, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vadim Smelyanskiy, Kevin J. Sung, Matthew D. Trevithick, Amit Vainsencher, Benjamin Villalonga, Theodore White, Z. Jamie Yao, Ping Yeh, Adam Zalcman, Hartmut Neven, and John M. Martinis. 2019. Quantum supremacy using a programmable superconducting processor. Nature 574, 7779 (2019), 505–510.Google Scholar
- [2] . 1997. Algebric decision diagrams and their applications. Formal Methods in System Design 10, 2–3 (1997), 171–206.Google ScholarDigital Library
- [3] . 1997. Quantum complexity theory. SIAM Journal on Computing 26, 5 (1997), 1411–1473.Google ScholarDigital Library
- [4] . 2019. Lectures on quantum tensor networks. arXiv:1912.10049. Retrieved from https://arxiv.org/abs/1912.10049.Google Scholar
- [5] . 2017. Simulation of low-depth quantum circuits as complex undirected graphical models. arXiv:1712.05384. Retrieved from https://arxiv.org/abs/1712.05384.Google Scholar
- [6] . 1990. Efficient implementation of a BDD package. In Proceedings of the 27th ACM/IEEE Design Automation Conference. IEEE, 40–45.Google ScholarDigital Library
- [7] . 1986. Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers 100, 8 (1986), 677–691.Google ScholarDigital Library
- [8] . 1995. Verification of arithmetic circuits with binary moment diagrams. In Proceedings of the 32nd Design Automation Conference. IEEE, 535–541.Google ScholarDigital Library
- [9] . 2020. Advanced equivalence checking for quantum circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 40, 9 (2020), 1810–1824.Google Scholar
- [10] . 2020. Improved DD-based equivalence checking of quantum circuits. In Proceedings of the 2020 25th Asia and South Pacific Design Automation Conference (ASP-DAC). IEEE, 127–132.Google ScholarDigital Library
- [11] . 2021. Towards verification of dynamic quantum circuits. arXiv:2106.01099. Retrieved from https://arxiv.org/abs/2106.01099.Google Scholar
- [12] . 2018. Classical simulation of intermediate-size quantum circuits. arXiv:1805.01450. Retrieved from https://arxiv.org/abs/1805.01450.Google Scholar
- [13] . 2018. 64-qubit quantum circuit simulation. Science Bulletin 63, 15 (2018), 964–971.Google ScholarCross Ref
- [14] . 2005. Distance measures to compare real and ideal quantum processes. Physical Review A 71, 6 (2005), 062310.Google ScholarCross Ref
- [15] . 2020. Hyper-optimized tensor network contraction. Quantum 5 (2021), 410.Google Scholar
- [16] . 2021. Equivalence checking of dynamic quantum circuits. arXiv:2106.01658. Retrieved from https://arxiv.org/abs/2106.01658.Google Scholar
- [17] . 2021. Approximate equivalence checking of noisy quantum circuits. In Proceedings of the 2021 58th ACM/IEEE DAC. IEEE, 1–6.Google ScholarDigital Library
- [18] . 2020. Classical simulation of quantum supremacy circuits. arXiv:2005.06787. Retrieved from https://arxiv.org/abs/2005.06787.Google Scholar
- [19] . 2019. Quantum supremacy circuit simulation on sunway taihulight. IEEE Transactions on Parallel and Distributed Systems 31, 4 (2019), 805–816.Google ScholarDigital Library
- [20] . 2021. Qubit mapping based on subgraph isomorphism and filtered depth-limited search. IEEE Transactions on Computers 70, 11 (2021), 1777–1788.
DOI: Google ScholarCross Ref - [21] . 2008. Simulating quantum computation by contracting tensor networks. SIAM Journal on Computing 38, 3 (2008), 963–981.Google ScholarDigital Library
- [22] . 2008. Quantum circuit placement. IEEE Transactions on CAD of Integrated Circuits and Systems 27, 4 (2008), 752–763.
DOI: Google ScholarDigital Library - [23] . 2006. QMDD: A decision diagram structure for reversible and quantum circuits. In Proceedings of the 36th International Symposium on Multiple-Valued Logic. IEEE, 30–30.Google ScholarDigital Library
- [24] . 2007. Equivalence Checking of Digital Circuits: Fundamentals, Principles, Methods. Springer Science & Business Media.Google Scholar
- [25] . 2018. Quantum optimization using variational algorithms on near-term quantum devices. Quantum Science and Technology 3, 3 (2018), 030503.Google ScholarCross Ref
- [26] . 2016. Quantum Computation and Quantum Information (10th Anniversary Edition). Cambridge University Press. Retrieved from https://www.cambridge.org/de/academic/subjects/physics/quantum-physics-quantum-information-and-quantum-computation/quantum-computation-and-quantum-information-10th-anniversary-edition?format=HB.Google Scholar
- [27] . 2015. QMDDs: Efficient quantum function representation and manipulation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 35, 1 (2015), 86–99.Google ScholarDigital Library
- [28] Edwin Pednault, John A. Gunnels, Giacomo Nannicini, Lior Horesh, Thomas Magerlein, Edgar Solomonik, Erik W. Draeger, Eric T. Holland, and Robert Wisnieff. 2017. Breaking the 49-qubit barrier in the simulation of quantum circuits. Journal of Environmental Sciences (China) English Ed, 2017.Google Scholar
- [29] . 2019. Tensornetwork: A library for physics and machine learning. arXiv:1905.01330. Retrieved from https://arxiv.org/abs/1905.01330.Google Scholar
- [30] . 2020. Bit-slicing the hilbert space: Scaling up accurate quantum circuit simulation to a new level. In 58th ACM/IEEE Design Automation Conference (DAC). IEEE, 2021, 439–444.Google Scholar
- [31] . 2003. Improving gate-level simulation of quantum circuits. Quantum Information Processing 2, 5 (2003), 347–380.Google ScholarDigital Library
- [32] . 2021. LIMDD: A decision diagram for simulation of quantum computing including stabilizer states. arXiv:2108.00931. Retrieved from https://arxiv.org/abs/2108.00931.Google Scholar
- [33] . 2020. Efficient and correct compilation of quantum circuits. In Proceedings of the IEEE International Symposium on Circuits and Systems.Google ScholarCross Ref
- [34] . 2008. DDMF: An efficient decision diagram structure for design verification of quantum circuits under a practical restriction. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 91, 12 (2008), 3793–3802.Google ScholarCross Ref
- [35] . 2018. An efficient methodology for mapping quantum circuits to the IBM QX architectures. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 38, 7 (2018), 1226–1236.Google ScholarCross Ref
- [36] . 2018. Advanced simulation of quantum computations. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 38, 5 (2018), 848–859.Google ScholarCross Ref
Index Terms
- A Tensor Network based Decision Diagram for Representation of Quantum Circuits
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