Matrix-Vector vs. Matrix-Matrix Multiplication: Potential in DD-based Simulation of Quantum Computations

Zulehner, Alwin; Wille, Robert

doi:10.23919/date.2019.8714836

Cited by 41 publications

(29 citation statements)

References 17 publications

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“…The estimated maximum simulation size will be increased from 48 qubits to 64 qubits. Our compression techniques can combine with other simulation techniques [16,33,43,69,71] to scale quantum circuit simulation.…”

Section: Discussionmentioning

confidence: 99%

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Full-state quantum circuit simulation by using data compression

Dasgupta

et al. 2019

Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis

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Quantum circuit simulations are critical for evaluating quantum algorithms and machines. However, the number of state amplitudes required for full simulation increases exponentially with the number of qubits. In this study, we leverage data compression to reduce memory requirements, trading computation time and fidelity for memory space. Specifically, we develop a hybrid solution by combining the lossless compression and our tailored lossy compression method with adaptive error bounds at each timestep of the simulation. Our approach optimizes for compression speed and makes sure that errors due to lossy compression are uncorrelated, an important property for comparing simulation output with physical machines. Experiments show that our approach reduces the memory requirement of simulating the 61-qubit Grover's search algorithm from 32 exabytes to 768 terabytes of memory on Argonne's Theta supercomputer using 4,096 nodes. The results suggest that our techniques can increase the simulation size by 2∼16 qubits for general quantum circuits.

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Section: Discussionmentioning

confidence: 99%

“…This approach exploits redundancies in a quantum state to gain more compact representations. Approximate simulation techniques also have been proposed for circuits using only restricted gates [13,69,71].…”

Section: Quantum Circuit Simulationmentioning

confidence: 99%

Full-state quantum circuit simulation by using data compression

Dasgupta

et al. 2019

Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis

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“…Hence, multiplication of decision diagrams mainly involves recursive traversals of the involved decision diagrams. On top of that, further optimizations are possible with respect to the precision of the simulation [20,33], the run-time performance [35], or a trade-off of both [31] 3 SIMULATION OF DECOHERENCE…”

Section: Decision Diagram-based Quantum Circuit Simulationmentioning

confidence: 99%

Considering decoherence errors in the simulation of quantum circuits using decision diagrams

Grurl

Fuß

Wille

2020

Proceedings of the 39th International Conference on Computer-Aided Design

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“…Overall, QMDDs allow for both, a compact representation as well as an efficient manipulation of unitary matrices for quantum systems of considerable size. As a consequence, they have already been used in a broad variety of applications in the design of quantum circuits (e.g., verification [7,8,27,39,42], simulation [45,47], or synthesis [26,36,44]).…”

Section: Examplementioning

confidence: 99%

Advanced exact synthesis of Clifford+T circuits

Niemann

Wille

Drechsler

2020

Quantum Inf Process

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Quantum systems provide a new way of conducting computations based on the so-called qubits. Due to the potential for significant speed-ups, this field received significant research attention in recent years. The Clifford+T library is a very promising and popular gate library for these kinds of computations. Unlike other libraries considered so far, it consists of only a small number of gates for all of which robust, fault-tolerant realizations are known for many technologies that seem to be promising for large-scale quantum computing. As a consequence, (logic) synthesis of Clifford+T quantum circuits became an important research problem. However, previous work in this area has several drawbacks: Corresponding approaches are either only applicable to very small quantum systems or lead to circuits that are far from being optimal. The latter is mainly caused by the fact that current synthesis realizes the desired circuit by a local, i.e., column-wise, consideration of the underlying unitary transformation matrix to be synthesized. In this paper, we analyze the conceptual drawbacks of this approach and propose to overcome them by taking a global view of the matrices and perform a separation of concerns regarding individual synthesis steps. We precisely describe a corresponding algorithm as well as its efficient implementation on top of decision diagrams. Experimental results confirm the resulting benefits and show improvements of up to several orders of magnitudes in costs compared to previous work.

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Matrix-Vector vs. Matrix-Matrix Multiplication: Potential in DD-based Simulation of Quantum Computations

Cited by 41 publications

References 17 publications

Full-state quantum circuit simulation by using data compression

Full-state quantum circuit simulation by using data compression

Considering decoherence errors in the simulation of quantum circuits using decision diagrams

Advanced exact synthesis of Clifford+T circuits

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