Lossy Compression for Schrödinger-style Quantum Simulations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913251375185920 |
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| author | Huffman, Noah Pavlichin, Dmitri Weissman, Tsachy |
| author_facet | Huffman, Noah Pavlichin, Dmitri Weissman, Tsachy |
| contents | Simulating quantum circuits on classical hardware is a powerful and necessary tool for developing and testing quantum algorithms and hardware as well as evaluating claims of quantum supremacy in the Noisy Intermediate-Scale Quantum (NISQ) regime. Schrödinger-style simulations are limited by the exponential growth of the number of state amplitudes which need to be stored. In this work, we apply scalar and vector quantization to Schrödinger-style quantum circuit simulations as lossy compression schemes to reduce the number of bits needed to simulate quantum circuits. Using quantization, we can maintain simulation fidelities $>0.99$ when simulating the Quantum Fourier Transform, while using only 7 significand bits in a floating-point number to characterize the real and imaginary components of each amplitude. Furthermore, using vector quantization, we propose a method to bound the number of bits/amplitude needed to store state vectors in a simulation of a circuit that achieves a desired fidelity, and show that for a 6 qubit simulation of the Quantum Fourier Transform, 15 bits/amplitude is sufficient to maintain fidelity $>0.9$ at $10^4$ depth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lossy Compression for Schrödinger-style Quantum Simulations Huffman, Noah Pavlichin, Dmitri Weissman, Tsachy Quantum Physics Simulating quantum circuits on classical hardware is a powerful and necessary tool for developing and testing quantum algorithms and hardware as well as evaluating claims of quantum supremacy in the Noisy Intermediate-Scale Quantum (NISQ) regime. Schrödinger-style simulations are limited by the exponential growth of the number of state amplitudes which need to be stored. In this work, we apply scalar and vector quantization to Schrödinger-style quantum circuit simulations as lossy compression schemes to reduce the number of bits needed to simulate quantum circuits. Using quantization, we can maintain simulation fidelities $>0.99$ when simulating the Quantum Fourier Transform, while using only 7 significand bits in a floating-point number to characterize the real and imaginary components of each amplitude. Furthermore, using vector quantization, we propose a method to bound the number of bits/amplitude needed to store state vectors in a simulation of a circuit that achieves a desired fidelity, and show that for a 6 qubit simulation of the Quantum Fourier Transform, 15 bits/amplitude is sufficient to maintain fidelity $>0.9$ at $10^4$ depth. |
| title | Lossy Compression for Schrödinger-style Quantum Simulations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.11088 |