The Efficient Preparation of Normal Distributions in Quantum Registers

Arthur G. Rattew, Yue Sun, Pierre Minssen, and Marco Pistoia

Future Lab for Applied Research and Engineering, JPMorgan Chase & Co.

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Abstract

The efficient preparation of input distributions is an important problem in obtaining quantum advantage in a wide range of domains. We propose a novel quantum algorithm for the efficient preparation of arbitrary normal distributions in quantum registers. To the best of our knowledge, our work is the first to leverage the power of Mid-Circuit Measurement and Reuse (MCMR), in a way that is broadly applicable to a range of state-preparation problems. Specifically, our algorithm employs a repeat-until-success scheme, and only requires a constant-bounded number of repetitions in expectation. In the experiments presented, the use of MCMR enables up to a 862.6x reduction in required qubits. Furthermore, the algorithm is provably resistant to both phase-flip and bit-flip errors, leading to a first-of-its-kind empirical demonstration on real quantum hardware, the MCMR-enabled Honeywell System Models H0 and H1-2.

The efficient preparation of input distributions is particularly important for a wide range of quantum algorithms, such as those for amplitude estimation, option pricing, principal-component analysis, matrix inversion, and machine learning. These algorithms all offer the potential for quantum advantage, notably in financial applications, so long as their initial distributions may be generated without introducing computational bottlenecks. Constructing an arbitrary quantum state necessitates exponential-depth circuits. As a result, any efficient state preparation technique must either be approximate in nature, or exploit information specific to the distribution being generated. For an algorithm to offer quantum advantage in the near future, it is even more important that state-generation procedures use as shallow circuits with as few ancillary qubits as possible, and produce high-fidelity states even in the presence of low gate-execution fidelity. We propose a novel quantum algorithm for the efficient preparation of arbitrary normal distributions in quantum registers. To the best of our knowledge, our work is the first to leverage the power of Mid-Circuit Measurement and Reuse (MCMR), in a way that is broadly applicable to a range of state-preparation problems. Specifically, our algorithm employs a repeat-until-success scheme, and only requires a constant-bounded number of repetitions in expectation. In the experiments presented, the use of MCMR enables up to a $862.6\times$ reduction in required qubits. Furthermore, the algorithm is provably resistant to both phase-flip and bit-flip errors, leading to a first-of-its-kind empirical demonstration on real quantum hardware, the MCMR-enabled Honeywell System Models H0 and H1-2.

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Cited by

[1] Bálint Koczor, "Exponential Error Suppression for Near-Term Quantum Devices", Physical Review X 11 3, 031057 (2021).

[2] Justin Yirka and Yigit Subasi, "Qubit-efficient entanglement spectroscopy using qubit resets", arXiv:2010.03080.

[3] Romina Yalovetzky, Pierre Minssen, Dylan Herman, and Marco Pistoia, "NISQ-HHL: Portfolio Optimization for Near-Term Quantum Hardware", arXiv:2110.15958.

[4] Marco Pistoia, Syed Farhan Ahmad, Akshay Ajagekar, Alexander Buts, Shouvanik Chakrabarti, Dylan Herman, Shaohan Hu, Andrew Jena, Pierre Minssen, Pradeep Niroula, Arthur Rattew, Yue Sun, and Romina Yalovetzky, "Quantum Machine Learning for Finance", arXiv:2109.04298.

The above citations are from SAO/NASA ADS (last updated successfully 2022-01-23 03:02:46). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2022-01-23 03:02:45).