arXiv subjects

Charlee Stefanski

Publications and source records attributed to Charlee Stefanski.

6 recordsLinked to original sources

arXiv2023

Designing a Fast and Flexible Quantum State Simulator

This paper describes the design and implementation of Spinoza, a fast and flexible quantum simulator written in Rust. Spinoza simulates the evolution of a quantum system's state by applying quantum gates, with the core design principle being that a single-qubit gate applied to a target qubit preserves the probability of pairs of amplitudes corresponding to measurement outcomes that differ only in the target qubit. Multiple strategies are employed for selecting pairs of amplitudes, depending on the gate type and other parameters, to optimize performance. Specific optimizations are also implemented for certain gate types and target qubits. Spinoza is intended to enable the development of quantum computing solutions by offering developers a simple, flexible, and fast tool for classical simulation. In this paper we provide details about the design and usage examples. Furthermore, we compare Spinoza's performance against several other open-source simulators to demonstrate its strengths.

quant-ph↗

arXiv2022

Implementation and Learning of Quantum Hidden Markov Models

In this article, we use the theory of quantum channels and open quantum systems to provide an efficient unitary characterization of a class of stochastic generators known as quantum hidden Markov models (QHMMs). By utilizing the unitary characterization, we demonstrate that any QHMM can be implemented as a quantum circuit with mid-circuit measurement. We prove that QHMMs are more compact and more expressive definitions of stochastic process languages compared to the equivalent classical hidden Markov models (HMMs). Starting with the formulation of QHMMs as quantum channels, we employ Stinespring's construction to represent these models as unitary quantum circuits with mid-circuit measurement. By utilizing the unitary parameterization of QHMMs, we define a formal QHMM learning model. The model formalizes the empirical distributions of target stochastic process languages, defines hypothesis space of quantum circuits, and introduces an empirical stochastic divergence measure - hypothesis fitness - as a success criterion for learning. We demonstrate that the learning model has a smooth search landscape due to the continuity of Stinespring's dilation. The smooth mapping between the hypothesis and fitness spaces enables the development of efficient heuristic and gradient descent learning algorithms. We propose two practical learning algorithms for QHMMs. The first algorithm is a hyperparameter-adaptive evolutionary search. The second algorithm learns the QHMM as a quantum ansatz circuit using a multi-parameter non-linear optimization technique.

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arXiv2022

Reservoir Computing via Quantum Recurrent Neural Networks

Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we approach sequential modeling by applying a reservoir computing (RC) framework to quantum recurrent neural networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea to this RC approach is that the QRNN with randomly initialized weights is treated as a dynamical system and only the final classical linear layer is trained. Our numerical simulations show that the QRNN-RC can reach results comparable to fully trained QRNN models for several function approximation and time series prediction tasks. Since the QRNN training complexity is significantly reduced, the proposed model trains notably faster. In this work we also compare to corresponding classical RNN-based RC implementations and show that the quantum version learns faster by requiring fewer training epochs in most cases. Our results demonstrate a new possibility to utilize quantum neural network for sequential modeling with greater quantum hardware efficiency, an important design consideration for noisy intermediate-scale quantum (NISQ) computers.

cs.NE↗

arXiv2022

Properties of The Discrete Sinc Quantum State and Applications to Measurement Interpolation

Extracting the outcome of a quantum computation is a difficult task. In many cases, the quantum phase estimation algorithm is used to digitally encode a value in a quantum register whose amplitudes' magnitudes reflect the discrete sinc function. In the standard implementation the value is approximated by the most frequent outcome, however, using the frequencies of other outcomes allows for increased precision without using additional qubits. One existing approach is to use Maximum Likelihood Estimation, which uses the frequencies of all measurement outcomes. We provide and analyze several alternative estimators, the best of which rely on only the two most frequent measurement outcomes. The Ratio-Based Estimator uses a closed form expression for the decimal part of the encoded value using the ratio of the two most frequent outcomes. The Coin Approximation Estimator relies on the fact that the decimal part of the encoded value is very well approximated by the parameter of the Bernoulli process represented by the magnitudes of the largest two amplitudes. We also provide additional properties of the discrete sinc state that could be used to design other estimators.

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arXiv2022

Quantum Amplitude Interpolation

In this paper we present a method for representing continuous signals with high precision by interpolating quantum state amplitudes. The method is inspired by the Nyquist-Shannon sampling theorem, which links continuous and discrete time signals. This method extends our previous method of computing generalized inner products from integer-valued functions to real-valued functions.

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arXiv2022

A Generalized Quantum Inner Product and Applications to Financial Engineering

In this paper we present a canonical quantum computing method to estimate the weighted sum w(k)f(k) of the values taken by a discrete function f and real weights w(k). The canonical aspect of the method comes from relying on a single linear function encoded in the amplitudes of a quantum state, and using register entangling to encode the function f. We further expand this framework by mapping function values to hashes in order to estimate weighted sums w(k)h(f(k)) of hashed function values with real hashes h. This generalization allows the computation of restricted weighted sums such as value at risk, comparators, as well as Lebesgue integrals and partial moments of statistical distributions. We also introduce essential building blocks such as efficient encodings of standardized linear quantum states and normal distributions.

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