Parallel quantum trajectories via forking for sampling without redundancy

Park, Daniel K.; Sinayskiy, Ilya; Fingerhuth, Mark; Petruccione, Francesco; Rhee, June-Koo Kevin

doi:10.1088/1367-2630/ab35fb

Cited by 19 publications

(19 citation statements)

References 35 publications

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“…The underlying idea is to adapt quantum forking introduced in refs. 12,13 to create an entangled state such that each subspace labeled by a basis state of the index qubits encodes a different training dataset. For brevity, we denote the controlled-swap operator by c-swap(a, b|c) to indicate that a and b are swapped if the control is c. With this notation, the classification can be expressed with the following equations.…”

Section: Kernel Construction From a Product Statementioning

confidence: 99%

“…We also show that the post-selection can be avoided by measuring an expectation value of a two-qubit observable. The swap-test classifier can be implemented without relying on the specific initial state by using a method based on quantum forking 12,13 at the cost of increasing the number of qubits. In this case, the training data, corresponding labels, and the test data are provided on separate registers as a product state.…”

Section: Introductionmentioning

confidence: 99%

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Quantum classifier with tailored quantum kernel

Blank¹,

et al. 2020

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Kernel methods have a wide spectrum of applications in machine learning. Recently, a link between quantum computing and kernel theory has been formally established, opening up opportunities for quantum techniques to enhance various existing machine-learning methods. We present a distance-based quantum classifier whose kernel is based on the quantum state fidelity between training and test data. The quantum kernel can be tailored systematically with a quantum circuit to raise the kernel to an arbitrary power and to assign arbitrary weights to each training data. Given a specific input state, our protocol calculates the weighted power sum of fidelities of quantum data in quantum parallel via a swap-test circuit followed by two single-qubit measurements, requiring only a constant number of repetitions regardless of the number of data. We also show that our classifier is equivalent to measuring the expectation value of a Helstrom operator, from which the well-known optimal quantum state discrimination can be derived. We demonstrate the performance of our classifier via classical simulations with a realistic noise model and proof-of-principle experiments using the IBM quantum cloud platform.

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Section: Kernel Construction From a Product Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum classifier with tailored quantum kernel

Blank¹,

et al. 2020

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“…( 2 ) using a circuit with depth and O ( N ) qubits. The devised method is based on quantum forking 13 , 14 and uses a divide-and-conquer strategy 15 . The circuit depth is decreased at the cost of increasing the circuit width and creating entanglement between data register qubits and an ancillary system.…”

Section: Introductionmentioning

confidence: 99%

A divide-and-conquer algorithm for quantum state preparation

Araujo

Park

Petruccione

et al. 2021

Sci Rep

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125

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Advantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with exponential time advantage using a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.

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“…In these algorithms, a classification score is evaluated by measuring an expectation value of certain observables, and hence repeating the same experiment multiple times is inevitable for a reliable statistics. However, due to the measurement postulate of quantum mechanics and the no-cloning theorem, a same input state must be created for every execution of the algorithm [23]. Since computational cost for preparing an arbitrary quantum input state can be substantial depending on the structure of data to be encoded, reducing the number of repetition is essential [23], especially for NISQ computing.…”

Section: Introductionmentioning

confidence: 99%

“…However, due to the measurement postulate of quantum mechanics and the no-cloning theorem, a same input state must be created for every execution of the algorithm [23]. Since computational cost for preparing an arbitrary quantum input state can be substantial depending on the structure of data to be encoded, reducing the number of repetition is essential [23], especially for NISQ computing.…”

Section: Introductionmentioning

confidence: 99%

Robust quantum classifier with minimal overhead

Park,

Blank,

Petruccione

2021

Preprint

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To witness quantum advantages in practical settings, substantial efforts are required not only at the hardware level but also on theoretical research to reduce the computational cost of a given protocol. Quantum computation has the potential to significantly enhance existing classical machine learning methods, and several quantum algorithms for binary classification based on the kernel method have been proposed. These algorithms rely on estimating an expectation value, which in turn requires an expensive quantum data encoding procedure to be repeated many times. In this work, we calculate explicitly the number of repetition necessary for acquiring a fixed success probability and show that the Hadamard-test and the swap-test circuits achieve the optimal variance in terms of the quantum circuit parameters. The variance, and hence the number of repetition, can be further reduced only via optimization over data-related parameters. We also show that the kernel-based binary classification can be performed with a single-qubit measurement regardless of the number and the dimension of the data. Finally, we show that for a number of relevant noise models the classification can be performed reliably without quantum error correction. Our findings are useful for designing quantum classification experiments under limited resources, which is the common challenge in the noisy intermediate-scale quantum era.

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Parallel quantum trajectories via forking for sampling without redundancy

Cited by 19 publications

References 35 publications

Quantum classifier with tailored quantum kernel

Quantum classifier with tailored quantum kernel

A divide-and-conquer algorithm for quantum state preparation

Robust quantum classifier with minimal overhead

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