Quantum Data 980

[Najla Ondik]

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We introduce the problem of unsupervised classification of quantum data, namely, of systems whose quantum states are unknown. We derive the optimal single-shot protocol for the binary case, where the states in a disordered input array are of two types. Our protocol is universal and able to automatically sort the input under minimal assumptions, yet partially preserves information contained in the states. We quantify analytically its performance for an arbitrary size and dimension of the data. We contrast it with the performance of its classical counterpart, which clusters data that have been sampled from two unknown probability distributions. We find that the quantum protocol fully exploits the dimensionality of the quantum data to achieve a much higher performance, provided the data are at least three dimensional. For the sake of comparison, we discuss the optimal protocol when the classical and quantum states are known.

A microphone placed in a street captures sounds from multiple sources that first look scrambled to a computer. By recognizing sound-wave patterns, the computer can discern a conversation, traffic, and a street musician. Unlike with sound waves, identifying patterns in quantum data is much more challenging, since a mere observation irretrievably degrades the data. We take a look at the problem of sorting a data array of quantum systems by the state in which they have been prepared. In the case of two possible preparations, we devise an optimal procedure that can identify clusters of identically prepared quantum systems.

Our protocol shows a natural connection to an archetypical use case of classical machine learning: clustering data samples according to whether they share a common underlying probability distribution. A classical clustering algorithm works with no knowledge of the distributions that generate the data. Likewise, our quantum protocol is oblivious to the quantum states of the systems in the input data array and is thus universal. Measuring each input system individually (a limited strategy) gives rise to a classical clustering problem, providing a quantitative performance comparison between quantum and classical clustering. We find that a quantum strategy using collective measurements on the whole data array outperforms classical clustering, and even more so for large dimensional data.

Our approach to quantum clustering is built with minimal assumptions and is applicable to general quantum scenarios. As such, it sets solid theoretical grounds on what is possible for automated classification and distribution of quantum information.

Pictorial representation of the clustering device for an input of eight quantum states. States of the same type have the same color. States are clustered according to their type by performing a suitable collective measurement, which also provides a classical description of the clustering.

All possible clusterings of N=4 systems when each can be in one of two possible states, depicted as blue and red. The pair of indices (n,σ) identifies each clustering, where n is the size of the smallest cluster and σ is a permutation of the reference clusterings (those on top of each box), wherein the smallest cluster falls on the right. The symbol e denotes the identity permutation, and (ij) the transposition of systems in positions i and j. Note that the choice of σ is not unique.

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Quantum machine learning with parametrised quantum circuits has attracted significant attention over the past years as an early application for the era of noisy quantum processors. However, the possibility of achieving concrete advantages over classical counterparts in practical learning tasks is yet to be demonstrated. A promising avenue to explore potential advantages is the learning of data generated by quantum mechanical systems and presented in an inherently quantum mechanical form. In this article, we explore the applicability of quantum data learning to practical problems in high-energy physics, aiming to identify domain specific use-cases where quantum models can be employed. We consider quantum states governed by one-dimensional lattice gauge theories and a phenomenological quantum field theory in particle physics, generated by digital quantum simulations or variational methods to approximate target states. We make use of an ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states in the Schwinger model, (de)confinement phases from time-evolved states in the Z2 gauge theory, and that it can extract fermion flavor/coupling constants in a quantum simulation of parton shower. The observation of nontrivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum data learning architecture in high-energy physics.

Representative QCNN circuit considered in this work, composed of alternating convolution and pooling layers (denoted by CL and PL, respectively), followed by a fully connected layer (FCL) and the measurement of the output state ρout with an observable O. In the QDL framework used in this paper, the input to the QCNN circuit is a quantum state ρin, either in the form of a ground state generated with VQE, a time-evolved state through Hamiltonian simulation, or a multiparticle state from a phenomenological quantum parton shower simulation. Precise QCNN circuits used in the numerical studies are described in Secs. 3, 4, and 5, with details in Appendix pp1.

(Top) QPS circuit (UQPS) to produce the dataset, followed by the QCNN circuit (UQCNN) and the single-qubit measurement. (Bottom) Unitary gates comprising the UQPS circuit. The circuit diagram follows the notation used in Ref. [59]. The unitaries U and Uia/b corresponding to Eqs. (11) and (43) in the Supplemental Material of Ref. [59], respectively, are given in Appendix pp5.

QCNN circuit used for the phase recognition task in the Z2 model. The unitaries Uconv and Upool correspond to those shown in Figs. 6 and 10, respectively. The truncated Uconv gate at the first CL indicates that the gate acts upon the top and bottom qubits.

QCNN circuit used in the QPS study with Nstep=8. The unitaries Uconv and Upool correspond to those shown in Figs. 6 and 10, respectively. The truncated Uconv gates at the same CL indicate that they act upon those two qubits.

A set of single-qubit rotation gates and a CNOT gate that composes a PL block. The single-qubit gates on the target qubit after the CNOT correspond to the adjoint of the set of single-qubit gates on the control qubit.

ARMONK, N.Y. and EHNINGEN, Germany, June 6, 2023 /PRNewswire/ -- Today, IBM (NYSE: IBM) announced plans to open its first Europe-based quantum data center to facilitate access to cutting-edge quantum computing for companies, research institutions and government agencies.

The data center will be located at IBM's facility in Ehningen, Germany, and will serve as IBM Quantum's European cloud region. Users in Europe and elsewhere in the world will be able to provision services at the data center for their cloud-based quantum computing research and exploratory activity. The data center is being designed to help clients continue to manage their European data regulation requirements, including processing all job data within EU borders. The facility will be IBM's second quantum data center and quantum cloud region, after Poughkeepsie, New York.

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