Optimal Universal Learning Machines for Quantum State Discrimination

Fanizza, Marco; Mari, Andrea; Giovannetti, Vittorio

doi:10.1109/tit.2019.2916646

Cited by 25 publications

(21 citation statements)

References 34 publications

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“…In other words, we have full knowledge about the meaning of the possible labels. Supervised quantum learning algorithms for quantum state classification [14][15][16][17] consider the intermediate scenario with limited training data. In this case, no description of the states is available.…”

Section: Introductionmentioning

confidence: 99%

Unsupervised Classification of Quantum Data

et al. 2019

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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 preserving information contained in the states. We quantify analytically its performance for arbitrary size and dimension of the data. We contrast it with the performance of its classical counterpart, which clusters data that has 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 data is at least three-dimensional. For the sake of comparison, we discuss the optimal protocol when the classical and quantum states are known.

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Section: Introductionmentioning

confidence: 99%

Unsupervised Classification of Quantum Data

et al. 2019

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“…This in particular distinguishes our work from previous results on quantum circuit learning, in particular very recent study in e.g. [43], who only optimise circuits for specific inputs. Note that prior work hence does not consider the generalisation ability and hence does not treat the actual learning problem which is aiming at optimisation as well as generalisation.…”

Section: Discussionmentioning

confidence: 66%

Sequence-Discriminative Training of Neural Networks

Chen

2017

New Era for Robust Speech Recognition

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Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by non-orthogonal quantum probability distributions using the Adam stochastic optimization algorithm. This is achieved by iterative interactions of a classical device with a quantum processor to discover the parameters of an unknown non-unitary quantum circuit. This circuit learns to simulates the unknown structure of a generalized quantum measurement, or Positive-Operator-Value-Measure (POVM), that is required to optimally distinguish possible distributions of quantum inputs. Notably we use universal circuit topologies, with a theoretically motivated circuit design, which guarantees that our circuits can in principle learn to perform arbitrary input-output mappings. Our numerical simulations show that shallow quantum circuits could be trained to discriminate among various pure and mixed quantum states exhibiting a trade-off between minimizing erroneous and inconclusive outcomes with comparable performance to theoretically optimal POVMs. We train the circuit on different classes of quantum data and evaluate the generalization error on unseen mixed quantum states. This generalization power hence distinguishes our work from standard circuit optimization and provides an example of quantum machine learning for a task that has inherently no classical analogue. *

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“…This training process generalizes well for the discrimination tasks on new data, i.e., states from the parameter range which have not been seen during the training process. This distinguishes our work from previous results on quantum circuit learning, in particular the very recent study in Fanizza et al (2018), which only optimizes circuits for specific inputs. Note that this prior work hence does not consider the generalization ability and hence does not treat the actual learning problem, which aims at optimization as well as generalization.…”

Section: Discussionmentioning

confidence: 81%

Universal discriminative quantum neural networks

Chen

Wossnig

Severini

et al. 2020

Quantum Mach. Intell.

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Recent results have demonstrated the successful applications of quantum-classical hybrid methods to train quantum circuits for a variety of machine learning tasks. A natural question to ask is consequentially whether we can also train such quantum circuits to discriminate quantum data, i.e., perform classification on data stored in form of quantum states. Although quantum mechanics fundamentally forbids deterministic discrimination of non-orthogonal states, we show in this work that it is possible to train a quantum circuit to discriminate such data with a trade-off between minimizing error rates and inconclusiveness rates of the classification tasks. Our approach achieves at the same time a performance which is close to the theoretically optimal values and a generalization ability to previously unseen quantum data. This generalization power hence distinguishes our work from previous circuit optimization results and furthermore provides an example of a quantum machine learning task that has inherently no classical analogue.

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Optimal Universal Learning Machines for Quantum State Discrimination

Cited by 25 publications

References 34 publications

Unsupervised Classification of Quantum Data

Unsupervised Classification of Quantum Data

Sequence-Discriminative Training of Neural Networks

Universal discriminative quantum neural networks

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