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arXiv:1704.03595 · npj Quantum Information

Scalable on-chip quantum state tomography

James Titchener, Markus Gräfe, René Heilmann, Alexander S. Solntsev, Alexander Szameit, Andrey A. Sukhorukov

Published Feb 20, 2018• 70 citations
arXivHTMLPDF

Abstract

Abstract Quantum information systems are on a path to vastly exceed the complexity of any classical device. The number of entangled qubits in quantum devices is rapidly increasing, and the information required to fully describe these systems scales exponentially with qubit number. This scaling is the key benefit of quantum systems, however it also presents a severe challenge. To characterize such systems typically requires an exponentially long sequence of different measurements, becoming highly resource demanding for large numbers of qubits. Here we propose and demonstrate a novel and scalable method for characterizing quantum systems based on expanding a multi-photon state to larger dimensionality. We establish that the complexity of this new measurement technique only scales linearly with the number of qubits, while providing a tomographically complete set of data without a need for reconfigurability. We experimentally demonstrate an integrated photonic chip capable of measuring two- and three-photon quantum states with statistical reconstruction fidelity of 99.71%.

DOI
10.1038/s41534-018-0063-5

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Abstract Quantum information systems are on a path to vastly exceed the complexity of any classical device. The number of entangled qubits in quantum devices is rapidly increasing, and the information required to fully describe these systems scales exponentially with qubit number. This scaling is the key benefit of quantum systems, however it also presents a severe challenge. To characterize such systems typically requires an exponentially long sequence of different measurements, becoming highly resource demanding for large numbers of qubits. Here we propose and demonstrate a novel and scalable method for characterizing quantum systems based on expanding a multi-photon state to larger dimensionality. We establish that the complexity of this new measurement technique only scales linearly with the number of qubits, while providing a tomographically complete set of data without a need for reconfigurability. We experimentally demonstrate an integrated photonic chip capable of measuring two- and three-photon quantum states with statistical reconstruction fidelity of 99.71%.
Summary form only given. Full characterization of quantum states is increasingly important as ever more complex quantum systems are realized. Quantum state tomography of these systems is a difficult task because individual measurements only give partial information about the underlying density matrix of the system. Thus, conventionally the measurement apparatus must be reconfigured to take multiple measurements in order to fully determine the density matrix. It is accepted that for an W-qubit system an exponentially increasing number of measurements are needed [1]. As a consequence, the complexity of typical quantum state tomography grows exponentially with increasing photon number, which makes characterizing large quantum systems highly challenging. We formulate a concept of on-chip quantum tomography where the complexity scales linearly with the number of photons. This is achieved by using a single specially designed non-reconfigurable linear optical circuit as in Fig. 1(a). Crucially, the number of waveguides in this circuit scales linearly with the number of photons in the state to be measured. Furthermore, our approach is simple and robust, and we demonstrate it experimentally with a specially designed photonic chip.
Technologies based on quantum mechanics promise to revolutionize the collection, processing and communication of information. However, due to the fragility of quantum coherence, complex quantum states can only exist in highly isolated and stable environments. One suitable environment is that of a quantum photonic chip. Quantum integrated photonics seeks to generate, process and detect complex quantum states inside a photonic chip. This thesis presents theory and experimental verification of novel approaches for the integration of various functionalities into quantum photonic chips in a scalable way. As such, this thesis encompasses a broad area of physics including quantum optics and nonlinear photonics. The results presented in this thesis have applications in the areas of quantum enhanced measurement, communication and information processing. In particular we develop the theory and experimentally demonstrate flexible on-chip sources of spatially entangled photons, the state of which can be reconfigured alloptically. We show how such techniques could enable the realization of simple cluster state quantum computing algorithms using spatially encoded two-photon states. Furthermore, we suggest new and practical approaches for the efficient characterization of mass produced nonlinear quantum photonic chips. Finally we develop and experimentally demonstrate a scalable method for the full quantum state tomography of multi-photon states on-chip. Importantly this technique only requires a linearly increasing number of single photon detectors relative to the number of photons in the state being characterized, and is also highly compatible with on-chip single photon detectors.
Abstract Reconstructing the state of a quantum system represents a pivotal task for quantum information applications. The standard approach based on quantum state tomography requires a number of measurements that scales exponentially with the number of qubits. Other methods have been proposed and tested to reduce the number of measurements, or to focus on specific properties of the output state rather than on its complete reconstruction. Here, we show experimentally the application of an approach, called threshold quantum state tomography, in an advanced hybrid photonic platform with states up to n = 4 qubits. This method does not require prior knowledge and selects only the informative projectors starting from the measurement of the density matrix diagonal. We demonstrate its effectiveness by showing that a consistent reduction in the number of measurements is obtained for relevant states, with only very limited loss of information. These results open perspective for its application in larger systems.
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields such as quantum computation, quantum communication, and quantum simulation. However, as the size of the quantum system increases, the number of measurement settings and sampling requirements for quantum state tomography grow exponentially with the number of qubits. This not only makes experimental design and implementation more complex, but also exacerbates the consumption of experimental resources. These limitations severely hinder the application of state tomography in large-scale quantum systems. To reduce measurement settings and improve sampling efficiency, this study proposes a state tomography method based on auxiliary systems. This method can be implemented through either entanglement between the quantum system to be measured and a quantum auxiliary system or through correlation between the quantum system and a probabilistic classical auxiliary system. Measurements on the entire joint system enable more efficient extraction of information about the quantum state to be measured. This method relies on standard quantum gate operations and requires only two measurement settings, with a total sampling complexity of O(d2)O(d^2)O(d2), significantly simplifying experimental operations and measurement processes. Additionally, this study provides two schemes for measuring purity based on the proposed circuit, one of which achieves measurement precision at the Heisenberg limit. This study validates the effectiveness of the proposed method through a detailed theoretical analysis, a series of numerical simulations, and experiments.
Reconstructing the state of a quantum system, called quantum state tomography, is an essential task in quantum technologies.Standard methods are inefficient, as they scale exponentially with the number of qubits.Better scaling methods, such as SIC-POVM tomography, are not yet widespread due to their measurement complexity.As such, there is an urgent need to find efficient and compact devices for performing tomography of photonic states.Here we present simulations of photonic devices implementing SIC-POVM tomography in photonic chips.We obtain fidelities F = 0.8452 (for qubits) and F = 0.7609 (for qutrits).Our results show that we can design efficient and compact SIC-POVM tomography modules for integrated-photonics quantum chips.Since integrated photonics is a major quantum technology platform, we expect our results to be instrumental in the future development of compact, costeffective quantum devices.Applications include quantum communications, quantum computing, quantum sensing and quantum imaging.
Quantum state tomography is the experimental procedure of determining an unknown state. It is not only essential for the verification of resources and processors of quantum information but is also important in its own right with regard to the foundation of quantum mechanics. Standard methods have been elusive for large systems because of the enormous number of observables to be measured and the exponential complexity of data post-processing. Here, we propose a new scheme of quantum state tomography that requires the measurement of only three observables (acting jointly on the system and pointer) regardless of the size of the system. The system is coupled to a "pointer" of single qubit, and the wavefunction of the system is "reaped" onto the pointer upon the measurement of the system. Subsequently, standard two-state tomography on the pointer and classical post-processing are used to reconstruct the quantum state of the system. We also developed an efficient and scalable iterative maximum likelihood algorithm to estimate states from statistically incomplete data.