## Periodic Reporting for period 1 - PIQUANT (Photonic Quantum Network with an Ultrafast Frequency Comb)

Reporting period: 2016-04-01 to 2018-03-31

The primary objective of this action is to develop a photonic quantum network for scalable quantum information processing. By exploiting the intrinsic multimode structure of an ultrafast frequency comb, a quantum network supporting multiple quantum systems is generated, and quantum correlations in the network are optimized to readily conduct a given quantum information task. To benefit from genuine speedup of quantum information processing, elaborate single-photon control is implemented, which affects only specific modes of interest out of multiple frequency modes in the quantum network. The resultant light field becomes a PhotonIc QUAtum NeTwork with an ultrafast frequency comb (PIQUANT), which is an essential quantum resource for quantum information processing. Details activities in this project are:

• Optimal preparation of a Gaussian quantum network with an ultrafast frequency comb

• Generation of photonic quantum network by employing single-photon control

• Full characterization of a photonic quantum network

• Measurement based quantum computing using a photonic quantum network

As a result of this project, we have generated a versatile photonic quantum network by engineering ultrafast frequency comb in various manners. In the initial step to generate a Gaussian quantum network, shaping the pump frequency comb enables us to modify the structure of the generated quantum network. In addition, we have implemented a single-photon subtractor by engineering ultrafast frequency comb, which converts the Gaussian quantum network into a photonic quantum network that exhibits non-Gaussian statistics. Such non-Gaussian statistics is important for quantum information processing, and is identified as a main resource in quantum computing. The photonic quantum network will have broad applications in quantum information science, e.g. quantum computing, quantum communication, and quantum enhanced measurement.

• Optimal preparation of a Gaussian quantum network with an ultrafast frequency comb

• Generation of photonic quantum network by employing single-photon control

• Full characterization of a photonic quantum network

• Measurement based quantum computing using a photonic quantum network

As a result of this project, we have generated a versatile photonic quantum network by engineering ultrafast frequency comb in various manners. In the initial step to generate a Gaussian quantum network, shaping the pump frequency comb enables us to modify the structure of the generated quantum network. In addition, we have implemented a single-photon subtractor by engineering ultrafast frequency comb, which converts the Gaussian quantum network into a photonic quantum network that exhibits non-Gaussian statistics. Such non-Gaussian statistics is important for quantum information processing, and is identified as a main resource in quantum computing. The photonic quantum network will have broad applications in quantum information science, e.g. quantum computing, quantum communication, and quantum enhanced measurement.

1. Optimal preparation of a Gaussian quantum network with an ultrafast frequency comb

- We have implemented a pulse shaper for the pump beam to generate a multimode squeezed vacuum state and another pulse shaper for the local oscillator to measure the generated state. The pulse shaper for the pump, for example, can shift the phase of a half of the pump spectrum, and as a result, we observed that the covariance matrix of the Gaussian quantum network is qualitatively changed. The pulse shaper for the local oscillator enables us to access an individual node in a quantum network. Moreover, it allows to accessing multiple nodes as a superposition, which is equivalent with having a quantum network in a different topology. Thanks to such versatility, we can generate a Gaussian quantum network optimized for a given quantum information task.

2. Generation of photonic quantum network by employing single-photon control

- We have implemented a single-photon subtractor based on nonlinear interaction between an input beam and an auxiliary gate beam. The spectral mode of the gate beam defines the mode of single-photon subtraction at the input beam, which is required for single-photon subtraction in a quantum network. Note that the conventional method of photon subtraction cannot be used in multimode quantum states such as a Gaussian quantum network because the resultant state becomes a mixed quantum state, while our method can be used to subtract a single photon at a desired mode or at a superposition of desired modes by maintaining quantum properties. To control the spectrum of the gate beam, we have implemented a pulse shaper, which can tune the amplitude and the phase at each frequency band. We have fully characterized the implemented device based on quantum process tomography. An important figure of merit of a single-photon subtractor is a mode selectivity, and the implemented one typically exhibits a high value amounting to 0.9. This result led to publication in Phys. Rev. X 7, 031012 (2017).

3. Full characterization of a photonic quantum network

- We have successfully generated a non-Gaussian quantum network based on the single-photon subtractor implemented in the aforementioned paragraph. This is, in fact, the main goal of this project, which combines a Gaussian quantum network and single-photon control to develop a photonic quantum network. We have experimentally observed that photon subtraction results in a non-Gaussian statistics at a desired mode or at a superposition of different modes. We have also reconstructed the generated quantum states by quantum state tomography.

4. Measurement based quantum computing using a photonic quantum network

- To fully exploit the photonic quantum network in quantum protocols (e.g. measurement based quantum computing), one needs simultaneous accesses to multiple modes, which requires multimode homodyne detection. We have implemented multimode homodyne detection for multiple frequency bands of light. In more detail, it is constructed by mixing a spectrally broadband local oscillator with a quantum state to be measured at a beam splitter; the two output beams are diffracted by optical gratings, which are subsequently focused by micro-lens arrays at multipixel photodiodes; a pair of photodiodes each from the two multipixel photodiodes construct a individual homodyne detection. This device will be useful to efficiently characterize a photonic quantum network and to conduct quantum information tasks.

- We have implemented a pulse shaper for the pump beam to generate a multimode squeezed vacuum state and another pulse shaper for the local oscillator to measure the generated state. The pulse shaper for the pump, for example, can shift the phase of a half of the pump spectrum, and as a result, we observed that the covariance matrix of the Gaussian quantum network is qualitatively changed. The pulse shaper for the local oscillator enables us to access an individual node in a quantum network. Moreover, it allows to accessing multiple nodes as a superposition, which is equivalent with having a quantum network in a different topology. Thanks to such versatility, we can generate a Gaussian quantum network optimized for a given quantum information task.

2. Generation of photonic quantum network by employing single-photon control

- We have implemented a single-photon subtractor based on nonlinear interaction between an input beam and an auxiliary gate beam. The spectral mode of the gate beam defines the mode of single-photon subtraction at the input beam, which is required for single-photon subtraction in a quantum network. Note that the conventional method of photon subtraction cannot be used in multimode quantum states such as a Gaussian quantum network because the resultant state becomes a mixed quantum state, while our method can be used to subtract a single photon at a desired mode or at a superposition of desired modes by maintaining quantum properties. To control the spectrum of the gate beam, we have implemented a pulse shaper, which can tune the amplitude and the phase at each frequency band. We have fully characterized the implemented device based on quantum process tomography. An important figure of merit of a single-photon subtractor is a mode selectivity, and the implemented one typically exhibits a high value amounting to 0.9. This result led to publication in Phys. Rev. X 7, 031012 (2017).

3. Full characterization of a photonic quantum network

- We have successfully generated a non-Gaussian quantum network based on the single-photon subtractor implemented in the aforementioned paragraph. This is, in fact, the main goal of this project, which combines a Gaussian quantum network and single-photon control to develop a photonic quantum network. We have experimentally observed that photon subtraction results in a non-Gaussian statistics at a desired mode or at a superposition of different modes. We have also reconstructed the generated quantum states by quantum state tomography.

4. Measurement based quantum computing using a photonic quantum network

- To fully exploit the photonic quantum network in quantum protocols (e.g. measurement based quantum computing), one needs simultaneous accesses to multiple modes, which requires multimode homodyne detection. We have implemented multimode homodyne detection for multiple frequency bands of light. In more detail, it is constructed by mixing a spectrally broadband local oscillator with a quantum state to be measured at a beam splitter; the two output beams are diffracted by optical gratings, which are subsequently focused by micro-lens arrays at multipixel photodiodes; a pair of photodiodes each from the two multipixel photodiodes construct a individual homodyne detection. This device will be useful to efficiently characterize a photonic quantum network and to conduct quantum information tasks.

Quantum information processing based on light has been based on encoding quantum information in one of two complementary aspects of light: particles (called discrete variable approach) or waves (called continuous-variable approach). Each of the approaches has its own advantages compared with the other. For example, in the continuous-variable approach, a large-scale entangled state can be generated deterministically, and in the discrete-variable approach, quantum processes that cannot be classically simulated can be implemented. A new approach, called hybrid quantum information processing, is to combine the two approaches to take both advantages.

The photonic quantum network generated in this project is in the line with the hybrid quantum information processing. A Gaussian quantum network corresponds with the continuous-variable approach, and single-photon control does with the discrete-variable approach, and their integration for generating a photonic quantum network fits exactly with the emerging hybrid quantum information processing. In particular, we have extended the hybrid approach to a multimode regime, which is an essential step for scalable quantum information processing; note that the conventional methods of single-photon control cannot operate in a multimode regime while we have overcome the limitation in this project. In addition, our method to generate a photonic quantum network is versatile because we can reconfigure connections between nodes (or topology) in the quantum network by pulse shaping techniques. The results of this project will stimulate development of quantum technologies and have broad applications in, e.g. universal quantum computing, entanglement distillation, and nonlocality test.

The photonic quantum network generated in this project is in the line with the hybrid quantum information processing. A Gaussian quantum network corresponds with the continuous-variable approach, and single-photon control does with the discrete-variable approach, and their integration for generating a photonic quantum network fits exactly with the emerging hybrid quantum information processing. In particular, we have extended the hybrid approach to a multimode regime, which is an essential step for scalable quantum information processing; note that the conventional methods of single-photon control cannot operate in a multimode regime while we have overcome the limitation in this project. In addition, our method to generate a photonic quantum network is versatile because we can reconfigure connections between nodes (or topology) in the quantum network by pulse shaping techniques. The results of this project will stimulate development of quantum technologies and have broad applications in, e.g. universal quantum computing, entanglement distillation, and nonlocality test.