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Quantum Information and Measurement (QIM)

Driven Boson Sampling

Sonja Barkhofen, Tim J. Bartley, Linda Sansoni, Regina Kruse, Craig S. Hamilton, Igor Jex, Christine Silberhorn

Published Jan 1, 2017• 0 citations
Publisher

Abstract

We present a scheme for Boson-sampling whereby photons are generated within the network of beam splitters. We demonstrate this approach has the required complexity, and is more scalable and less noisy than most existing implementations.
DOI
10.1364/qim.2017.qw6b.3

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Acta Physica Sinica•Jan 1, 2022•0 citations
Sampling the distribution of bosons that have undergone a random unitary evolution is strongly believed to be a computationally hard problem. Key to outperforming classical simulations of this task is to increase both the number of input photons and the size of the network. We propose driven boson sampling, in which photons are input within the network itself, as a means to approach this goal. We show that the mean number of photons entering a boson sampling experiment can exceed one photon per input mode, while maintaining the required complexity, potentially leading to less stringent requirements on the input states for such experiments. When using heralded single-photon sources based on parametric down-conversion, this approach offers an ∼e-fold enhancement in the input state generation rate over scattershot boson sampling, reaching the scaling limit for such sources. This approach also offers a dramatic increase in the signal-to-noise ratio with respect to higher-order photon generation from such probabilistic sources, which removes the need for photon number resolution during the heralding process as the size of the system increases.
Boson sampling arising from multiphoton interference in linear-optical networks is a prominent non-universal model for quantum computation. Here, by encoding the multi-qubit state to bosonic Fock state, we present a scalable quantum-circuit framework for simulating boson sampling on a universal quantum computing platform. Beginning with balanced beam-splitter transformations on the single- and two-photon sectors, we derive equivalent quantum-circuit implementations and unify them within a common Hilbert-space representation using an ancilla-assisted encoding. This construction is then generalized to arbitrary interferometers by replacing each optical beam splitter with a repeating quantum-circuit unit that selectively acts only within the relevant local interference subspace, requiring N+1N+1N+1 qubits for a two-photon NNN-mode interferometer and a linear-overhead subspace-identification procedure. Using this framework, gate-based quantum circuit for a four-mode boson-sampling circuit is developed and experimentally implemented on a four-qubit gate-based photonic qubit system. The qubit framework for emulating boson sampling of n−n-n−photons in m−m-m−mode will be useful to solve a broad class of sampling complexity problem on a gate-based quantum computers.
Boson sampling, the task of sampling the probability distribution of photons at the output of a photonic network, is believed to be hard for any classical device. Unlike other models of quantum computation that require thousands of qubits to outperform classical computers, boson sampling requires only a handful of single photons. However, a scalable implementation of boson sampling is missing. Here, we show how superconducting circuits provide such platform. Our proposal differs radically from traditional quantum-optical implementations: rather than injecting photons in waveguides, making them pass through optical elements like phase shifters and beam splitters, and finally detecting their output mode, we prepare the required multiphoton input state in a superconducting resonator array, control its dynamics via tunable and dispersive interactions, and measure it with nondemolition techniques.
Boson sampling is a candidate for quantum protocols to truly realize the quantum computation advantage and to be used in advanced fields where complex computations are needed, such as quantum chemistry. However, this proposal is hard to achieve due to the existence of noise sources such as photon losses. In order to quantificationally analyze the influences of photon losses in optical networks, boson sampling is classically simulated based on the equivalent beam splitter mechanism, where the photon loss happening in optical units is equivalent to the photon transmission into the environmental paths through a virtual beam splitter. In our simulation, networks corresponding to random unitary matrices are made up, considering both the Reck structure and the Clements structure. The photon loss probability in an optical unit is well controlled by adjusting the parameters of the virtual beam splitter. Therefore, to simulate boson sampling with photon losses in optical networks is actually to simulate ideal boson sampling with more modes. It is found that when the photon loss probability is constant, boson sampling with Clements structures distinctly performs much better than that with Reck structures. Furthermore, the photon loss probability is also set to follow the normal distribution, which is thought to be closer to the situation in reality. It is found that when the mean value of photon loss probability is constant, for both network structures, errors of outputs become more obvious with the increase of standard deviation. It can be inferred that the increase of error rate can be explained by the network depth and the conclusion is suitable for larger-scale boson sampling. Finally, the number of output photons is taken into consideration, which is directly related to the classical computation complexity. It is found that with the photon loss probability, the ratio of output combinations without photon losses decreases sharply, implying that photon losses can obviously affect the quantum computation advantage of boson sampling. Our results indicate that photon losses can result in serious errors for boson sampling, even with a stable network structure such as that of Clements. This work is helpful for boson sampling experiments in reality and it is desired to develop a better protocol, for example, a well-designed network or excellent optical units, to well suppress photon losses.