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arXiv:2401.16875 · Optics Express

Quantum circuit mapping for universal and scalable computing in MZI-based integrated photonics

Yong Sung Kwon, Alessio Baldazzi, Lorenzo Pavesi, Byung-Soo Choi

Published Mar 13, 2024• 12 citations
arXivHTMLPDF

Abstract

Linear optical quantum computing (LOQC) offers a quantum computation paradigm based on well-established and robust technology and flexible environmental conditions following DiVincenzo's criteria. Within this framework, integrated photonics can be utilized to achieve gate-based quantum computing, defining qubits by path-encoding, quantum gates through the use of Mach-Zehnder interferometers (MZIs), and measurements through single-photon detectors. In particular, universal two-qubit gates can be achieved by suitable structures of MZIs together with post-selection or heralding. The most resource-efficient choice is given by the post-selected Controlled-Z (CZ) gate. However, this implementation is characterized by a design which has a non-regular structure and cannot be cascaded. This limits the implementation of large-scale LOQC. Starting from these issues, we suggest an approach to move toward a universal and scalable LOQC on the integrated photonic platform. First of all, choosing the post-selected CZ as a universal two-qubit gate, we extend the path-encoded dual-rail qubit to a triplet of waveguides, composed of an auxiliary waveguide and the pair of waveguides corresponding to the qubit basis states. Additionally, we introduce a swap photonic network that maps the regularly-labeled structure of the new path-encoded qubits to the structure needed for the post-selected CZ. We also discuss the optical swap gate that allows the connection of non-nearest neighbor path-encoded qubits. In this way, we can deterministically exchange the locations of the qubits and execute controlled quantum gates between any path-encoded qubits. Next, by truncating the auxiliary waveguides after any post-selected CZ, we find that it is possible to cascade this optical gate when it acts on different pairs that share only one qubit. Finally, we show the Bell state and the Greenberger-Horne-Zeilinger (GHZ) state generation circuits implementing the regular structure, the cascading procedure of post-selected CZ and the optical swap.

DOI
10.1364/oe.520492

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Linear optical quantum computing (LOQC) offers a quantum computation paradigm based on well-established and robust technology and flexible environmental conditions following DiVincenzo's criteria. Within this framework, integrated photonics can be utilized to achieve gate-based quantum computing, defining qubits by path-encoding, quantum gates through the use of Mach-Zehnder interferometers (MZIs), and measurements through single-photon detectors. In particular, universal two-qubit gates can be achieved by suitable structures of MZIs together with post-selection or heralding. The most resource-efficient choice is given by the post-selected Controlled-Z (CZ) gate. However, this implementation is characterized by a design which has a non-regular structure and cannot be cascaded. This limits the implementation of large-scale LOQC. Starting from these issues, we suggest an approach to move toward a universal and scalable LOQC on the integrated photonic platform. First of all, choosing the post-selected CZ as a universal two-qubit gate, we extend the path-encoded dual-rail qubit to a triplet of waveguides, composed of an auxiliary waveguide and the pair of waveguides corresponding to the qubit basis states. Additionally, we introduce a swap photonic network that maps the regularly-labeled structure of the new path-encoded qubits to the structure needed for the post-selected CZ. We also discuss the optical swap gate that allows the connection of non-nearest neighbor path-encoded qubits. In this way, we can deterministically exchange the locations of the qubits and execute controlled quantum gates between any path-encoded qubits. Next, by truncating the auxiliary waveguides after any post-selected CZ, we find that it is possible to cascade this optical gate when it acts on different pairs that share only one qubit. Finally, we show the Bell state and the Greenberger-Horne-Zeilinger (GHZ) state generation circuits implementing the regular structure, the cascading procedure of post-selected CZ and the optical swap.
Optical quantum computers represent qubits as photons created by laser and implement arbitrary quantum operations through Mach-Zehnder interferometers (MZIs) which is called linear optical quantum computing (LOQC). Since the number of qubits and quantum system is getting bigger, we need a scalable and universal quantum computing platform based on LOQC. In this work, we propose a software framework which can support a universal programming with flexibility of LOQC hardware configuration. The framework consists of four parts such as decomposer, mapper, controller, and user-interface controller. As an example, we show a use case of this framework for Bell state generation on Recket al.’s MZI network.
Linear optical quantum computation (LOQC) offers a promising platform for scalable quantum information processing, but its scalability is fundamentally constrained by the probabilistic nature of non-local entangling gates. Qudit circuit compression schemes mitigate this issue by encoding multiple qubits onto qudits. However, these schemes become inefficient when only a subset of the encoded qubits is required to participate in the non-local entangling gate, leading to an exponential increase in the number of non-local gates. In this Letter, we address this bottleneck by demonstrating the existence of multi-level control-Z (CZ) gates for qudits encoded in multiple spatial modes in LOQC. Unlike conventional two-level CZ gates, which act only on a single pair of modes, multi-level CZ gates impart a conditional phase shift for an arbitrarily chosen subset of the spatial modes. We present two explicit linear optical schemes that realize such operations, illustrating a fundamental trade-off between prior information about the input quantum state and the physical resources required. The first scheme is realized with a constant success probability of 1/81/81/8 independent of the qudit dimension using a single non-local entangling gate, at the cost of state dependence, which is significantly better than the current success probability of 1/91/91/9. Our second scheme provides a fully state independent realization reducing the number of non-local gates to O(2r1+2r2)\mathcal{O}(2^{r_1}+2^{r_2})O(2r1​+2r2​) as compared to the existing bound of O(2r1+r2)\mathcal{O}(2^{r_1+r_2})O(2r1​+r2​) where r1r_1r1​ and r2r_2r2​ are the number of qubits to be removed as control in the qudits. The success probability of the realization is 12(18)2r1+2r2\frac{1}{2} \left(\frac{1}{8}\right)^{2^{r_1}+2^{r_2}}21​(81​)2r1​+2r2​. When combined with qudit circuit compression schemes, our results improve upon a key scalability limitation and significantly improve the efficiency of LOQC architectures.
A software platform for quantum computing is required to run a complex algorithm on a real quantum device through automatically converting a quantum circuit level algorithm to a control sequence of target device. Moreover, the software platform must be tailored for the target quantum system by exploiting the properties of qubits and gates. In this work, we show how to implement a software platform for a photonic integrated circuit (PIC) platform with path-encoded photon qubits and quantum gates realized by means of interference in a mesh of tuneable Mach-Zehnder interferometers (MZIs). For universal and programmable quantum computing, the software platform consists of three standard modules: decomposer, mapper, and controller. To verify the software we runs example circuit through software and hardware integration platform and confirm each module generates correct output. Also the validation is done by comparing two results for conventionally used manual way and the software supported automatic way. These two points ensure that the implemented software works correctly when applied to the PIC.
Abstract The single-photon quantum computing paradigm currently relies on the multi-port interference in linear optical devices, which is intrinsically based on probabilistic measurements outcome, and thus non-deterministic. Devising a fully deterministic, universal, and practically achievable quantum computing platform based on single-photon encoding and integrated photonic circuits is still an open challenge. Here we propose to exploit the interplay of distributed self-Kerr nonlinearity and localized hopping in quantum photonic interferometers to implement deterministic entangling quantum gates with dual rail photonic qubits. It is shown that a universal set of single- and two-qubit gates can be designed by a suitable concatenation of few optical interferometric elements, reaching optimal fidelities arbitrarily close to 100% that are theoretically demonstrated through a bound constrained optimization algorithm. The actual realization would require the concatenation of a few tens of elementary operations, as well as on-chip optical nonlinearities that are compatible with some of the existing quantum photonic platforms, as it is finally discussed.
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.
Abstract The swap test is a quantum algorithm capable of computing the absolute value of the scalar product of two arbitrary wavefunctions. Scalar products represent a crucial ingredient to many quantum machine learning (QML) methods, but their evaluation is not straightforward at all. For this reason, many research efforts have been made without achieving an efficient and robust implementation. Here, we present an integrated photonic circuit designed to implement the swap test algorithm. Our approach relies solely on linear optical integrated components and qudits, represented by single photons from an attenuated laser beam propagating through a set of waveguides. By utilizing 23 spatial degrees of freedom for the qudits, we can configure all the necessary arrangements to set any two-qubit state and perform the swap test. This simplifies the requirements on the circuitry elements and eliminates the need for non-linearity, heralding, or post-selection to achieve multi-qubit gates. Our photonic swap test circuit successfully encodes two qubits and estimates their scalar product with a measured root mean square error smaller than 0.05. This result paves the way for the development of integrated photonic architectures capable of performing QML tasks with robust devices operating at room temperature.