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arXiv:2408.02832 · Advanced Quantum Technologies

Universal Multiport Interferometers for Post‐Selected Multi‐Photon Gates

Alessio Baldazzi, Lorenzo Pavesi

Published Dec 1, 2024• 7 citations
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Abstract

Abstract It is showed how to use universal multiport interferometers' schemes in order to create photonic post‐selected Controlled‐Z and Controlled–Controlled‐Z gates, which are equivalent, modulo single‐qubit gates, to Controlled‐NOT and Toffoli gates, respectively. The new proposed method is based on the following ingredients: identical single photons, Mach–Zehnder interferometer networks, single‐photon detectors and post‐selection. In particular, by using dual‐rail path encoding together with auxiliary paths and single photons, the success probabilities of such gates is improved. This result further proves the complexity and richness of Reck and Clements schemes beyond the usual notions and practices of Boson Sampling.

DOI
10.1002/qute.202400418

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Abstract It is showed how to use universal multiport interferometers' schemes in order to create photonic post‐selected Controlled‐Z and Controlled–Controlled‐Z gates, which are equivalent, modulo single‐qubit gates, to Controlled‐NOT and Toffoli gates, respectively. The new proposed method is based on the following ingredients: identical single photons, Mach–Zehnder interferometer networks, single‐photon detectors and post‐selection. In particular, by using dual‐rail path encoding together with auxiliary paths and single photons, the success probabilities of such gates is improved. This result further proves the complexity and richness of Reck and Clements schemes beyond the usual notions and practices of Boson Sampling.
Abstract Universal quantum entangling gates are a crucial building block in the large‐scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the implementation of a controlled‐NOT (CNOT) gate is constructed by introducing a non‐computational quantum state in the auxiliary space. Furthermore, the method is extended to the construction of a general n ‐control‐qubit Toffoli gate with qubit–qudit gates and single‐qudit gates. Based on the presented quantum circuits, the polarization CNOT and Toffoli gates with linear optics are designed by operating on the spatial‐mode degree of freedom of photons. The proposed optical schemes can be achieved with a higher success probability and no extra auxiliary photons are needed.
Multiport interferometers with NNN ports are basic devices in both classical and quantum photonics. Ideally, they implement a linear unitary transformation between the input and output electric field vectors with NNN components, each associated with a spatial mode of classical coherent light or a single photon. Standard designs for a fully reconfigurable universal multiport interferometer are given by the Reck or the Clements schemes. In this work, we introduce routing schemes to implement a generic unitary transformation on classical coherent light or single photons using linear or tree geometries via multiple projective measurements on a single detector with the minimum number of components. Then, we generalize this result to the case of any multi-photon state for scattershot boson sampling experiments with multi-routing schemes. Finally, we test the robustness of routing schemes compared to universal schemes with respect to losses and phase noise.
As primitives for entanglement generation, controlled phase gates have a central role in quantum computing. Especially in ideas realizing instances of quantum computation in linear optical gate arrays, a closer look can be rewarding. In such architectures, all effective nonlinearities are induced by measurements. Hence the probability of success is a crucial parameter of such quantum gates. In this paper, we discuss this question for controlled phase gates that implement an arbitrary phase with one and two control qubits. Within the class of post-selected gates in dual-rail encoding with vacuum ancillas, we identify the optimal success probabilities. We construct networks that allow for implementation using current experimental capabilities in detail. The methods employed here appear specifically useful with the advent of integrated linear optical circuits, providing stable interferometers on monolithic structures.
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.
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.
Abstract Universal quantum gates lie at the heart of designing quantum computer. Here two compact quantum circuits for implementing post‐selected controlled‐phase‐flip (CPF) gate and Toffoli gate with linear optics are constructed assisted by one and two single photons, respectively. The current existing maximum success probability of 1/4 for linear optical CPF gate is achieved by resorting to an ancillary single photon rather than an entangled photon pair or two single photons. Remarkably, the presented Toffoli gate is accomplished with current maximum success probability of 1/30 and unity fidelity in principle, without using additional entangled photon pairs and the standard decomposition‐based approach. Linear optical implementations of the presented two universal gates are feasible and economical under current technology, and provide a potential application in large‐scale optical quantum computing.