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.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.

arXiv:2105.10631Advanced Quantum TechnologiesMar 18, 202230 citations

The optical quantum entanglement experiments

F. J. Duarte

Institute of Physics eBooksSep 1, 20220 citations

Depth dependence of entanglement and circuit complexity in random linear optical networks

Laura Shou, Joseph T. Iosue, Yu-Xin Wang +2 more

We study the growth of entanglement and circuit complexity in random passive linear optical networks as a function of the circuit depth. For entanglement dynamics, we start with an initial Gaussian state with all $n$ modes equally squeezed. For random brickwork circuits, we show that entanglement, as measured by the Rényi-2 entropy, grows diffusively as a function of the depth, in contrast to the linear growth for random qubit brickwork circuits. In the other direction, for arbitrary circuit geometries we prove bounds on depths which ensure the average-case subsystem entanglement reaches within a constant factor of the maximum value in all subsystems, and bounds which ensure closeness of the random linear optical unitary to a Haar random unitary in $L^2$ Wasserstein distance. We also consider robust circuit complexity for random one-dimensional brickwall circuits, as measured by the minimum number of gates required in any circuit that approximately implements the linear optical unitary. Viewing this as a function of the number of modes and the circuit depth, we show the robust circuit complexity for random one-dimensional brickwall circuits scales at most diffusively in the depth with high probability, again in contrast to the linear scaling for certain random qubit circuits. The corresponding Gaussian unitary $\tilde{\mathcal U}$ for the approximate implementation retains high output fidelity $|\langleψ|\mathcal U^\dagger \tilde{\mathcal U}|ψ\rangle|^2$ for pure states $|ψ\rangle$ with constrained expected photon-number.We study the growth of entanglement and circuit complexity in random passive linear optical networks as a function of the circuit depth. For entanglement dynamics, we start with an initial Gaussian state with all $n$ modes equally squeezed. For random brickwork circuits, we show that entanglement, as measured by the Rényi-2 entropy, grows diffusively as a function of the depth, in contrast to the linear growth for random qubit brickwork circuits. In the other direction, for arbitrary circuit geometries we prove bounds on depths which ensure the average-case subsystem entanglement reaches within a constant factor of the maximum value in all subsystems, and bounds which ensure closeness of the random linear optical unitary to a Haar random unitary in $L^2$ Wasserstein distance. We also consider robust circuit complexity for random one-dimensional brickwall circuits, as measured by the minimum number of gates required in any circuit that approximately implements the linear optical unitary. Viewing this as a function of the number of modes and the circuit depth, we show the robust circuit complexity for random one-dimensional brickwall circuits scales at most diffusively in the depth with high probability, again in contrast to the linear scaling for certain random qubit circuits. The corresponding Gaussian unitary $\tilde{\mathcal U}$ for the approximate implementation retains high output fidelity $|\langleψ|\mathcal U^\dagger \tilde{\mathcal U}|ψ\rangle|^2$ for pure states $|ψ\rangle$ with constrained expected photon-number.

quant-pharXiv:2604.14277Apr 17, 20260 citations

Understanding the role of entanglement in quantum computing

Benoît Vermersch

Sep 1, 20220 citations

Entanglement-assisted logical Bell state measurement with linear optics

Ji Qi, Chang‐Qi Yu, Rui‐Yang Yuan +2 more

Optics & Laser TechnologyJun 25, 20255 citations

Linear-Optical Fusion Boosted by High-Dimensional Entanglement

Tomohiro Yamazaki, Koji Azuma

We propose a quantum measurement that probabilistically projects a pair of qudits of dimension d onto a Bell state in a two-qubit subspace. It can be implemented using linear-optical circuits with the success probabilities of 1-d^{-1} without ancilla photons and 1-d^{-(k+1)} with 2(2^{k}-1) ancilla photons. It allows us to entangle two independently prepared high-dimensional entangled states two dimensionally with higher success probabilities than ones of linear-optical fusion gates on qubits. As an application, we propose a fast quantum repeater protocol with three-qudit GHZ states and quantum memories.We propose a quantum measurement that probabilistically projects a pair of qudits of dimension d onto a Bell state in a two-qubit subspace. It can be implemented using linear-optical circuits with the success probabilities of 1-d^{-1} without ancilla photons and 1-d^{-(k+1)} with 2(2^{k}-1) ancilla photons. It allows us to entangle two independently prepared high-dimensional entangled states two dimensionally with higher success probabilities than ones of linear-optical fusion gates on qubits. As an application, we propose a fast quantum repeater protocol with three-qudit GHZ states and quantum memories.

arXiv:2407.10893Physical Review LettersMay 20, 20256 citations

n

modes equally squeezed. For random brickwork circuits, we show that entanglement, as measured by the Rényi-2 entropy, grows diffusively as a function of the depth, in contrast to the linear growth for random qubit brickwork circuits. In the other direction, for arbitrary circuit geometries we prove bounds on depths which ensure the average-case subsystem entanglement reaches within a constant factor of the maximum value in all subsystems, and bounds which ensure closeness of the random linear optical unitary to a Haar random unitary in

L^2

Wasserstein distance. We also consider robust circuit complexity for random one-dimensional brickwall circuits, as measured by the minimum number of gates required in any circuit that approximately implements the linear optical unitary. Viewing this as a function of the number of modes and the circuit depth, we show the robust circuit complexity for random one-dimensional brickwall circuits scales at most diffusively in the depth with high probability, again in contrast to the linear scaling for certain random qubit circuits. The corresponding Gaussian unitary

\tilde{\mathcal U}

for the approximate implementation retains high output fidelity

|\langleψ|\mathcal U^\dagger \tilde{\mathcal U}|ψ\rangle|^2

for pure states

|ψ\rangle

with constrained expected photon-number.