A Quantum Gate Architecture via Teleportation and Entanglement

TL;DR

QGATE presents a universal quantum computing architecture that fuses measurement-based quantum computing with circuit-model entanglement generation, using Clifford operations, QGATE ancillas, and arbitrary-angle single-qubit measurements to drive unitary evolution on a data-qubit register. It provides two core strategies for Hamiltonian simulation: (i) evolutions generated by Pauli strings, via CP_m entanglement and ancilla rotations, and (ii) direct handling of arbitrary sparse matrices using a fan-out/parity approach to implement controlled rotations, supplemented by efficient entanglement-graph techniques. The approach is demonstrated through quantum chemistry and computational fluid dynamics examples, with a photonic architecture featuring foliated rotated surface codes and fault-tolerant logical qubits; error thresholds around 10% for intra/inter-layer fusion and up to ≈26% under optimistic intra-layer QE entanglement are reported, depending on entanglement strategies. The work also shows how non-Clifford operations can be managed via magic-state-assisted gate teleportation, and discusses practicalities for implementing QGATE with deterministic photon emitters and photonic fusion, outlining a path toward scalable, fault-tolerant photonic quantum computation.

Abstract

We present a universal quantum computing architecture which combines the measurement-driven aspect of MBQC with the circuit model's algorithm dependent generation of qubit entanglement. Our architecture, which we call QGATE, is tailored for discrete-variable photonic quantum computers with deterministic photon sources capable of generating 1D entangled photonic states. QGATE achieves universal quantum computing on a logical data qubit register via the implementation of Clifford operations, QGATE ancilla, and arbitrary angle single-qubit measurements. We realise unitary evolutions defined by multi-qubit Pauli strings via the generation of entanglement between a sub-set of logical qubits and a mutual QGATE ancilla qubit. Measurement of the QGATE ancilla in the appropriate basis then implements a given term of the desired unitary operation. This enables QGATE to both directly perform Hamiltonian evolutions in terms of a series of multi-qubit Pauli operators, in terms of projectors for an arbitrary sparse Hamiltonian, or realise multi-controlled gates enabling direct translation of circuit models to QGATE. We consider examples inspired by quantum chemistry and computational fluid dynamics. We propose an example photonic implementation of QGATE and calculate thresholds of $10.36\pm0.02\%$ or $25.98\pm0.28\%$ on the photonic loss for logical qubits constructed from foliated rotated surface codes, dependent on the deployment of intra-layer or inter-layer fusion respectively.

Figures (14)

• Figure 1: An overview of the elements required to implement QGATE. Entangling gates generate entanglement between logical and ancilla qubits. Single qubit rotations applied to the ancilla qubits before measurement in the computational basis apply single- and multi-qubit unitary evolutions to the logical qubits. Single-qubit gates applied to the logical qubits can be realised without using ancilla qubits.
• Figure 2: An entanglement graph illustrating how a single gate ancilla qubit (circle) implements a logical gate between an arbitrary number of logical qubits (squares). Solid lines indicate a CZ gate acting between the two qubits while a dashed line indicates a CX gate acting between the two qubits. Performing an X rotation on ancilla over angle $\varphi$ and measuring in the computational basis applies the unitary $\exp{i\varphi (Z\mathbb{I}XZX)/2}$ to the logical qubits.
• Figure 3: The calculated fidelity $\mathcal{F} = \abs{\braket{\phi}{\psi}}^2$ of the state returned by QGATE $\ket{\psi}$ to that return by the exact application of the two-qubit molecular Hydrogen unitary operator $\ket{\phi}$ as a function of the Trotter number $r$. The molecular Hydrogen unitary is defined by the Hamiltonian $H=\alpha I_1I_2 + \beta Z_1I_2 + \gamma I_1Z_2 + \delta Z_1Z_2 + \zeta X_1X_2$ganzhorn2019gateabu2021quantum and is applied to the initial state $(\ket{01}+\ket{10})/\sqrt{2}$. We set $\alpha=-0.96028$, $\beta=0.08240$, $\gamma=-0.08240$, $\delta=-0.00226$, and $\zeta=0.24801$ for a bond length $R=1.8$ Å ganzhorn2019gate.
• Figure 4: Entanglement graphs showing two examples of entanglement transfer between ancilla qubits. (a) Applying a CX gate (dotted line) between two ancillas (orange circles) after the generation of logical-ancilla entanglement results in a state that is equivalent to (b) copying the neighbourhood of the CX target ancilla qubit to the CX control ancilla qubit. (c,d) Entanglement transfer can be used to reduce physical connectivity requirements by copying entanglement from many ancilla qubits with limited logical-ancilla connectivity to a single ancilla that then implements the complete unitary defined by the product of the separate Pauli strings.
• Figure 5: Entanglement graphs illustrating how entanglement via $CZ$ operations (solid lines) between ancilla qubits (orange circles) and logical qubits (purple squares) can be used to implement (a) a controlled $Z$-rotation $CR_Z(\varphi)$ gate, (b) a controlled-phase $CP(\varphi)$ gate or (c) Toffoli-Z $CCZ$ gate (adapted from browne2016one) between potentially distant logical qubits. Labels on the ancilla qubits indicate the unitary operations they individually apply to the logical when measured.