Long-ranged gates in quantum computation architectures with limited connectivity

TL;DR

The paper addresses the challenge of implementing long-range gates on quantum processors with limited connectivity by proposing a measurement-assisted architecture that partitions qubits into data and auxiliary roles. It leverages a pre-generated 2D cluster state on the auxiliary qubits, transformable via single-qubit measurements into multiple long-range Bell states to perform parallel remote gates on data qubits, with a goal of achieving $O(\sqrt{n})$ parallel gates at constant overhead. It introduces concrete planar (and 3D) lattice schemes, the zipper entanglement-preserving method for Bell-pair generation, and remote multi-qubit gates including $\exp(-i\alpha Z^{\otimes m})$ and Clifford circuits, along with fidelity analyses under depolarizing noise. The work contrasts this hybrid gate-and-measurement approach with MBQC and sequential gate routing, highlighting platform independence, resource-state reuse, and potential improvements in scalability and flexibility for superconducting and other architectures. Overall, it provides a versatile blueprint for scalable, parallel long-range operations using only nearest-neighbor interactions and mid-circuit measurements, with practical implications for a wide range of quantum hardware implementations.

Abstract

We propose a quantum computation architecture based on geometries with nearest-neighbor interactions, including e.g. planar structures. We show how to efficiently split the role of qubits into data and entanglement-generation qubits. Multipartite entangled states, e.g. 2D cluster states, are generated among the latter, and flexibly transformed via mid-circuit measurements to multiple, long-ranged Bell states, which are used to perform several two-qubit gates in parallel on data qubits. We introduce planar architectures with $n$ data and $n$ auxiliary qubits that allow one to perform $O(\sqrt n)$ long-ranged two-qubit gates simultaneously, with only one round of nearest neighbor gates and one round of mid-circuit measurements. We also show that our approach is applicable in existing superconducting quantum computation architectures, with only a constant overhead.

Figures (7)

• Figure 1: Rectangular lattice with open leaves: (a) shows the connectivity pattern, and the separation into data qubits (green) and auxiliary qubits (red). Multipartite entanglement (indicated by dashed lines) in the form of a 2D cluster state is generated between auxiliary qubits (red) using only nearest-neighbor gates (see (b)), and manipulated by means of suitable measurements using the zipper scheme to generate multiple Bell pairs (c). The Bell pairs are used to implement multiple long-ranged two-qubit CZ gates on data qubits (green).
• Figure 2: (a) Zipper scheme to generate entanglement among a diagonal path by performing $X$-measurements on a 2D cluster state. The remaining entanglement structure, indicated by red dotted lines, closes over the hole. This can be checked by applying the rule for $X$-measurements sequentially on qubits among the path, with the remaining neighboring vertex chosen as special neighbor. (b) Second Bell pair is generated from the remaining structure, where the connecting pathes cross in the original 2D lattice. Around end-nodes, some qubits need to be measured in $Z$ to disconnect the Bell pair from the remaining state.
• Figure 3: Triangle-square lattice: (a) shows the connectivity pattern and the separation into data qubits (green) and auxiliary qubits (red). Multipartite entanglement (indicated by dashed lines) in the form of a 2D cluster state is generated between auxiliary qubits (red) (see (b)), and manipulated by means of suitable measurements using the zipper scheme to generate multiple Bell pairs (c). The Bell pairs are used to implement multiple two-qubit CZ gates on data qubits (green).
• Figure 4: Decorated honeycomb lattice: (a) shows the connectivity pattern corresponding to superconducting quantum processors (IBMQ). The qubits are separated into auxiliary qubits for entanglement generation (red, original honeycomb lattice), data qubits (green) and ancilla qubits (blue) to assist in the entanglement generation, both corresponding to decoration qubits of the lattice. Entanglement (indicated by dashed lines) in the form of a 2D cluster state is generated between auxiliary qubits (red) (see (b)), and manipulated by means of suitable measurements using the zipper scheme to generate multiple Bell pairs (c). The Bell pairs are used to implement multiple two-qubit CZ gates on data qubits (green).
• Figure 5: Required steps to generate a 2D cluster state among the auxiliary qubits (red). The following operations are performed (where the auxiliary qubits 2, 4, 6, 8, 4’ and 6’ and the ancilla qubits 5 and 5’ are initially prepared in the state $|+\rangle$, and qubits 4',5',6' are actually also part of the next block, where the same sequence of operations is performed (and hence 4'-6' are entangled)). Step 1: Entangle qubits 4 and 5, entangle qubits 5 and 6, SWAP qubits 2 and 3, and SWAP qubits 7 and 8. Step 2: measure qubit 5 in the $Y$ basis, which results in qubits 4 and 6 being entangled; also, SWAP qubits 2 and 4 and SWAP qubits 6 and 8. Step 3: entangle qubits 2 and 4, entangle qubits 6 and 8, entangle qubits 2 and 5 and entangle qubits 5 and 8. Step 4: measure qubit 5 in the $Y$ basis, which results in qubits 2 and 8 being entangled; also, SWAP qubits 2 and 4 and SWAP qubits 6 and 8. Step 5: SWAP qubits 2 and 3, SWAP qubits 7 and 8, SWAP qubits 1 and 4’ and SWAP qubits 9 and 6’. Step 6: entangle qubits 2 and 4’ and entangle qubits 8 and 6’. Step 7: SWAP qubits 1 and 4’ and SWAP qubits 9 and 6’. In the preceding steps, the operation “Entangle qubits a and b” means that a CZ gate is applied to the qubits in question. Further, “SWAP qubits a and b” means that a SWAP gate is applied. After performing steps 1 through 6 on all plaquettes, a 2D cluster state is prepared on the auxiliary qubits, as illustrated in Fig. \ref{['Figure_decorated_honexcomb_lattice']}(b).