Qubit-efficient embedding of parity-encoded Hamiltonians in quantum annealers

• URL: http://arxiv.org/abs/2603.28667v1
• Date: Mon, 30 Mar 2026 16:51:32 GMT
• Title: Qubit-efficient embedding of parity-encoded Hamiltonians in quantum annealers
• Abstract summary: We propose a qubit-efficient embedding scheme for parity-encoded Hamiltonians on quantum annealers.<n>Our embedding maps each spin to a two-qubit chain using systematic chain-assignment rules.<n>The number of required qubits per spin in the parity Hamiltonian is three, which is fewer than that for a known embedding scheme for the Pegasus graph.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Sourlas-Lechner-Hauke-Zoller (SLHZ) scheme for quantum annealing uses the parity to encode logical variables and has several advantages, but it has not been implemented for large-scale quantum annealers. If the SLHZ-based approach can be implemented on currently available quantum annealers, we can evaluate its performance. An efficient method to embed the parity-encoded model into the hardware graphs of available quantum annealers is one of the key elements for this approach. We propose a qubit-efficient embedding scheme for parity-encoded Hamiltonians on quantum annealers with the Zephyr connectivity. We give an explicit constructive embedding of the interaction graph of an intermediate Hamiltonian, which contains only one- and two-body interactions, into the Zephyr graph. Our embedding maps each spin to a two-qubit chain using systematic chain-assignment rules. Its validity is verified via the resulting chain-to-chain connectivity. Our embedding also offers practical flexibility. Chains assigned to ancillary spins allow reduction to a single physical qubit, leading to options to avoid inactive qubits. The number of required qubits per spin in the parity Hamiltonian is three, which is fewer than that for a known embedding scheme for the Pegasus graph.

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