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Abstract:

Blind quantum computation (BQC) allows clients with limited quantum capabilities to delegate computational tasks to remote quantum servers while keeping the privacy of their data. However, existing BQC protocols often fail to balance resource consumption and practical feasibility, which is particularly significant in the noisy intermediate-scale quantum era. In this paper, we propose a practical BQC model based on the parity quantum computing framework. It requires the server to perform operations only on adjacent qubits and eliminates the need for additional SWAP gates when two-qubit gates should be applied to non-adjacent qubits, greatly facilitating the physical implementation on real quantum devices. Furthermore, we prove that the proposed BQC model ensures the privacy of client’s information and satisfies the property of verifiability which enables clients to identify dishonest servers. Finally, a detailed example is given and simulated on the IBM’s quantum platform to demonstrate its feasibility.

Abstract:

Estimating the eigenstate properties of quantum systems is a long-standing, challenging problem for both classical and quantum computing. Existing universal quantum algorithms typically rely on ideal and efficient query models (e.g., time evolution operator or block encoding of the Hamiltonian), which, however, become suboptimal for actual implementation at the quantum circuit level. Here, we present a full-stack design of quantum algorithms for estimating the eigenenergy and eigenstate properties, which can achieve high precision and good scaling with system size. The gate complexity per circuit for estimating generic Hamiltonians' eigenstate properties is [Formula: see text], which has a logarithmic dependence on the inverse precision ε. For lattice Hamiltonians, the circuit depth of our design achieves near-optimal system-size scaling, even with local qubit connectivity. Our full-stack algorithm has low overhead in circuit compilation, which thus results in a small actual gate count (cnot and non-Clifford gates) for lattice and molecular problems compared to advanced eigenstate algorithms. The algorithm is implemented on IBM quantum devices using up to 2000 two-qubit gates and 20,000 single-qubit gates and achieves high-precision eigenenergy estimation for Heisenberg-type Hamiltonians, demonstrating its noise robustness.