Delegating Multi-Party Quantum Computations vs. Dishonest Majority in\n Two Quantum Rounds

Multi-Party Quantum Computation (MPQC) has attracted a lot of attention as a\npotential killer-app for quantum networks through it's ability to preserve\nprivacy and integrity of the highly valuable computations they would enable.\nContributing to the latest challenges in this field, we present a composable\nprotocol achieving blindness and verifiability even in the case of a single\nhonest client. The security of our protocol is reduced, in an\ninformation-theoretically secure way, to that of a classical composable Secure\nMulti-Party Computation (SMPC) used to coordinate the various parties. Our\nscheme thus provides a statistically secure upgrade of such classical scheme to\na quantum one with the same level of security.\n In addition, (i) the clients can delegate their computation to a powerful\nfully fault-tolerant server and only need to perform single qubit operations to\nunlock the full potential of multi-party quantum computation; (ii) the amount\nof quantum communication with the server is reduced to sending quantum states\nat the beginning of the computation and receiving the output states at the end,\nwhich is optimal and removes the need for interactive quantum communication;\nand (iii) it has a low constant multiplicative qubit overhead compared to the\nsingle-client delegated protocol it is built upon.\n The main technical ingredient of our paper is the bootstraping of the MPQC\nconstruction by Double Blind Quantum Computation, a new composable resource for\nblind multiparty quantum computation, that demonstrates the surprising fact\nthat the full protocol does not require verifiability of all components to\nachieve security.\n