Universal Blind Quantum Computation

Abstract

We present a protocol which allows a client to have a server carry out a quantum computation for her such that the client's inputs, outputs and computation remain perfectly private, and where she does not require any quantum computational power or memory. The client only needs to be able to prepare single qubits randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. Our protocol is interactive: after the initial preparation of quantum states, the client and server use two-way classical communication which enables the client to drive the computation, giving single-qubit measurement instructions to the server, depending on previous measurement outcomes. Our protocol works for inputs and outputs that are either classical or quantum. We give an authentication protocol that allows the client to detect an interfering server; our scheme can also be made fault-tolerant.We also generalize our result to the setting of a purely classical client who communicates classically with two non-communicating entangled servers, in order to perform a blind quantum computation. By incorporating the authentication protocol, we show that any problem in BQP has an entangled two-prover interactive proof with a purely classical verifier.Our protocol is the first universal scheme which detects a cheating server, as well as the first protocol which does not require any quantum computation whatsoever on the client's side. The novelty of our approach is in using the unique features of measurementbased quantum computing which allows us to clearly distinguish between the quantum and classical aspects of a quantum computation.

Quantum computing on encrypted data

“…While some of these schemes, in principle, can be used to accomplish similar outcomes as our protocol, they can lead to very different client-server relationships in practice. For example, a recent experiment used the measurement-based model of quantum computing to demonstrate the complementary problem of hiding from a server the circuit that is to be performed 7,8 . This method, known as blind quantum computing, can be extended to compute on encrypted data, but would require more than eight times as many auxiliary qubits and significantly more rounds of classical communication.…”

“…There have been several novel approaches to this problem, including hiding a circuit from the remote quantum server 7,8 , computing on encrypted quantum data using multiple rounds and bits of quantum communication [9][10][11][12] and sophisticated methods that provide an additional verification mechanism [10][11][12] (see Table 1). While some of these schemes, in principle, can be used to accomplish similar outcomes as our protocol, they can lead to very different client-server relationships in practice.…”

“…The overhead in quantum resources required to compute on encrypted quantum data is so low (only one auxiliary qubit per non-Clifford gate) that it will be straightforward for future quantum servers to incorporate our protocol in their design, dramatically enhancing the security of client-server quantum computing; our protocol has even less overhead than the best classical fully homomorphic encryption scheme, and provides information-theoretic (as opposed to just computational) security. This method for computing on encrypted quantum data, combined with the techniques developed for quantum circuit hiding 7,8 , form a complete security system that will enable secure distributed quantum computing to take place, ensuring the privacy and security of future quantum networks.…”

Quantum Walks with Encrypted Data

“…Universal classical homomorphic encryption was only first discovered in 2009 [6] and subsequently simplified [7]. Closely related is blind computing, where Alice possesses both the data and the algorithm, and Bob owns the computer [8][9][10], as is the quantum private queries protocol [11], which is used to query a database while keeping the query secret.In this paper we describe a technique for solving the above problem, and hence achieving a limited quantum homomorphic encryption using the Boson sampling and multi-walker quantum walk models for quantum computation.The Boson sampling model -A first protocol for universal LOQC was introduced by Knill, Laflamme & Milburn (KLM) [4]. While universal for quantum computation, their protocol is extremely demanding, requiring fast-feedforward and quantum memory, which are technologically challenging and well beyond the capabilities of present-day experiments.…”

“…Universal classical homomorphic encryption was only first discovered in 2009 [6] and subsequently simplified [7]. Closely related is blind computing, where Alice possesses both the data and the algorithm, and Bob owns the computer [8][9][10], as is the quantum private queries protocol [11], which is used to query a database while keeping the query secret.…”