How to Verify a Quantum Computation

We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive proof systems. Specifically, we show that any language in $\mathsf{BQP}$ has a quantum interactive proof system with a polynomial-time classical verifier (who can also prepare random single-qubit pure states), and a quantum polynomial-time prover. Here, soundness is unconditional--i.e., it holds even for computationally unbounded provers. Compared to prior work achieving similar results, our technique does not require the encoding of the input or of the computation; instead, we rely on encryption of the input (together with a method to perform computations on encrypted inputs), and show that the random choice between three types of input (defining a computational run, versus two types of test runs) suffices. Because the overhead is very low for each run (it is linear in the size of the circuit), this shows that verification could be achieved at minimal cost compared to performing the computation. As a proof technique, we use a reduction to an entanglement-based protocol; to the best of our knowledge, this is the first time this technique has been used in the context of verification of quantum computations, and it enables a relatively straightforward analysis.Comment: Published in Theory of Computing, Volume 14 (2018), Article 11; Received: October 3, 2016, Revised: October 27, 2017, Published: June 11, 201

Information-Theoretically Secure Voting Without an Honest Majority

We present three voting protocols with unconditional privacy and information-theoretic correctness, without assuming any bound on the number of corrupt voters or voting authorities. All protocols have polynomial complexity and require private channels and a simultaneous broadcast channel. Our first protocol is a basic voting scheme which allows voters to interact in order to compute the tally. Privacy of the ballot is unconditional, but any voter can cause the protocol to fail, in which case information about the tally may nevertheless transpire. Our second protocol introduces voting authorities which allow the implementation of the first protocol, while reducing the interaction and limiting it to be only between voters and authorities and among the authorities themselves. The simultaneous broadcast is also limited to the authorities. As long as a single authority is honest, the privacy is unconditional, however, a single corrupt authority or a single corrupt voter can cause the protocol to fail. Our final protocol provides a safeguard against corrupt voters by enabling a verification technique to allow the authorities to revoke incorrect votes. We also discuss the implementation of a simultaneous broadcast channel with the use of temporary computational assumptions, yielding versions of our protocols achieving everlasting security

Vector plotting as an indication of the approach to flutter

A binary flexure-torsion analysis was made to check theoretically a method for predicting flutter which depends on plotting vectorially the amplitudes of response relative to the exciting force and extracting the relevant damping rate. The results of this calculation are given in graphs both of the vector plots themselves and of the estimated damping rate against forward speed. The estimated damping rates are compared with calculated values. The method has the advantage that in a flight flutter test damping can be estimated from continuous excitation records: the method is an extension of the Kennedy and Pancu technique used in ground resonance testing

Entanglement swapping, light cones and elements of reality

Recently, a number of two-participant all-versus-nothing Bell experiments have been proposed. Here, we give local realistic explanations for these experiments. More precisely, we examine the scenario where a participant swaps his entanglement with two other participants and then is removed from the experiment; we also examine the scenario where two particles are in the same light cone, i.e. belong to a single participant. Our conclusion is that, in both cases, the proposed experiments are not convincing proofs against local realism.Comment: 10 pages, no figure, LHV models given explicitely, more explanation

Universal blind quantum computation

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 measurement-based quantum computing which allows us to clearly distinguish between the quantum and classical aspects of a quantum computation.Comment: 20 pages, 7 figures. This version contains detailed proofs of authentication and fault tolerance. It also contains protocols for quantum inputs and outputs and appendices not available in the published versio