Permutation-invariant codes encoding more than one qubit

A permutation-invariant code on m qubits is a subspace of the symmetric subspace of the m qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading order spontaneous decay errors. To prove the result, we use elementary number theory with prior theory on permutation invariant codes and quantum error correction.Comment: 4 pages, minor change

Post hoc verification of quantum computation

With recent progress on experimental quantum information processing, an important question has arisen as to whether it is possible to verify arbitrary computation performed on a quantum processor. A number of protocols have been proposed to achieve this goal, however all are interactive in nature, requiring that the computation be performed in an interactive manner with back and forth communication between the verifier and one or more provers. Here we propose two methods for verifying quantum computation in a non-interactive manner based on recent progress in the understanding of the local Hamiltonian problem. Provided that the provers compute certain witnesses for the computation, this allows the result of a quantum computation to be verified after the fact, a property not seen in current verification protocols.Comment: 4 pages, 2 figure

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

Probabilistic growth of large entangled states with low error accumulation

The creation of complex entangled states, resources that enable quantum computation, can be achieved via simple 'probabilistic' operations which are individually likely to fail. However, typical proposals exploiting this idea carry a severe overhead in terms of the accumulation of errors. Here we describe an method that can rapidly generate large entangled states with an error accumulation that depends only logarithmically on the failure probability. We find that the approach may be practical for success rates in the sub-10% range, while ultimately becoming unfeasible at lower rates. The assumptions that we make, including parallelism and high connectivity, are appropriate for real systems including measurement-induced entanglement. This result therefore shows the feasibility for real devices based on such an approach.Comment: 5 pages, 3 figure

Distributed quantum computation with arbitrarily poor photon detection

In a distributed quantum computer scalability is accomplished by networking together many elementary nodes. Typically the network is optical and inter-node entanglement involves photon detection. In complex networks the entanglement fidelity may be degraded by the twin problems of photon loss and dark counts. Here we describe an entanglement protocol which can achieve high fidelity even when these issues are arbitrarily severe; indeed the method succeeds with finite probability even if the detectors are entirely removed from the network. An experimental demonstration should be possible with existing technologies.Comment: 5 pages, 4 fig

Quantum walks with encrypted data

In the setting of networked computation, data security can be a significant concern. Here we consider the problem of allowing a server to remotely manipulate client supplied data, in such a way that both the information obtained by the client about the server's operation and the information obtained by the server about the client's data are significantly limited. We present a protocol for achieving such functionality in two closely related models of restricted quantum computation -- the Boson sampling and quantum walk models. Due to the limited technological requirements of the Boson scattering model, small scale implementations of this technique are feasible with present-day technology.Comment: 4 pages, 2 figure