The aim of this survey is to provide the reader with an overview about the main challenges and open problems arising with distributed quantum computing from a computer and communications engineering p

The gap

Consensus across the literature

Supporting evidence — 3 representative gaps

• Private quantum computation: an introduction to blind quantum computing and related protocols (2017) · doi

  Given recent developments in quantum technologies and the longstanding paradigm in classical computing of delegating computationally intensive tasks to shared systems, the emerging interest in delegated quantum computation is both understand- able and timely. While the progress discussed in this review illustrates the potential of BQC and related protocols, the field is still in its infancy, with new results coming on a regular basis but with many open questions still remaining. Perhaps the most prominent open question is that of whether or not blind or verifiable computation is possible with a single server and a completely classical client. In this setting, even when multiple non- entangled non-communicating servers are allowed, the existence of secure protocols for blind and verifiable computation remains an open question. the precise relationship between blindness and verification is currently unresolved. In the context of homomorphic encryption, the existence of fully homomorphic quantum encryption under plausible computational assumptions remains open, despite the promising progress of Dulek et al.63 In the context of verification, the most significant challenges facing the field include the necessity to drastically reduce overhead and Indeed, the variety of sensitivity to noise of current device-independent verification protocols, and the development of methods to verify analogue quantum simulators and other special purpose devices. While some progress has been made on the question of verifying non- universal devices,93–96 much more progress in this direction is necessary to fully unlock the potential of such devices. Lastly it should be noted that progress to date has only scratched the future quantum surface of networks may unlock. Recent developments, in terms of multi- user blind computation97 and publicly verifiable quantum computation,98 together with established results on secure multi-party quantum computation28, 99, 100 give some indication of the potential for new secure quantum computing protocols beyond the two party setting. Given these open questions, there is the potential for significant theoretical advance in the coming years. Harnessing the latest advances in experimental capabilities to go beyond the current generation of proof-of-principle experiments is also likely to be an important future direction. functionality that ACKNOWLEDGEMENTS

  Keywords: quantum computation veri progress open able potential protocols question blind secure cation devices given recent
• Verification of Quantum Computation: An Overview of Existing Approaches (2018) · doi

  5.1 Sub-Universal Protocols So far we have presented protocols for the verification of universal quantum compu- tations, i.e. protocols in which the provers are assumed to be BQP machines. In the near future, however, quantum computers might be more limited in terms of the type of computations that they can perform. Examples of this include the class of so-called instantaneous quantum computations, denoted IQP, boson sampling or the one-pure qubit model of quantum computation [1, 2, 84]. While not universal, these examples are still highly relevant since, assuming some plausible complexity theoretic conjec- tures hold, they could solve certain problems or sample from certain distributions that are intractable for classical computers. One is therefore faced with the question of how to verify the correctness of outcomes resulting from these models. In particular, when considering an interactive protocol, the prover should be restricted to the corre- sponding sub-universal class of problems and yet still be able to prove statements to a computationally limited verifier. We will see that many of the considered approaches are adapted versions of the VUBQC protocol from Section 2.2. It should be noted, however, that the protocols themselves are not direct applications of VUBQC. In each instance, the protocol was constructed so as to adhere to the constraints of the model. The first sub-universal verification protocol is for the one-pure (or one-clean) qubit model. A machine of this type takes as input a state of limited purity (for instance, a system comprising of the totally mixed state and a small number of single qubit pure states), and is able to coherently apply quantum gates. The model was consid- ered in order to reflect the state of a quantum computer with noisy storage. In [85], Kapourniotis, Kashefi and Datta introduced a verification protocol for this model by adapting VUBQC to the one-pure qubit setting. The verifier still prepares indi- vidual pure qubits, as in the original VUBQC protocol, however the prover holds a mixed state of limited purity at all times.46 Additionally, the prover can inject or remove pure qubits from his state, during the computation, as long as it does not increase the total purity of the state. The resulting protocol has an inverse polyno- mial completeness-soundness gap. However, unlike the universal protocols we have reviewed, the constraints on the prover’s state do not allow for the protocol to be repeated. This means that the completeness-soundness gap cannot be boosted through repetition. Another model, for which verification protocols have been proposed, is that of instantaneous quantum computations, or IQP [2, 86]. An IQP machine is one which can only perform unitary operations that are diagonal in the X basis and therefore commute with each other. The name “instantaneous quantum computation” illus- trates that there is no temporal structure to the quantum dynamics [2]. Additionally, the machine is restricted to measurements in the computational basis. It is impor- tant to mention that IQP does not represent a decision class, like BQP, but rather a 46The purity of a d-qubit state, ρ, is quantified by the purity parameter defined in [85] as: π(ρ) = log(T r(ρ2)) + d.

  Keywords: quantum protocol state universal protocols pure model qubit purity verification limited prover vubqc computations class
• Distributed quantum computing: A survey (2024) · doi

  The aim of this survey is to provide the reader with an overview about the main challenges and open problems arising with distributed quantum computing from a computer and communications engineering perspective.

  Keywords: survey provide reader overview main challenges open problems arising distributed quantum computing computer communications engineering