# Techniques: Verification of Quantum Computations without Trusted Preparations or Measurements

## What the paper contributes (one paragraph)
The paper settles an open question in Secure Delegated Quantum Computing: whether universal quantum computations can be verified with information-theoretic security when the client trusts neither its state-preparation nor its measurement devices. The answer is yes. The authors give a modular, composable reduction that turns existing verification schemes into protocols relying only on trusted gates. The core building block is Remote State Preparation (RSP) implemented without trusted preparation. For BQP computations, RSP of single-plane states reduces to trusted single-qubit Z-rotations and bit flips, with no degradation of the security error and no server overhead. For arbitrary computations with quantum output, RSP of any pure state reduces to trusted single-qubit unitaries and a number of CNOT gates scaling linearly in the security parameter and logarithmically in the computation size. All resources lift to the multi-party setting, generalising the results to Delegated Quantum Secure Multi-Party Computation. Security holds against unbounded adversaries.

## Techniques offered
- **Information-theoretic verification of delegated quantum computation without trusted preparations or measurements** - Converts known Secure Delegated Quantum Computing verification schemes into protocols where the client trusts only gates, certifying that the server either computes correctly or the client aborts.
  - guarantee: composable (Abstract Cryptography) information-theoretic soundness against unbounded adversaries, with at most negligible degradation of the security error versus protocols with trusted preparations.
  - quote: "In this paper, we settle this question in the affirmative by presenting a modular, composable, and efficient way to turn known verification schemes into protocols that rely only on trusted gates."
- **Verifiable Remote State Preparation (RSP) without trusted preparation** - Securely prepares secret states from a fixed ensemble on the server using only trusted client unitaries (single-qubit Z-rotations and bit flips for single-plane states; single-qubit unitaries plus CNOT gates for arbitrary states), supplying a drop-in replacement for the trusted-preparation subroutine of SDQC protocols.
  - guarantee: composable secret-independence (blindness) plus verifiability, so any server deviation maps to a state-independent deviation applied after preparation; no degradation of security error in the single-plane case.
  - quote: "We show that RSP can be implemented securely without trusting the qubit preparation, if the client has access to trusted unitary transformations."
- **Generalisation to Delegated Quantum Secure Multi-Party Computation** - Lifts every resource defined in the paper to a collaborative multi-client version, supplying verifiable joint delegation of arbitrary quantum computations to an untrusted server.
  - guarantee: verifiability and input/output privacy from the perspective of any single non-deviating client against arbitrary coalitions of malicious parties.
  - quote: "This allows us to generalise all our results to the realm of Delegated Quantum Secure Multi-Party Computations in which multiple clients want to jointly delegate a computation to an untrusted server without revealing their inputs or outputs to each other."

## Where it could apply
- Target primitive(s): sampling, and arbitrary BQP computations with classical or quantum output delegated to a remote server; not tied to a specific variational or simulation primitive.
- Target application group(s): platforms_tooling, quantum networking and distributed quantum computing.
- Code family / hardware assumptions: hardware-agnostic at the protocol level; photonic / dual-rail implementation highlighted (phase-shifters and beam-splitters for single-plane rotations), assuming fixed input dimension (e.g. single photons).

## Caveats
The paper is a cryptographic protocol contribution rather than an error-correction, decoding, or benchmarking result, so what it supplies is verification, blind or delegated computation, and secure multi-party computation rather than anything code-specific. The second (arbitrary-state) construction requires the verifier to perform trusted multi-qubit Clifford gates on a register whose size grows with the security parameter, though it stays independent of the computation size. All resources accepting a quantum input fix its dimension as an implicit assumption that must be guaranteed separately. The Selective-NOT variant from single-qubit unitaries alone is weaker and is not known to suffice for verifying arbitrary computations. Full access to the LaTeX source was available; no paywall.