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Universal Blind Quantum Computation with Recursive Rotation Gates

Mohit Joshi, Manoj Kumar Mishra, S. Karthikeyan

TL;DR

The paper extends blind quantum computation by enabling universal blindness for parametric gates via recursive decryption of $R_z(θ)$. It introduces a four-qubit resource state $J(ε)=H_1CZ_{2,3}R_z(υ)_4$ with $υ$ independent of the computation angle, ensuring blindness while supporting universal computation. The approach reduces interactivity and obviates the need to decompose parametric gates into non-parametric sets, achieving favorable communication round complexity $O((n_p+n_{np})\log^{2}(π/ε))$ and offering a clear cross-over point where parametric-rich algorithms benefit over non-parametric baselines. This work provides a practical path toward secure, variational, hybrid quantum-classical workflows in the NISQ era.

Abstract

Blind Quantum Computation lets a limited-capability client delegate its complex computation to a remote server without revealing its data or computation. Several such protocols have been proposed under varied quantum computing models. However, these protocols either rely on highly entangled resource states (in measurement-based models) or are based on non-parametric resource sets (in circuit-based models). These restrictions hinder the practical applicability of such an algorithm in the NISQ era, especially concerning the hybrid quantum-classical infrastructure, which depends on parametric gates. We present a protocol for universal blind quantum computation based on recursive decryption of parametric rotation gates, which does not require a highly entangled state at the server side and substantially reduces the communication rounds required for practical prototyping of secure variational algorithms.

Universal Blind Quantum Computation with Recursive Rotation Gates

TL;DR

The paper extends blind quantum computation by enabling universal blindness for parametric gates via recursive decryption of . It introduces a four-qubit resource state with independent of the computation angle, ensuring blindness while supporting universal computation. The approach reduces interactivity and obviates the need to decompose parametric gates into non-parametric sets, achieving favorable communication round complexity and offering a clear cross-over point where parametric-rich algorithms benefit over non-parametric baselines. This work provides a practical path toward secure, variational, hybrid quantum-classical workflows in the NISQ era.

Abstract

Blind Quantum Computation lets a limited-capability client delegate its complex computation to a remote server without revealing its data or computation. Several such protocols have been proposed under varied quantum computing models. However, these protocols either rely on highly entangled resource states (in measurement-based models) or are based on non-parametric resource sets (in circuit-based models). These restrictions hinder the practical applicability of such an algorithm in the NISQ era, especially concerning the hybrid quantum-classical infrastructure, which depends on parametric gates. We present a protocol for universal blind quantum computation based on recursive decryption of parametric rotation gates, which does not require a highly entangled state at the server side and substantially reduces the communication rounds required for practical prototyping of secure variational algorithms.

Paper Structure

This paper contains 11 sections, 1 theorem, 49 equations, 4 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Decryption of arbitrary $R_z$ gate
  4. Proposed Protocol
  5. Blind Decryption of $R_z(\theta)$
  6. Universal Blind Quantum Computation
  7. Comparative Analysis
  8. Conclusion
  9. $\upsilon$ is independent of $\theta$
  10. Decryption of arbitrary $z$ gate
  11. Equivalence of $Swap$ circuit

Key Result

Theorem B.1

The decryption of arbitrary $R_z(\eta)$ where $\eta = (-1)^q \theta$ is dependent on $R_z(2\theta)$, i.e., $R_z(\eta)Z^bX^a = R^{a \oplus q}_z(2\theta)X^aZ^bR_z(\eta)$.

Figures (4)

  • Figure 1: Resource set $J(\epsilon) =H_1CZ_{2,3}R_z(\upsilon)_4$ for Universal Blind Quantum Computation, where (a) represents recursive decryption of $R_z(\upsilon)$ using representation $D(R_z(\pi/2^m))$$\forall m\in \{1,\cdots,M\}$. (b) represents the exact procedure of recursive decryption using encryption keys $a_i,b_i \in_r \{0,1\}$$\forall i \in \{1, \cdots, m\}$ and boolean variables $s_m$ and $q_m$ such that $p_m = (-1)^{q_m}s_m$ for blind decryption of $R_z(\theta) = R_z(p_o\pi)\prod_{m=1}^M R_z(p_m\pi/2^m)$.
  • Figure 2: Comparison of communication cost between protocols using only parametric gates $C_p$ using Solovay-Kitaev decomposition vs the proposed protocol $C_{np}$ that can inherently decrypt non-parametric gates without prior decomposition. Here $\epsilon=10^{-2}$.
  • Figure 3: The plot of critical ratio $c$ needed for the proposed protocol to require fewer communication rounds than the protocols based on parametric resources only with respect to the precision of computation $\epsilon$.
  • Figure 4: Equivalent circuit without Swap gate for circuit given in Fig. \ref{['fig:ubqc_resource_set']}(b) using identies associated with $Swap$ gate. The recursive decryption is equivalent to $R_z((-1)^{q_m}\pi/2^m)^{s_m}$ using Eq. (\ref{['eq:minus_rz_theorem']}).

Theorems & Definitions (2)

  • Theorem B.1
  • proof