Unifying communication paradigms in measurement-based delegated quantum computing

Abstract

Delegated quantum computing (DQC) allows clients with low quantum capabilities to outsource computations to a server hosting a quantum computer. This process is often envisioned within the measurement-based quantum computing framework, as it naturally facilitates blindness of inputs and computation. Hence, the overall process of setting up and conducting the computation encompasses a sequence of three stages: preparing the qubits, entangling the qubits to obtain the resource state, and measuring the qubits to run the computation. There are two primary approaches to distributing these stages between the client and the server that impose different constraints on cryptographic techniques and experimental implementations. In the prepare-and-send setting, the client prepares the qubits and sends them to the server, while in the receive-and-measure setting, the client receives the qubits from the server and measures them. Although these settings have been extensively studied independently, their interrelation and whether setting-dependent theoretical constraints are inevitable remain unclear. By implementing the key components of most DQC protocols in the respective missing setting, we provide a method to build prospective protocols in both settings simultaneously and to translate existing protocols from one setting into the other.

Figures (4)

• Figure 1: Visualization of the secure construction with $\I=\{A,B,C,D\}$ and $\Hi = \{A,B\}$.
• Figure 2: Visualization of $\S^{\rm blind}$. $\ell^{|\psi_C|}$ is the size of the register for the client's input $\psi_C$ (which they might have obtained from some third party), $\mathcal{E}$ is a completely positive trace-preserving (CPTP) map to the space of linear operators on $\C^{\ell^{|\psi_C|}}$, $\psi_S$ is a register of the server and $c$ denotes the server's behavior. If the server is honest, we assume a filter $\sharp_S$ which inputs $c=0$, ignores the received dimensionality of the client's state and inputs any CPTP map and register.
• Figure 3: Visualization of $\S^{\rm ver}$. $\ell^{|\psi_C|}$ is the size of the register for the client's input $\psi_C$ (which they might have obtained from some third party). If the server is honest, we assume a filter $\flat_S$ which inputs $c=0$ and ignores the received dimensionality of the client's state. The actual verification property is encoded into the behavior of the resource if $c=1$. Since $\ketbra{\bot}$ is orthogonal to the space of possible honest outputs, the client can easily learn whether the server cheated or not.
• Figure 4: The two measurement patterns on a two-colorable graph state. The figure is reproduced from Ref. HM15.

Theorems & Definitions (1)

• definition 1: Secure construction