Towards practical secure delegated quantum computing with semi-classical light

TL;DR

This paper tackles the challenge of securely delegating quantum computations by enabling end-users with only semi-classical light to interact with a quantum server that provides spin-photon entanglement. It introduces a best-of-both-worlds SDQC protocol that is information-theoretically secure and composable within Abstract Cryptography, relying on phase-randomised weak coherent pulses and GHZ-based privacy amplification to protect the client's secret angles. The approach eliminates the need for photon-number QND measurements and deterministic photon-photon gates on the server, while also providing verifiability through tests, and it discusses concrete emission schemes and experimental feasibility. If realized, this framework offers a practical path toward secure, verifiable delegated quantum computing with readily available laser and emitter technologies, bridging theory and experiment for near-term quantum infrastructure.

Abstract

Secure Delegated Quantum Computation (SDQC) protocols are a vital piece of the future quantum information processing global architecture since they allow end-users to perform their valuable computations on remote quantum servers without fear that a malicious quantum service provider or an eavesdropper might acquire some information about their data or algorithm. They also allow end-users to check that their computation has been performed as they have specified it. However, existing protocols all have drawbacks that limit their usage in the real world. Most require the client to either operate a single-qubit source or perform single-qubit measurements, thus requiring them to still have some quantum technological capabilities albeit restricted, or require the server to perform operations which are hard to implement on real hardware (e.g isolate single photons from laser pulses and polarisation-preserving photon-number quantum non-demolition measurements). Others remove the need for quantum communications entirely but this comes at a cost in terms of security guarantees and memory overhead on the server's side. We present an SDQC protocol which drastically reduces the technological requirements of both the client and the server while providing information-theoretic composable security. More precisely, the client only manipulates an attenuated laser pulse, while the server only handles interacting quantum emitters with a structure capable of generating spin-photon entanglement. The quantum emitter acts as both a converter from coherent laser pulses to polarisation-encoded qubits and an entanglement generator. Such devices have recently been used to demonstrate the largest entangled photonic state to date, thus hinting at the readiness of our protocol for experimental implementations.

Figures (15)

• Figure 1: Typical client-server configuration where a limited client delegates a quantum computation to a quantum server. Clients might have a limited quantum capability e.g. the ability to send single qubits [left] or entirely classical channels [right]. In this work we focus on a hybrid proposal where clients have a semi-classical channels [centre] meaning that the client is able to send a coherent state.
• Figure 2: Hardware setup for performing three delegated computation protocols. The operations in the blue dashed boxes are performed by the client while the server handles those in the pink dashed boxes. Red, yellow, and blue elements corresponds to operations that have a high, moderate, and low technological requirements respectively. In all three cases the client classically sends measurement instructions to the server and recovers the outcome. Top: UBQC protocol from Ref. Broadbent2010. Middle: BDQC protocol from Ref. Dunjko2012. Bottom: our SDQC protocol.
• Figure 3: A cluster state of $n = 3$ rows and $m = 4$ columns. Each circle represents a qubit in the $\ket{+}$ state and each edge corresponds to the application of a $\mathsf{CZ}$ operator between adjacent qubits.
• Figure 4: Energy level structure of a quantum emitter suitable for our BDQC protocol with semi-classical light communications, such as a negatively-charged quantum dot.
• Figure 5: Basic linear cluster generation process. Starting from an appropriate quantum emitter in the $\ket{+}_{qe}$ state (purple square), a Bell state $\ket{\Psi}$ is created via emission of a photon (purple dot) and then transformed into a cluster state. The middle circle containing two elements represents the Bell state as a redundantly-encoded $\ket{+}$ state.

Theorems & Definitions (25)

• Theorem 1: Blind state preparation from weak coherent pulses, informal
• Theorem 2: Blind Delegated Quantum Computation (BDQC) from weak coherent pulses, informal
• Theorem 3: Secure Delegated Quantum Computation from weak coherent pulses, informal
• Theorem 4: AC security of Protocol \ref{['prot:graph-rsp']}
• Theorem 5: AC security of Protocol \ref{['prot:ghz-gadget']}
• Theorem 6: BDQC with semi-classical client
• Theorem 7: SDQC with semi-classical client
• Definition 1: Statistical indistinguishability of resources
• Definition 2: Statistical construction of resources
• Theorem 8: General composition of resources