We present a novel approach to cryptographically secure verification and benchmarking of quantum computing, demonstrating our approach on an ion-trap quantum computer. Unlike previous cryptographically secure verification protocols, which typically require quantum communication between client and server, our approach is implemented entirely on chip. This eliminates the need for a quantum capable client, and significantly enhances practicality. We perform tomography to justify the additionally required assumption that the noise is independent of the secret used to prepare the server's single-qubit states. We quantify the soundness error that may be caused by residual secret dependencies. We demonstrate our protocol on the 20-qubit Quantinuum H1-1 ion-trap quantum processing unit, using qubit measurements and resets to construct measurement patterns with up to 52 vertices. To our knowledge, these are the largest verified measurement-based quantum computations performed to date.
We present a novel approach to cryptographically secure verification and benchmarking of quantum computing, demonstrating our approach on an ion-trap quantum computer. Unlike previous cryptographically secure verification protocols, which typically require quantum communication between client and server, our approach is implemented entirely on chip. This eliminates the need for a quantum capable client, and significantly enhances practicality. We perform tomography to justify the additionally required assumption that the noise is independent of the secret used to prepare the server's single-qubit states. We quantify the soundness error that may be caused by residual secret dependencies. We demonstrate our protocol on the 20-qubit Quantinuum H1-1 ion-trap quantum processing unit, using qubit measurements and resets to construct measurement patterns with up to 52 vertices. To our knowledge, these are the largest verified measurement-based quantum computations performed to date.
Abstract Although quantum computers can perform a wide range of practically important tasks beyond the abilities of classical computers 1,2 , realizing this potential remains a challenge. An example is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy 3 . Certified randomness has many applications but is impossible to achieve solely by classical computation. Here we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the Internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations 4,5 : a client generates quantum ‘challenge’ circuits using a small randomness seed, sends them to an untrusted quantum server to execute and verifies the results of the server. We analyse the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of 1.1 × 10 18 floating-point operations per second across multiple supercomputers, we certify 71,313 bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of present-day quantum computers.
Abstract In blind quantum computing (BQC), a user with a simple client device can perform a quantum computation on a remote quantum server such that the server cannot gain knowledge about the computation. Here, we numerically investigate hardware requirements for verifiable BQC using an ion trap as server and a distant measurement-only client. While the client has no direct access to quantum-computing resources, it can remotely execute quantum programs on the server by measuring photons emitted by the trapped ion. We introduce a numerical model for trapped-ion quantum devices in NetSquid, a discrete-event simulator for quantum networks. Using this, we determine the minimal hardware requirements on a per-parameter basis to perform the verifiable BQC protocol. We benchmark these for a five-qubit linear graph state, with which any single-qubit rotation can be performed, where client and server are separated by 50 km. Current state-of-the-art ion traps satisfy the minimal requirements on a per-parameter basis, but all current imperfections combined make it impossible to perform the blind computation securely over 50 km using existing technology. Using a genetic algorithm, we determine the set of hardware parameters that minimises the total improvements required, finding directions along which to improve hardware to reach our threshold error probability that would enable experimental demonstration. In this way, we lay a path for the near-term experimental progress required to realise the implementation of verifiable BQC over a 50 km distance.
Verification protocols provide cryptographic guarantees that the outcome of a delegated quantum computation is correct, a key requirement for scalable and trustworthy quantum computing. A central assumption underlying these protocols is secret independence: the noise affecting state preparation must not depend on the classical secrets that specify the prepared states. In earlier protocols this assumption was enforced by the physical separation of client and server; in the recent on-chip setting it becomes a property of the hardware itself, and one that high-fidelity devices do not automatically satisfy. We first make the requirement quantitative, deriving a bound that shows how residual secret dependence limits the size of any verifiable computation within this framework. Motivated by this, we introduce a calibration framework that enforces secret independence through pulse-level quantum control, producing state preparations that are simultaneously high-fidelity and secret-independent. We assess its performance on a nitrogen-vacancy centre system via emulation, showing that it reduces the secret dependence of the preparations by more than an order of magnitude compared to standard optimal control, and that it is robust against detuning and drive-amplitude errors commonly encountered in experiment. The framework operates entirely at the calibration stage and is platform-agnostic, offering a practical pathway towards verifiable quantum computing at scale.
In order to guarantee the output of a quantum computation, we usually assume that the component devices are trusted. However, when the total computation process is large, it is not easy to guarantee the whole system when we have scaling effects, unexpected noise, or unaccounted for correlations between several subsystems. If we do not trust the measurement basis or the prepared entangled state, we do need to be worried about such uncertainties. To this end, we propose a self-guaranteed protocol for verification of quantum computation under the scheme of measurement-based quantum computation where no prior-trusted devices (measurement basis or entangled state) are needed. The approach we present enables the implementation of verifiable quantum computation using the measurement-based model in the context of a particular instance of delegated quantum computation where the server prepares the initial computational resource and sends it to the client, who drives the computation by single-qubit measurements. Applying self-testing procedures, we are able to verify the initial resource as well as the operation of the quantum devices and hence the computation itself. The overhead of our protocol scales with the size of the initial resource state to the power of 4 times the natural logarithm of the initial state's size.
How can a user with limited quantum resources verify the output of an untrusted, fully quantum server? This manuscript provides a conceptual synthesis of some recent developments toward answering this question under statistical (information-theoretic) security. Rather than duplicating the dense technical proofs of the underlying publications, our focus here is on the physical motivations, the structural connections between different protocols, and the path toward hardware-efficient implementation.
We begin by introducing a modular, composable framework that partitions verification into three distinct, independent primitives: remote state preparation, trap-based deviation detection, and error-correcting embedding. Using this framework, we show how the demanding hardware requirements of early protocols can be systematically relaxed. We review schemes that eliminate the spatial overhead, remove the need to prepare computational-basis dummy states, and replace single-photon sources with trusted local rotations or weak coherent pulses. Finally, we examine how these techniques scale, both to asymmetric multi-party settings and to the delegation of fully fault-tolerant computations in the presence of gate-level noise. This document is intended as a guide to the architectural principles of practical quantum verification.
With today’s quantum processors venturing into regimes beyond the capabilities of classical devices, we face the challenge to verify that these devices perform as intended, even when we cannot check their results on classical computers. In a recent breakthrough in computer science, a protocol was developed that allows the verification of the output of a computation performed by an untrusted quantum device based only on classical resources. Here, we follow these ideas, and demonstrate in a first, proof-of-principle experiment the verification of the output of a quantum computation using only classical means on a small trapped-ion quantum processor. We contrast this to verification protocols, which require trust and detailed hardware knowledge, as in gate-level benchmarking, or additional quantum resources in case we do not have access to or trust in the device to be tested. While our experimental demonstration uses a simplified version of Mahadev’s protocol we demonstrate the necessary steps for verifying fully untrusted devices. A scaled-up version of our protocol will allow for classical verification, requiring no hardware access or detailed knowledge of the tested device. Its security relies on post–quantum secure trapdoor functions within an interactive proof. The conceptually straightforward, but technologically challenging scaled-up version of the interactive proofs, considered here, can be used for a variety of additional tasks such as verifying quantum advantage, generating and certifying quantum randomness, or composable remote state preparation.