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arXiv:2510.06323 · Physical Review A

Blind quantum computing with different qudit resource state architectures

Alena Romanova, Wolfgang Dür

Published Feb 11, 2026• 0 citations
arXivHTMLPDF

Abstract

We discuss how blind quantum computing generalizes to multilevel quantum systems (qudits), which offers advantages compared with the qubit approach. Here, a quantum computing task is delegated to an untrusted server while simultaneously preventing the server from retrieving information about the computation it performs, the input, and the output, enabling secure cloud-based quantum computing. In the standard approach with qubits, measurement-based quantum computing is used: single-qubit measurements on cluster or brickwork states implement the computation, while random rotations of the resource qubits hide the computation from the server. We generalize finite-sized approximately universal gate sets to prime-power-dimensional qudits and show that qudit versions of the cluster and brickwork states enable a similar server-blind execution of quantum algorithms. Furthermore, we compare the overheads of different resource state architectures and discuss which hiding strategies apply to alternative qudit resource states beyond graph states.

DOI
10.1103/1p5p-zywx

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We discuss how blind quantum computing generalizes to multilevel quantum systems (qudits), which offers advantages compared with the qubit approach. Here, a quantum computing task is delegated to an untrusted server while simultaneously preventing the server from retrieving information about the computation it performs, the input, and the output, enabling secure cloud-based quantum computing. In the standard approach with qubits, measurement-based quantum computing is used: single-qubit measurements on cluster or brickwork states implement the computation, while random rotations of the resource qubits hide the computation from the server. We generalize finite-sized approximately universal gate sets to prime-power-dimensional qudits and show that qudit versions of the cluster and brickwork states enable a similar server-blind execution of quantum algorithms. Furthermore, we compare the overheads of different resource state architectures and discuss which hiding strategies apply to alternative qudit resource states beyond graph states.
Current cloud-based quantum processors offer access to advanced hardware hosted on a remote server, but do not guarantee data or algorithm privacy. Blind quantum computation provides information-theoretic privacy by enabling a client to execute an algorithm without disclosing information about either the task or the final result. Here, we execute a measurement-based blind quantum computation protocol on a superconducting processor comprising two flip-chip-bonded modules, one acting as a server and the other as a client. The server generates a two-dimensional cluster state and forwards it to the client. Using this resource, the client implements a universal gate set with only adaptive single-qubit rotations and measurements. To illustrate this approach, we execute a three-qubit instance of the Deutsch-Jozsa algorithm. We analyze the server's quantum state after each rotation of a measurement-based single-qubit gate to verify that negligible information about the computation is revealed to the server, consistent with the one-way flow of information that guarantees blindness. This proof-of-principle demonstration establishes key elements of blind quantum computation in superconducting-circuit architectures, indicating that intermediate-scale implementations of blind protocols may become feasible with realistic near-term improvements in gate fidelities.
Abstract We show how to perform measurement-based quantum computing on qudits (high-dimensional quantum systems) using alternative resource states beyond the cluster state. Estimating overheads for gate decomposition, we find that generalizing standard qubit measurement patterns to the qudit cluster state is suboptimal in most dimensions, so that alternative qudit resource states could enable enhanced computational efficiency. In these resources, the entangling interaction is a block-diagonal Clifford operation rather than the usual controlled-phase gate for cluster states. This simple change has remarkable consequences: the applied entangling operation determines an intrinsic single-qudit gate associated with the resource that drives the quantum computation when performing single-qudit measurements on the resource state. We prove a condition for the intrinsic gate allowing for the measurement-based implementation of arbitrary single-qudit unitaries. Furthermore, we demonstrate for prime-power-dimensional qudits that the complexity of the realization depends linearly both on the dimension and the Pauli order of the intrinsic gate. These insights also allow us to optimize the efficiency of the standard qudit cluster state by effectively mimicking more favorable intrinsic-gate structures, thereby reducing the required measurement depth. Finally, we discuss the required two-dimensional geometry of the resource state for universal measurement-based quantum computing. As concrete examples, we present multiple alternative resource states. In certain dimensions, we show the existence of resource states achieving optimal intrinsic gates, enabling more efficient measurement-based quantum information processing than the qudit cluster state and highlighting the potential of qudit stabilizer state resources for future quantum computing architectures.
Blind quantum computation (BQC) allows low-resource clients to securely delegate computations to a quantum server, but server resource costs scale with the computation size, posing a bottleneck for implementations. By leveraging Pauli-based computation (PBC), we achieve BQC with a server whose size depends only on the non-Clifford gate count. Our protocol inherits fault tolerance and qubit virtualization from PBC and reveals that classical-client BQC is possible even in the absence of classical simulability. Finally, we present an entanglement-based dual protocol that performs a resource state computation with a dramatically reduced execution cost.
Quantum computing systems are powerful for allowing a client to perform any quantum computations from a remote quantum server while concealing the structure and content of the computation fall under the category of blind quantum computing (BQC). In BQC, the client delegates the quantum processing to one or more powerful quantum servers while retaining privacy over the input, computation and output. This makes it suitable for secure quantum cloud computing. This feature is powerful to ensure that even untrusted servers cannot learn the details of the user's computation. With quantum computing, there is a fast-growing need to transition from general-purpose quantum systems to customized architectures tailored to specific application requirements. This transition is critical while considering sustainability goals and financial limitations. With this advanced computing architecture, a custom system can optimize energy use, hardware complexity, and resource allocation to better serve individual user needs while staying within budgetary boundaries.
Universal blind quantum computation allows a client who has limited quantum abilities to delegate his or her private computation to an untrusted quantum server. The first universal blind quantum computation protocol was proposed by Broadbent, Fitzsimons, and Kashefi. In their work the computation resource is the so-called brickwork state, which can be constructed by a number of specific single qubits. The number of single qubits is in theory linearly related to the size of the quantum circuit. However, due to the fixed structure of the brickwork states, the actual number of qubits is usually far more than the linear size. In this work we mainly construct three improved brickwork states whose structures are no longer fixed, thus they can efficiently reduce the client's qubit consumption. Using those improved brickwork states we propose a class of efficient universal blind quantum computation protocols. In our basic protocol, to implement a single-qubit basic gate the client needs to prepare only two ancillary qubits, while in the original protocol it will consume four ancillary qubits. Making use of our improved brickwork states the qubit consumption of implementing a nonadjacent two-qubit gate such as a control-XXX gate can be sharply reduced.
Quantum computers, besides offering substantial computational speedups, are also expected to preserve the privacy of a computation. We present an experimental demonstration of blind quantum computing in which the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. Various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover quantum algorithms, are demonstrated. The client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantum computers widely available.