Blind quantum computing is a new approach to quantum computing that allows you to use your classical computer to simulate a quantum system without knowing the underlying quantum state.
Since quantum computing requires expensive, complicated gear and isn’t commercially available, blind quantum computing allows customers to outsource their computing tasks to quantum servers to get the jobs done. As a result, interaction would have to be on a quantum client: quantum server basis.
BQC has been examined in different scenarios, with varied constraints on the client and server or servers’ capabilities. The ideal configuration would be a verified BQC protocol that could be executed between a non-quantum client and a single quantum server. However, progress on such a protocol has been slow. Here’s the progress of blind quantum computing throughout the years.
Restricted Quantum Computation
Childs, in 2005, came up with an interactive protocol that allows a user with restricted quantum capabilities to do universal quantum computing through a second party who had a universal quantum computer while keeping the details of the computation concealed.
In the original case, the client had a large quantum memory with the capacity to rearrange qubits and conduct Pauli operations but couldn’t do non-Pauli gates and measurements. The client could choose a qubit(s) to work on, encrypt them using a quantum one-time pad and send them to the server.
The server performs the desired action and returns the qubit to the client. In this method, measurements taken by the server did not give any information about the state of the encoded qubit, but the client could still decode them using the one-time pad key.
In this BQC protocol, the quantum resources required of the client are determined by the computation being done. Subsequent work aimed to lower the client’s requirements while ensuring the computation’s verifiability.
Quantum Interactive Proof Model
Aharonov in 2010, teamed with physicists to develop the quantum interactive proof model. Here, the client sets up a quantum authentication method for the computation’s starting state, encoded using a polynomial code.
Because computation can be done logically, qubit by logical qubit, the size of the client’s device does not need to scale as a function of the number of qubits in their chosen computation and can be as little as three qubits.
The algebraic nature of the encoding allows the server to build Clifford gates transversally, provided he updates his encryption keys. Hence, the client can implement an approximately universal gate set by using gate teleportation.
The encoding hides the client’s input state and not the computation. However, using a fixed programmable unitary, the quantum interactive proof model may be included in a BQC protocol, concealing the input and the intended calculation. In addition, using an authentication code assures that the computation can be verified with a constant probability of error.
Universal Blind Quantum Computation
The UBQC protocol achieves blindness by successfully concealing the measurement bases for a measurement-based computation on a fixed resource state. Barz and a group of researchers developed a proof-of-principle protocol that demonstrates perfect security for both the client and the server using the measurement-based quantum computation conceptual framework, which allows a client to delegate a calculation to a quantum server.
The client can verify whether the server has quantum technology by measuring the probability distributions of a fixed measurement setting for all blind cluster states and comparing them to theoretical predictions. This blind cluster state feature runs a delegated computation on a server while keeping all data and the entire computation concealed.
The only quantum power required from the client is to prepare and transmit each qubit to the server; no quantum memory or capacity to run quantum gates is required. After transmitting the qubits, the client will only communicate measurement instructions in the protocol, which may be considered classical.
The universal blind quantum computation protocol Barz demonstrated fits well with measurement-based quantum computation. Still, the required operations can be implemented in any universal model of computation for quantum computation on unencoded data that allows for intermediate measurements.
There are various technological obstacles to implementing the BQC scheme fully: In theory, photons emitted that do not contribute to the development of the cluster state can give information about the blind phases.
Furthermore, postselection and photon losses reduce the protocol’s efficiency. As a result, creating single-qubit states on demand and fabricating blind cluster states with high fidelity and minimal losses using measurement-induced interactions will be critical for future applications.
Delegation And Verification Of Quantum Computation
Reichardt, Unger, and Vazirani proposed the first schemes based on CHSH games to accomplish quantum computation delegation and verification by an entirely classical client to a collection of entangled servers. At the same time, McKague introduced the first methods based on the self-testing of graph states.
While the protocols’ structures differ, neither discloses the computation to the servers and may thus be termed blind. The drawback of these methods was the communication overheads which scale as the computation gets deeper.
Further work by Dulek, Schaffner, and Speelman reduced this to a polynomial overhead, bringing about a computationally safe leveled homomorphic encryption technique. Despite his progress, the existence of fully homomorphic quantum encryption isn’t achievable.
The availability of safe protocols enabling blind and verifiable computing is still an open subject, but BQC is in its infancy. Since Crépeau, Ben-Or, and Colbeck’s prior works have established secure multi-party quantum computation, there’s potential for multi-user blind computation and publicly verifiable quantum computation.
- Childs, A. M. Secure assisted quantum computation. Quant. Inf. Comput. 5, 456 (2005).
- Aharonov, D., Ben-Or, M. & Eban, E. Proceedings of Innovations in Computer Science (2010).
- Barz, S. et al. Demonstration of blind quantum computing. Science 335, 303 (2012).
- Reichardt, W., Unger, F. & Vazirani, U. Classical command of quantum systems. Nature 496, 456 (2013).
- McKague, M. Interactive Proofs for BQP via Self-Tested Graph States. Theor. Comput. 12, 1 (2016).
- Dulek, Y., Schaffner C., & Speelman, F. in Advances in Cryptology–CRYPTO 2016: 36th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 14–18, 2016, Proceedings, Part III (eds Robshaw M. & Katz J.) 3–32 (Springer, 2016).
- Crépeau, C., Gottesman, D. & Smith, A. in Proceedings of the thiry-fourth annual ACM symposium on Theory of computing 643–652 (ACM, 2002).
- Ben-Or, M., Crépeau, C., Gottesman, D., Hassidim, A., & Smith, A. in 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS’06) 249–260 (IEEE, 2006).
- Colbeck, R. Quantum and relativistic protocols for secure multi-party computation. Preprint at arXiv:0911.3814 (2009).