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Register a new userQuantum computation by teleportation and symmetry
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Authors
Dong-Sheng Wang
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A preliminary overview of measurement-based quantum computation in the setting of symmetry and topological phases of quantum matter is given. The underlying mechanism for universal quantum computation by teleportation or symmetry are analyzed, with the emphasis on the relation with tensor-network states in the presence of various symmetries. Perspectives are also given for the role of symmetry and phases of quantum matter in measurement-based quantum computation and fault tolerance.
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Blind quantum computation (BQC) allows that a client who has limited quantum abilities can delegate quantum computation to a server who has advanced quantum technologies but learns nothing about the clients private information. For example, measurement-based model can guarantee privacy of clients inputs, quantum algorithms and outputs. However, it still remains a challenge to directly encrypt quantum algorithms in circuits model. To solve the problem, we propose GTUBQC, the first gate teleportation-based universal BQC protocol. Specifically, in this paper we consider a scenario where there are a trusted center responsible for preparing initial states, a client with the ability to perform X, Z, and two non-communicating servers conducting UBQC (universal BQC) and Bell measurements. GTUBQC ensures that all quantum outputs are at the clients side and the client only needs to detect whether servers honestly return correct measurement outcomes or not. In particular, GTUBQC can hide the universal quantum gates by encrypting the rotation angles, because arbitrary unitary operation can be decomposed into a combination of arbitrary rotation operators. Also, GTUBQC protocol can facilitate realizing UBQC in circuits, since GTUBQC uses one-time-pad to guarantee blindness. We prove the blindness and correctness of GTUBQC, and apply our approach to other types of computational tasks, such as quantum Fourier transform.
We consider a model of quantum computation using qubits where it is possible to measure whether a given pair are in a singlet (total spin $0$) or triplet (total spin $1$) state. The physical motivation is that we can do these measurements in a way that is protected against revealing other information so long as all terms in the Hamiltonian are $SU(2)$-invariant. We conjecture that this model is equivalent to BQP. Towards this goal, we show: (1) this model is capable of universal quantum computation with polylogarithmic overhead if it is supplemented by single qubit $X$ and $Z$ gates. (2) Without any additional gates, it is at least as powerful as the weak model of permutational quantum computation of Jordan[1, 2]. (3) With postselection, the model is equivalent to PostBQP.
Quantum computers promise dramatic speed ups for many computational tasks. For large-scale quantum computation however, the inevitable coupling of physical qubits to the noisy environment imposes a major challenge for a real-life implementation. A scheme introduced by Gottesmann and Chuang can help to overcome this difficulty by performing universal quantum gates in a fault-tolerant manner. Here, we report a non-trivial demonstration of this architecture by performing a teleportation-based two-qubit controlled-NOT gate through linear optics with a high-fidelity six-photon interferometer. The obtained results clearly prove the involved working principles and the entangling capability of the gate. Our experiment represents an important step towards the feasibility of realistic quantum computers and could trigger many further applications in linear optics quantum information processing.
The stored-program architecture is canonical in classical computing, while its power has not been fully recognized for the quantum case. We study quantum information processing with stored quantum program states, i.e., using qubits instead of bits to encode quantum operations. We develop a stored-program model based on Choi states, following from channel-state duality, and a symmetry-based generalization of deterministic gate teleportation. Our model enriches the family of universal models for quantum computing, and can also be employed for tasks including quantum simulation and communication.
Teleportation is a cornerstone of quantum technologies, and has played a key role in the development of quantum information theory. Pushing the limits of teleportation is therefore of particular importance. Here, we apply a different aspect of quantumness to teleportation -- namely exchange-free computation at a distance. The controlled-phase universal gate we propose, where no particles are exchanged between control and target, allows complete Bell detection among two remote parties, and is experimentally feasible. Our teleportation-with-a-twist, which we extend to telecloning, then requires no pre-shared entanglement nor classical communication between sender and receiver, with the teleported state gradually appearing at its destination.
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