scholarly journals Symmetry Protected Quantum Computation

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 554
Author(s):  
Michael H. Freedman ◽  
Matthew B. Hastings ◽  
Modjtaba Shokrian Zini
Keyword(s):  
Quantum Computation ◽  
Total Spin ◽  
Weak Model ◽  
Single Qubit ◽  
Other Information ◽  
Universal Quantum ◽  
Symmetry Protected

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 [14, 18]. (3) With postselection, the model is equivalent to PostBQP.

Both Toffoli and Controlled-NOT need little help to universal quantum computing

2003 ◽  
Vol 3 (1) ◽  
pp. 84-92
Author(s):  
Y-Y Shi
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Quantum Circuit ◽  
Single Qubit ◽  
Universal Quantum ◽  
Qubit Gate ◽  
Computational Basis ◽  
Universal Gates

What additional gates are needed for a set of classical universal gates to do universal quantum computation? We prove that any single-qubit real gate suffices, except those that preserve the computational basis. The Gottesman-Knill Theorem implies that any quantum circuit involving only the Controlled-NOT and Hadamard gates can be efficiently simulated by a classical circuit. In contrast, we prove that Controlled-NOT plus any single-qubit real gate that does not preserve the computational basis and is not Hadamard (or its like) are universal for quantum computing. Previously only a generic gate, namely a rotation by an angle incommensurate with \pi, is known to be sufficient in both problems, if only one single-qubit gate is added.

scholarly journals Blind quantum computation where a user only performs single-qubit gates

2021 ◽  
Vol 142 ◽  
pp. 107190
Author(s):  
Qin Li ◽  
Chengdong Liu ◽  
Yu Peng ◽  
Fang Yu ◽  
Cai Zhang
Keyword(s):  
Quantum Computation ◽  
Single Qubit ◽  
Blind Quantum Computation

scholarly journals Extending matchgates into universal quantum computation

2011 ◽  
Vol 84 (2) ◽  
Author(s):  
Daniel J. Brod ◽  
Ernesto F. Galvão
Keyword(s):  
Quantum Computation ◽  
Universal Quantum

Universal quantum computation with quantum-dot cellular automata in decoherence-free subspace

2008 ◽  
Vol 8 (10) ◽  
pp. 977-985
Author(s):  
Z.-Y. Xu ◽  
M. Feng ◽  
W.-M. Zhang
Keyword(s):  
Cellular Automata ◽  
Quantum Dot ◽  
Quantum Computation ◽  
Two Dimensions ◽  
High Fidelity ◽  
Electron Pairs ◽  
Quantum Dot Cellular Automata ◽  
Single Spin ◽  
Universal Quantum ◽  
Decoherence Free Subspace

We investigate the possibility to have electron-pairs in decoherence-free subspace (DFS), by means of the quantum-dot cellular automata (QCA) and single-spin rotations, to deterministically carry out a universal quantum computation with high-fidelity. We show that our QCA device with electrons tunneling in two dimensions is very suitable for DFS encoding, and argue that our design favors a scalable quantum computation robust to collective dephasing errors.

scholarly journals Roads towards fault-tolerant universal quantum computation

Nature ◽  
2017 ◽  
Vol 549 (7671) ◽  
pp. 172-179 ◽  
Author(s):  
Earl T. Campbell ◽  
Barbara M. Terhal ◽  
Christophe Vuillot
Keyword(s):  
Quantum Computation ◽  
Fault Tolerant ◽  
Universal Quantum
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