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Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
- M. Bremner, R. Jozsa, D. Shepherd
- Computer Science, MathematicsProceedings of the Royal Society A: Mathematical…
- 9 May 2010
The class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection is introduced, and it is proved first that post- IQP equals the classical class PP, and that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, then the infinite tower of classical complexity classes known as the polynomial hierarchy would collapse to its third level.
Average-case complexity versus approximate simulation of commuting quantum computations
It is shown that, if either of two plausible average-case hardness conjectures holds, then IQP computations are hard to simulate classically up to constant additive error.
Temporally unstructured quantum computation
Using the theory of binary matroids, it is argued that the paradigm is rich enough to enable sampling from probability distributions that cannot, classically, be sampled efficiently and accurately.
Achieving quantum supremacy with sparse and noisy commuting quantum computations
It is shown that purely classical error-correction techniques can be used to design IQP circuits which remain hard to simulate classically, even in the presence of arbitrary amounts of noise of this form.
Efficient distributed quantum computing
- R. Beals, S. Brierley, M. Stather
- Computer ScienceProceedings of the Royal Society A: Mathematical…
- 10 July 2012
A parallel quantum search algorithm is presented that can be used by algorithm designers without worrying whether the underlying architecture supports the connectivity of the circuit and improves the time–space trade-off for the element distinctness and collision finding problems.
Computation with Unitaries and One Pure Qubit
- D. Shepherd
- 17 August 2006
We define a semantic complexity class based on the model of quantum computing with just one pure qubit (as introduced by Knill and Laflamme) and discuss its computational power in terms of the…
Quantum Key Search with Side Channel Advice
- Daniel P. Martin, A. Montanaro, E. Oswald, D. Shepherd
- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 16 August 2017
This work presents a novel variation of a key enumeration algorithm that produces batches of keys that can be efficiently tested using Grover’s algorithm, and results in the first quantum key search that benefits from side channel information.
Instantaneous Quantum Computation
We examine theoretic architectures and an abstract model for a restricted class of quantum computation, called here temporally unstructured (“instantaneous”) quantum computation because it allows for…
Universally programmable quantum cellular automaton.
Employing the structure theorem for quantum cellular automata, a general construction scheme is given to turn an arbitrary cellular automaton with external classical control into an autonomous one, thereby proving the computational equivalence of these two models.
Quantum Complexity: restrictions on algorithms and architectures
- D. Shepherd
- Computer ScienceArXiv
- 9 May 2010
A dissertation submitted to the University of Bristol in accordance with the requirements of the degree of Doctor of Philosophy (PhD) in the Faculty of Engineering, Department of Computer Science,…