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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.
Quantum speedup of Monte Carlo methods
- A. Montanaro
- Computer ScienceProceedings of the Royal Society A: Mathematical…
- 27 April 2015
A quantum algorithm which can accelerate Monte Carlo methods in a very general setting, achieving a near-quadratic speedup over the best possible classical algorithm.
Optimal Verification of Entangled States with Local Measurements.
This work finds the optimal strategy in this case and shows that quadratically fewer total measurements are needed to verify to within a given fidelity than in published results for quantum state tomography, Bell test, or fidelity estimation protocols.
On the Quantum Chromatic Number of a Graph
- P. Cameron, A. Montanaro, M. Newman, S. Severini, A. Winter
- MathematicsElectron. J. Comb.
- 1 August 2006
We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince a referee that they have a…
Quantum algorithms and the finite element method
The quantum algorithm can achieve a polynomial speedup, the extent of which grows with the dimension of the partial differential equation, and there is evidence that no improvement of the quantum algorithm could lead to a super-polynomial speedup when the dimension is fixed and the solution satisfies certain smoothness properties.
Complexity Classification of Local Hamiltonian Problems
This work characterises the complexity of the k-local Hamiltonian problem for all 2-local qubit Hamiltonians and proves for the first time QMA-completeness of the Heisenberg and XY interactions in this setting.
On the communication complexity of XOR functions
A structural conjecture about the Fourier spectra of boolean functions is made which would imply that the quantum and classical exact communication complexities of all XOR functions are asymptotically equivalent.
Universal quantum Hamiltonians
- T. Cubitt, A. Montanaro, Stephen Piddock
- PhysicsProceedings of the National Academy of Sciences
- 18 January 2017
It is proved that the entire physics of any quantum many-body system can be replicated by certain simple, “universal” spin-lattice models, and that certain simple models can simulate all others, and hence are universal.
On Exact Quantum Query Complexity
The model of nonadaptive exact quantum query complexity in terms of coding theory is characterised and the query complexity of symmetric boolean functions in this context is completely characterised.
Quantum algorithms: an overview
- A. Montanaro
- Computer Science
- 13 November 2015
A survey of known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details, including a discussion of recent developments and near-term applications.