The computational complexity of linear optics
- S. Aaronson, Alexei Y. Arkhipov
- Computer ScienceSymposium on the Theory of Computing
- 14 November 2010
A model of computation in which identical photons are generated, sent through a linear-optical network, then nonadaptively measured to count the number of photons in each mode is defined, giving new evidence that quantum computers cannot be efficiently simulated by classical computers.
Improved Simulation of Stabilizer Circuits
- S. Aaronson, D. Gottesman
- Computer ScienceArXiv
- 25 June 2004
The Gottesman-Knill theorem, which says that a stabilizer circuit, a quantum circuit consisting solely of controlled-NOT, Hadamard, and phase gates can be simulated efficiently on a classical computer, is improved in several directions.
Quantum computing, postselection, and probabilistic polynomial-time
- S. Aaronson
- Computer ScienceProceedings of the Royal Society A
- 23 December 2004
It is shown that several simple changes to the axioms of quantum mechanics would let us solve PP-complete problems efficiently, or probabilistic polynomial-time, and implies, as an easy corollary, a celebrated theorem of Beigel, Reingold and Spielman that PP is closed under intersection.
Quantum search of spatial regions
- S. Aaronson, A. Ambainis
- Computer Science44th Annual IEEE Symposium on Foundations of…
- 9 March 2003
An 0(/spl radic/n)-qubit communication protocol for the disjointness problem is given, which improves an upper bound of Hoyer and de Wolf and matches a lower bound of Razborov.
Algebrization: A New Barrier in Complexity Theory
- S. Aaronson, A. Wigderson
- Mathematics, Computer ScienceTOCT
- 1 February 2009
This article systematically goes through basic results and open problems in complexity theory to delineate the power of the new algebrization barrier, and shows that almost all of the major open problems---including P versus NP, P versus RP, and NEXP versus P/poly---will require non-algebrizing techniques.
The learnability of quantum states
- S. Aaronson
- PhysicsProceedings of the Royal Society A
- 18 August 2006
This theorem has the conceptual implication that quantum states, despite being exponentially long vectors, are nevertheless ‘reasonable’ in a learning theory sense and has two applications to quantum computing: first, a new simulation of quantum one-way communication protocols and second, the use of trusted classical advice to verify untrusted quantum advice.
Quantum money from hidden subspaces
- S. Aaronson, Paul Christiano
- Computer ScienceSymposium on the Theory of Computing
- 21 March 2012
The first quantum money scheme that is (1) public-key---meaning that anyone can verify a banknote as genuine, not only the bank that printed it, and (2) cryptographically secure, under a "classical" hardness assumption that has nothing to do with quantum money is proposed.
Quantum Computing since Democritus
- S. Aaronson
- Physics
- 14 March 2013
This fascinating book takes readers on a tour through some of the deepest ideas of maths, computer science and physics, beginning in antiquity with Democritus and progressing through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics.
Complexity-Theoretic Foundations of Quantum Supremacy Experiments
- S. Aaronson, Lijie Chen
- Computer ScienceCybersecurity and Cyberforensics Conference
- 18 December 2016
General theoretical foundations are laid for how to use special-purpose quantum computers with 40--50 high-quality qubits to demonstrate "quantum supremacy": that is, a clear quantum speedup for some task, motivated by the goal of overturning the Extended Church-Turing Thesis as confidently as possible.
Limitations of quantum advice and one-way communication
- S. Aaronson
- Computer ScienceProceedings. 19th IEEE Annual Conference on…
- 14 February 2004
It is shown in three settings that quantum messages have only limited advantages over classical ones, and the polynomial method is used to give the first correct proof of a direct product theorem for quantum search.
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