Combinatorica
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Sampling and integration of near log-concave functions
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
On the limits of non-approximability of lattice problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Honest-verifier statistical zero-knowledge equals general statistical zero-knowledge
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Faster random generation of linear extensions
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Quantum algorithms for solvable groups
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum lower bound for the collision problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A Complete Promise Problem for Statistical Zero-Knowledge
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
How Powerful is Adiabatic Quantum Computation?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A study of statistical zero-knowledge proofs
A study of statistical zero-knowledge proofs
Finding cliques by quantum adiabatic evolution
Quantum Information & Computation
Hidden translation and orbit coset in quantum computing
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Multilinear formulas and skepticism of quantum computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Limitations of quantum coset states for graph isomorphism
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Statistical Zero Knowledge and quantum one-way functions
Theoretical Computer Science
Expert Systems with Applications: An International Journal
Quantum algorithms using the curvelet transform
Proceedings of the forty-first annual ACM symposium on Theory of computing
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
A study of heuristic guesses for adiabatic quantum computation
Quantum Information Processing
Simulating sparse Hamiltonians with star decompositions
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
Complexity of Stoquastic Frustration-Free Hamiltonians
SIAM Journal on Computing
A promiseBQP-complete string rewriting problem
Quantum Information & Computation
Efficient circuits for quantum walks
Quantum Information & Computation
Limitations on the simulation of non-sparse hamiltonians
Quantum Information & Computation
Quantum algorithms for subset finding
Quantum Information & Computation
Physically-motivated dynamical algorithms for the graph isomorphism problem
Quantum Information & Computation
The complexity of stoquastic local Hamiltonian problems
Quantum Information & Computation
Eigenpath traversal by phase randomization
Quantum Information & Computation
Measuring 4-local qubit observables could probabilistically solve PSPACE
Quantum Information & Computation
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Quantum algorithms for a set of group theoretic problems
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Computational indistinguishability between quantum states and its cryptographic application
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
On the efficiency of quantum algorithms for Hamiltonian simulation
Quantum Information Processing
Black-box hamiltonian simulation and unitary implementation
Quantum Information & Computation
Quantum walks: a comprehensive review
Quantum Information Processing
Hamiltonian simulation using linear combinations of unitary operations
Quantum Information & Computation
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
Efficient algorithms for universal quantum simulation
RC'13 Proceedings of the 5th international conference on Reversible Computation
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The design of new quantum algorithms has proven to be an extremely difficult task. This paper considers a different approach to the problem, by studying the problem of 'quantum state generation'.We first show that any problem in Statistical Zero Knowledge (including eg. discrete log, quadratic residuosity and gap closest vector in a lattice) can be reduced to an instance of the quantum state generation problem. Having shown the generality of the state generation problem, we set the foundations for a new paradigm for quantum state generation. We define 'Adiabatic State Generation' (ASG), which is based on Hamiltonians instead of unitary gates. We develop tools for ASG including a very general method for implementing Hamiltonians (The sparse Hamiltonian lemma), and ways to guarantee non negligible spectral gaps (The jagged adiabatic path lemma). We also prove that ASG is equivalent in power to state generation in the standard quantum model. After setting the foundations for ASG, we show how to apply our techniques to generate interesting superpositions related to Markov chains.The ASG approach to quantum algorithms provides intriguing links between quantum computation and many different areas: the analysis of spectral gaps and groundstates of Hamiltonians in physics, rapidly mixing Markov chains, statistical zero knowledge, and quantum random walks. We hope that these links will bring new insights and methods into quantum algorithms.