A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Fault-tolerant quantum computation with constant error
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Teleportation as a quantum computation
PhysComp96 Proceedings of the fourth workshop on Physics and computation
Molecular scale heat engines and scalable quantum computation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A new universal and fault-tolerant quantum basis
Information Processing Letters
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Fault-tolerant quantum computation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Polynomial simulations of decohered quantum computers
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Fault Tolerant Computation on Ensemble Quantum Computers
DSN '04 Proceedings of the 2004 International Conference on Dependable Systems and Networks
Physical Limits of Heat-Bath Algorithmic Cooling
SIAM Journal on Computing
Optimal algorithmic cooling of spins
UC'07 Proceedings of the 6th international conference on Unconventional Computation
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In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor's factorization algorithm, Grover's search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and $$\sigma_{z}^{1/4},$$ as these operations cannot be implemented "bitwise", and their standard fault-tolerant implementations require measurement.