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The Quantum Schur Transform: I. Efficient Qudit Circuits
Dave Bacon, Isaac L. Chuang, Aram W. Harrow
We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum sy…
Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
Dave Bacon
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilber…
From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups
Dave Bacon, Andrew M. Childs, Wim van Dam
We approach the hidden subgroup problem by performing the so-called pretty good measurement on hidden subgroup states. For various groups that can be expressed as the semidirect pr…
Optimal classical-communication-assisted local model of n-qubit Greenberger-Horne-Zeilinger correlations
Tracey E. Tessier, Carlton M. Caves, Ivan H. Deutsch +2
We present a model, motivated by the criterion of reality put forward by Einstein, Podolsky, and Rosen and supplemented by classical communication, which correctly reproduces the q…
Optimal measurements for the dihedral hidden subgroup problem
Dave Bacon, Andrew M. Childs, Wim van Dam
We consider the dihedral hidden subgroup problem as the problem of distinguishing hidden subgroup states. We show that the optimal measurement for solving this problem is the so-ca…