The Quantum Schur Transform: I. Efficient Qudit Circuits
read the original abstract
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 systems is a transform between a standard computational basis to a labelling related to the representation theory of the symmetric and unitary groups. If we desire to implement the Schur transform to an accuracy of epsilon, then our circuit construction uses a number of gates which is polynomial in n, d and log(1/epsilon). The important insights we use to perform this construction are the selection of the appropriate subgroup adapted basis and the Wigner-Eckart theorem. Our efficient circuit construction renders numerous protocols in quantum information theory computationally tractable and is an important new efficient quantum circuit family which goes significantly beyond the standard paradigm of the quantum Fourier transform.
This paper has not been read by Pith yet.
Forward citations
Cited by 3 Pith papers
-
Efficient Quantum Circuits for Coherent Conversion Between General First- and Second-Quantized Many-Body Representations
Constructs an explicit unitary Q using the quantum Schur transform to coherently map fixed-N first-quantized states to occupation-number form with poly(N,d,log(1/ε)) gate complexity.
-
Random dilation superchannel
Presents a poly-complexity quantum circuit implementing the random dilation superchannel for parallel channel queries, with approximate sequential extension, a no-go theorem for exact sequential dilation, and an appli...
-
Scaling-optimal purification of noisy qubit unitary channels
A U(2)-covariant parallel protocol based on a novel entanglement-assisted QECC purifies noisy qubit unitaries with O(1/n) noise scaling shown to be asymptotically optimal in the low-noise regime.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.