In this paper, we study quantum computing with twists. Twists are yet another form of defects in a lattice. They arise from dislocations in the lattice and can be used to encode and process quantum information. Surface codes with twists are also called dislocation codes. Hastings and Geller showed that dislocation codes could provide gains in space-time complexity of quantum computation. In this paper, we undertake a detailed study of generalized dislocation codes. We develop the theory of qubit dislocation codes over arbitrary four-valent and bicolorable lattices. We give a construction to introduce twists in such lattices and also study the structure of logical operators. We then study dislocation codes over odd prime dimensions in square lattices. Using the theory developed, we present protocols for implementing a universal gate set in qubit dislocation codes. We also show how to implement the generalized Clifford group in qudit dislocation codes in odd prime dimensions.In this paper, we study quantum computing with twists. Twists are yet another form of defects in a lattice. They arise from dislocations in the lattice and can be used to encode and process quantum information. Surface codes with twists are also called dislocation codes. Hastings and Geller showed that dislocation codes could provide gains in space-time complexity of quantum computation. In this paper, we undertake a detailed study of generalized dislocation codes. We develop the theory of qubit dislocation codes over arbitrary four-valent and bicolorable lattices. We give a construction to introduce twists in such lattices and also study the structure of logical operators. We then study dislocation codes over odd prime dimensions in square lattices. Using the theory developed, we present protocols for implementing a universal gate set in qubit dislocation codes. We also show how to implement the generalized Clifford group in qudit dislocation codes in odd prime dimensions.

Physical Review AOct 29, 20204 citations

Toward Quantum Computing

ScienceFeb 16, 20120 citations

On quantum computation of Kloosterman sums

Peter Bruin

We give two quantum algorithms for computing (twisted) Kloosterman sums attached to a finite field $\mathbf{F}$ of $q$ elements. The first algorithm computes a quantum state containing, as its coefficients with respect to the standard basis, all Kloosterman sums for $\mathbf{F}$ twisted by a given multiplicative character, and runs in time polynomial in $\log q$ . The second algorithm computes a single Kloosterman sum to a prescribed precision, and runs in time quasi-linear in $\sqrt{q}$ .We give two quantum algorithms for computing (twisted) Kloosterman sums attached to a finite field $\mathbf{F}$ of $q$ elements. The first algorithm computes a quantum state containing, as its coefficients with respect to the standard basis, all Kloosterman sums for $\mathbf{F}$ twisted by a given multiplicative character, and runs in time polynomial in $\log q$. The second algorithm computes a single Kloosterman sum to a prescribed precision, and runs in time quasi-linear in $\sqrt{q}$.

arXiv:1807.03600Jul 10, 20180 citations

Quantum Computing, Part 3

Andrew S. Glassner

IEEE Computer Graphics and ApplicationsJan 1, 20015 citations

The Promise of Quantum Computing

Jeff Kabachinski

Biomedical Instrumentation & TechnologyDec 1, 20130 citations

quantum computation with charge-color permuting twists in qudit color codes

Manoj G. Gowda, Pradeep Kiran Sarvepalli

twists are defects in the lattice which can be utilized to perform computations on encoded data. twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes and qubit subsystem color codes. they are known to exhibit projective non-abelian statistics which is exploited to perform encoded gates. in this paper, we initiate the study of twists in qudit color codes over odd prime alphabet. to the best of our knowledge, this is the first study of twists in qudit color codes. specifically, we present a systematic construction of twists in qudit color codes that permute both charge and color of the excitations. we also present a mapping between generalized pauli operators and strings in the lattice. making use of the construction, we give protocols to implement generalized clifford gates using charge-color permuting twists.twists are defects in the lattice which can be utilized to perform computations on encoded data. twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes and qubit subsystem color codes. they are known to exhibit projective non-abelian statistics which is exploited to perform encoded gates. in this paper, we initiate the study of twists in qudit color codes over odd prime alphabet. to the best of our knowledge, this is the first study of twists in qudit color codes. specifically, we present a systematic construction of twists in qudit color codes that permute both charge and color of the excitations. we also present a mapping between generalized pauli operators and strings in the lattice. making use of the construction, we give protocols to implement generalized clifford gates using charge-color permuting twists.

Oct 16, 20210 citations

We give two quantum algorithms for computing (twisted) Kloosterman sums attached to a finite field

\mathbf{F}

q

elements. The first algorithm computes a quantum state containing, as its coefficients with respect to the standard basis, all Kloosterman sums for

\mathbf{F}

twisted by a given multiplicative character, and runs in time polynomial in

\log q

. The second algorithm computes a single Kloosterman sum to a prescribed precision, and runs in time quasi-linear in

\sqrt{q}