Related papers: Multiqubit Clifford groups are unitary 3-designs
Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. But the spin group is not the only subgroup of the Clifford algebra. An algebraist's perspective on…
The stabilizer formalism for quantum error-correcting codes has been, without doubt, the most successful at producing examples of quantum codes with strong error-correcting properties. In this paper, we discuss strong automorphism groups of…
The group of local unitary transformations partitions the space of n-qubit quantum states into orbits, each of which is a differentiable manifold of some dimension. We prove that all orbits of the n-qubit quantum state space have dimension…
Epsilon-nets and approximate unitary $t$-designs are natural notions that capture properties of unitary operations relevant for numerous applications in quantum information and quantum computing. The former constitute subsets of unitary…
Dynamical characterization of topological phases under quantum quench dynamics has been demonstrated as a powerful and efficient tool. Previous studies have been focused on systems of which the Hamiltonian consists of matrices that commute…
Local random circuits scramble efficiently and accordingly have a range of applications in quantum information and quantum dynamics. With a global $U(1)$ charge however, the scrambling ability is reduced; for example, such random circuits…
An algebraic description of basic discrete symmetries (space inversion P, time reversal T, charge conjugation C and their combinations PT, CP, CT, CPT) is studied. Discrete subgroups {1,P,T,PT} of orthogonal groups of multidimensional…
The unitary group acting on the Hilbert space of three quantum bits admits a Lie subgroup, of elements which permute with the symmetric group of permutations. Under the action of such Lie subgroup, the Hilbert space splits into three…
We prove that local random quantum circuits acting on n qubits composed of O(t^{10} n^2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design…
We present a simple algorithm that implements an arbitrary $n$-qubit unitary operator using a Clifford+T circuit with T-count $O(2^{4n/3} n^{2/3})$. This improves upon the previous best known upper bound of $O(2^{3n/2} n)$, while the best…
The $n$-qubit stabilizer states are those left invariant by a $2^n$-element subset of the Pauli group. The Clifford group is the group of unitaries which take stabilizer states to stabilizer states; a physically--motivated generating set,…
Linear codes and $t$-designs are interactive with each other. It is well known that some $t$-designs have been constructed by using certain linear codes in recent years. However, only a small number of infinite families of the extended…
Graph states are computationally powerful quantum states with many applications including use as resource states for measurement-based quantum computing (MBQC). We demonstrate construction of graph states on a Rydberg atom quantum analogue…
Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is…
In this paper, we show that a qutrit version of ZX-calculus, with rules significantly different from that of the qubit version, is complete for pure qutrit stabilizer quantum mechanics, where state preparations and measurements are based on…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
Current quantum computing hardware is restricted by the availability of only few, noisy qubits which limits the investigation of larger, more complex molecules in quantum chemistry calculations on quantum computers in the near-term. In this…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0\rangle$ computational basis. In addition, we allow the creation of a one-qubit ancilla in a…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…