相关论文: Clifford Circuits Augmented Grassmann Matrix Produ…

One of the prominent current challenges in complexity theory is the attempt to prove lower bounds for $TC^0$, the class of constant-depth, polynomial-size circuits with majority gates. Relying on the results of Williams (2013), an appealing…

The Clifford hierarchy, introduced by Gottesman and Chuang in 1999, is an increasing sequence of sets of quantum gates crucial to the gate teleportation model for fault-tolerant quantum computation. Gates in the hierarchy can be…

We develop and analyze a method for simulating quantum circuits on classical computers by representing quantum states as rooted tree tensor networks. Our algorithm first determines a suitable, fixed tree structure adapted to the expected…

We present a quantum circuit model which emulates the interface growth of the classical raise-and-peel model. Our model consists of Clifford unitary gates interspersed with projective measurements, applied according to prescribed feedback…

Error mitigation is likely to be key in obtaining near term quantum advantage. In this work we present one of the first implementations of several Clifford data regression based methods which are used to mitigate the effect of noise in real…

A fundamental problem of fault-tolerant quantum computation with quantum low-density parity-check (qLDPC) codes is the tradeoff between connectivity and universality. It is widely believed that in order to perform native logical…

Numerical studies of the reduced density matrix of a gapped spin-1/2 Heisenberg antiferromagnet on a two-leg ladder find that it has the same form as the Gibbs density matrix of a gapless spin-1/2 Heisenberg antiferromagnetic chain at a…

In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of $m$…

Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We…

After a short introduction on Clifford algebras of polynomials, we give a general method of constructing a matrix representation. This process of linearization leads naturally to two fundamental structures: the generalized Clifford algebra…

The $(1+1)$-dimensional two-color lattice QCD is studied with the Grassmann tensor renormalization group. We construct tensor network representations of theories with the staggered fermion and the Wilson fermion and show that Grassmann…

We describe our implementation of fermionic tensor network contraction on arbitrary lattices within both a globally ordered and locally ordered formalism. We provide a pedagogical description of these two conventions as implemented for the…

The Clifford hierarchy is a foundational concept for universal quantum computation (UQC). It was introduced to show that UQC can be realized via quantum teleportation, given access to certain standard resources. While the full structure of…

We establish the emergence of a conformal field theory (CFT) in a (1+1)-dimensional hybrid quantum circuit right at the measurement-driven entanglement transition by revealing space-time conformal covariance of entanglement entropies and…

Stabilizer states along with Clifford manipulations (unitary transformations and measurements) thereof -- despite being efficiently simulable on a classical computer -- are an important tool in quantum information processing, with…

We study temporal entanglement in dual-unitary Clifford circuits with probabilistic measurements preserving spatial unitarity. We exactly characterize the temporal entanglement barrier in the measurement-free regime, exhibiting ballistic…

We describe the structure of the $n$-qubit Clifford group $C_n$ via Cayley graphs, whose vertices represent group elements and edges represent generators. In order to obtain the action of Clifford gates on a given quantum state, we…

Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation…

Real Clifford algebras play a fundamental role in the eight real Altland-Zirnbauer symmetry classes and the classification tables of topological phases. Here, we present another elegant realization of real Clifford algebras in the…

Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…