Related papers: Quantum State Designs with Clifford Enhanced Matri…
We show that the quantized free relativistic point particle can be understood as a string in a Clifford space which generates the space-time coordinates through its inner product. The generating algebra is preserved by a unitary symmetry…
Magic states are fundamental building blocks on the road to fault-tolerant quantum computing. CSS codes play a crucial role in the construction of magic distillation protocols. Previous work has cast quantum computing with magic states for…
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 $m$…
We investigate the statistical properties of orthogonal, or real, Clifford circuits doped with magic and imaginary resources. By developing the Weingarten calculus for the real Clifford group, we derive the exact overlap distribution of…
Magic-state resource theory is a powerful tool with applications in quantum error correction, many-body physics, and classical simulation of quantum dynamics. Despite its broad scope, finding tractable resource monotones has been…
As in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is…
We prove that the stabilizer fidelity is multiplicative for the tensor product of an arbitrary number of single-qubit states. We also show that the relative entropy of magic becomes additive if all the single-qubit states but one belong to…
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the…
We consider the costs and benefits of embedding the states of one quantum system within those of another. Such embeddings are ubiquitous, e.g., in error correcting codes and in symmetry-constrained systems. In particular we investigate the…
We study the computational power of unitary Clifford circuits with solely magic state inputs (CM circuits), supplemented by classical efficient computation. We show that CM circuits are hard to classically simulate up to multiplicative…
Encoding classical data in a quantum state is a key prerequisite of many quantum algorithms. Recently matrix product state (MPS) methods emerged as the most promising approach for constructing shallow quantum circuits approximating input…
Monitored random circuits, consisting of alternating layers of entangling two-qubit gates and projective single-qubit measurements applied to some fraction $p$ of the qubits, have been a topic of recent interest. In particular, the…
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…
We pursue the identification of quantum resources carried by topological order, by evaluating quantum magic, quantified through the rank-$2$ Stabilizer R\'enyi entropy $\mathcal{M}_2$, in one-dimensional systems hosting symmetry-protected…
While there is strong evidence for advantages of quantum over classical computation, the repertoire of computational primitives with proven or conjectured quantum advantage remains limited. A big challenge of quantum algorithmic design is a…
Gauging a global symmetry of a system amounts to introducing new degrees of freedom whose transformation rule makes the overall system observe a local symmetry. In quantum systems there can be obstructions to gauging a global symmetry. When…
Canonical forms are central to the analytical understanding of tensor network states, underpinning key results such as the complete classification of one-dimensional symmetry-protected topological phases within the matrix product state…
Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.
Towards the efficient simulation of near-term quantum devices using tensor network states, we introduce an improved real-space parallelizable matrix-product state (MPS) compression method. This method enables efficient compression of all…
We investigate the use of matrix product states (MPS) to approximate ground states of critical quantum spin chains with periodic boundary conditions (PBC). We identify two regimes in the (N,D) parameter plane, where N is the size of the…