Related papers: Statistical mechanics model for Clifford random te…
Certain families of quantum mechanical models can be described and solved efficiently on a classical computer, including qubit or qudit Clifford circuits and stabilizer codes, free-boson or free-fermion models, and certain rotor and GKP…
We present a theory of the entanglement transition tuned by measurement strength in qudit chains evolved by random unitary circuits and subject to either weak or random projective measurements. The transition can be understood as a…
We map the dynamics of entanglement in random unitary circuits, with finite on-site Hilbert space dimension $q$, to an effective classical statistical mechanics, and develop general diagrammatic tools for calculations in random unitary…
We resolve the space-time canonical variables of the relativistic point particle into inner products of Weyl spinors with components in a Clifford algebra and find that these spinors themselves form a canonical system with generalized…
We show that qubit stabilizer states can be represented by non-negative quasi-probability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by…
Recent advances in combining Clifford circuits with tensor-network (TN) methods have shown that classically simulable disentanglers can suppress substantial portions of the entanglement structure, effectively alleviating the bond-dimension…
We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results…
Tensor network methods leverage the limited entanglement of quantum states to efficiently simulate many-body systems. Alternatively, Clifford circuits provide a framework for handling highly entangled stabilizer states, which have low magic…
We show that quantum mechanics can be represented as an asymptotic projection of statistical mechanics of classical fields. Thus our approach does not contradict to a rather common opinion that quantum mechanics could not be reduced to…
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…
Anticoncentration describes how an ensemble of quantum states spreads over the allowed Hilbert space, leading to statistically uniform output probability distributions. In this work, we investigate the anticoncentration of random Clifford…
A class of network models with symmetry group $G$ that evolve as a Lie-Poisson system is derived from the framework of geometric mechanics, which generalises the classical Heisenberg model studied in statistical mechanics. We considered two…
Clifford circuits are insufficient for universal quantum computation or creating $t$-designs with $t\ge 4$. While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum is: the entanglement levels are…
Let $A$ and $B$ be local operators in Hamiltonian quantum systems with $N $ degrees of freedom and finite-dimensional Hilbert space. We prove that the commutator norm $\lVert [A(t),B]\rVert$ is upper bounded by a topological combinatorial…
A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements.…
This work proposes a minimal model extending the duality between classical statistical spin systems and fermionic systems beyond the case of free fermions. A Jordan-Wigner transformation applied to a two-dimensional tensor network maps the…
At higher energies the present complex quantum theory with its unitary group might expand into a real quantum theory with an orthogonal group, broken by an approximate $i$ operator at lower energies. Implementing this possibility requires a…
We study locality preserving automorphisms of operator algebras on $D$-dimensional uniform lattices of prime $p$-dimensional qudits (QCA), specializing in those that are translation invariant (TI) and map every prime $p$-dimensional Pauli…
Motivated by Heisenberg's observable-only stance, we replace latent "information" (filtrations, hidden diffusions, state variables) with observable transitions between price states. On a discrete price lattice with a Hilbert-space…
Classical simulation of quantum circuits plays a crucial role in validating quantum hardware and delineating the boundaries of quantum advantage. Among the most effective simulation techniques are those based on the stabilizer extent, which…