We show that the network of quantum register states of a quantum computer (QC), coupled through residual two-body interactions between qubits, exhibits small-world properties analogous to those of complex networks found in human society. The most probable Erd\H{o}s number between any two states is about 9, comparable to the six degrees of separation reported by Milgram for social networks. Using the $\mathring{A}$berg criterion, which retains only interactions exceeding the local energy spacing, we construct an effective ($\mathring{A}$berg) network and show that, above a critical coupling strength, this network percolates into a giant component spanning nearly the whole quantum register space. This percolation transition closely matches the onset of quantum chaos and dynamical thermalization established previously via costly exact diagonalization, while our approach extends the accessible system size up to $n_q=30$ qubits.
We propose a novel approach to state preparation by embracing the full power of open quantum systems. Instead of working with the whole unitary group in $n$ qubits, we identify a small Lie group $G$ in $(n+3)$ qubits. The dimension of its Lie algebra is $\text{poly}(n)$. Every state can be approximated starting from an...
Ji-Hong Cai, Advith Govindarajan, M. Junge· 0 citations
We study both the classical and the quantum complexity of the problem of estimating disorder-averaged quench dynamics for all-to-all spin Hamiltonians such as quantum Hopfield, Sherrington--Kirkpatrick (SK) or Dicke-type models. Disorder averaging restores permutation invariance in this setting, so states of $N$ spins...
Maximilian Lutz, Rahul Trivedi, J. I. Cirac· 0 citations
It is shown how this algorithm is able to take advantage of emerging dynamical circuit capabilities in near-term hardware to roughly halve the number required qubits, as well as how quantum readout error mitigation is trivial for this method.
Graham Van Goffrier, Debasish Banerjee, Bipasha Chakraborty et al.· 0 citations
We introduce a distinct route for extending classical atomistic spin dynamics into the quantum regime for arbitrary spin $s$, based on a variational product-state \textit{ansatz} that includes both pure and mixed local states. By construction, intersite entanglement -- expected to remain negligible even on very short t...
The output state of a 2D geometrically local shallow random quantum circuit does not have long range correlations due to its lightcone structure. But this changes if one measures a subset of the qubits: long-range entanglement can be induced by the measurement process, leading to conditional correlations between distan...
Yin-Chen Liu, Max McGinley, T. Schuster et al.· 6 citations
Quantum state preparation is a basic primitive of quantum computation and control, but its resource cost is usually analyzed for one target state or under an independent-copy construction. Here we study the many-copy problem under weighted Pauli control, where a Pauli-product rotation $e^{i\phi P}$ is charged by its ro...
Lin Zhu, Ranyiliu Chen, Xin Wang et al.· 0 citations
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