Related papers: Understanding Stabilizer Codes Under Local Decoher…
We generalize the proof of stability of topological order, due to Bravyi, Hastings and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity check (LDPC) codes without the restriction of geometric locality in Euclidean…
Protecting information in systems that have more than two basis states (qudits) not only offers a promising route for reducing the number of individual quantum locations that must be protected, while more accurately reflecting the structure…
Multi-parameter statistical models may depend only on some functions of the parameters that are fewer than the number of initial parameters themselves. Such \emph{sloppy} statistical models are characterized by a degenerate Fisher…
We study properties of stabilizer codes that permit a local description on a regular D-dimensional lattice. Specifically, we assume that the stabilizer group of a code (the gauge group for subsystem codes) can be generated by local Pauli…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…
The challenge of quantum computing is to combine error resilience with universal computation. Diagonal gates such as the transversal $T$ gate play an important role in implementing a universal set of quantum operations. This paper…
The Local Hamiltonian problem (finding the ground state energy of a quantum system) is known to be QMA-complete. The Local Consistency problem (deciding whether descriptions of small pieces of a quantum system are consistent) is also known…
We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated…
A dynamical signature of localization in quantum systems is the absence of transport which is governed by the amount of coherence that configuration space states possess with respect to the Hamiltonian eigenbasis. To make this observation…
Protecting quantum information from the detrimental effects of decoherence and lack of precise quantum control is a central challenge that must be overcome if a large robust quantum computer is to be constructed. The traditional approach to…
Dynamical stabilizer codes may offer a practical route to large-scale quantum computation. Such codes are defined by a schedule of error-detecting measurements, which allows for flexibility in their construction. In this work, we ask how…
The decay of the overlap between a wave packet evolved with a Hamiltonian H and the same state evolved with H}+$\Sigma $ serves as a measure of the decoherence time $\tau_{\phi}$. Recent experimental and analytical evidence on classically…
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum…
In the absence of fault tolerant quantum error correction for analog, Hamiltonian quantum computation, error suppression via energy penalties is an effective alternative. We construct families of distance-$2$ stabilizer subsystem codes we…
A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable…
In this work, we study the Hamiltonian Decoded Quantum Interferometry (HDQI) for the general Hamiltonians $H=\sum_ic_iP_i$ on an $n$-qubit system, where the coefficients $c_i\in \mathbb{R}$ and $P_i$ are Pauli operators. We show that, given…
Quantum error correction requires accurate and efficient decoding to optimally suppress errors in the encoded information. For concatenated codes, where one code is embedded within another, optimal decoding can be achieved using a…
Estimating many-body Hamiltonians has wide applications in quantum technology. By allowing coherent evolution of quantum systems and entanglement across multiple probes, the precision of estimating a fully connected $k$-body interaction can…
Topological quantum error correcting codes have emerged as leading candidates towards the goal of achieving large-scale fault-tolerant quantum computers. However, quantifying entanglement in these systems of large size in the presence of…