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  • We propose a non-commutative extension of the Pauli stabilizer formalism. The aim is to describe a class of many-body quantum states which is richer than the standard Pauli stabilizer states. In our framework, stabilizer operators are tensor products of single-qubit operators drawn from the group $\langle \alpha I, X,S\rangle$, where $\alpha=e^{i\pi/4}$ and $S=\operatorname{diag}(1,i)$. We provide techniques to efficiently compute various properties related to bipartite entanglement, expectation values of local observables, preparation by means of quantum circuits, parent Hamiltonians etc. We also highlight significant differences compared to the Pauli stabilizer formalism. In particular, we give examples of states in our formalism which cannot arise in the Pauli stabilizer formalism, such as topological models that support non-Abelian anyons.
  • Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here I show that for suitable topological stabilizer codes, such as gauge color codes, a single round is indeed enough. This feature is generic and is related to self-correction in the corresponding quantum Hamiltonian model.
  • Recently, it was shown that Repeat-Until-Success (RUS) circuits can achieve a $2.5$ times reduction in expected $T$-count over ancilla-free techniques for single-qubit unitary decomposition. However, the previously best known algorithm to synthesize RUS circuits requires exponential classical runtime. In this paper we present an algorithm to synthesize an RUS circuit to approximate any given single-qubit unitary within precision $\varepsilon$ in probabilistically polynomial classical runtime. Our synthesis approach uses the Clifford+$T$ basis, plus one ancilla qubit and measurement. We provide numerical evidence that our RUS circuits have an expected $T$-count on average $2.5$ times lower than the theoretical lower bound of $3 \log_2 (1/\varepsilon)$ for ancilla-free single-qubit circuit decomposition.
  • Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise. Previous work tackling this problem has relied on the original circuit model for quantum computing. However, recently a family of entangled resources known as graph states has emerged as a versatile alternative for protecting quantum information. Depending on the graph's structure, errors can be detected and corrected in an efficient way using measurement-based techniques. In this article we report an experimental demonstration of error correction using a graph state code. We have used an all-optical setup to encode quantum information into photons representing a four-qubit graph state. We are able to reliably detect errors and correct against qubit loss. The graph we have realized is setup independent, thus it could be employed in other physical settings. Our results show that graph state codes are a promising approach for achieving scalable quantum information processing.
  • Quantum spin ice represents a paradigmatic example on how the physics of frustrated magnets is related to gauge theories. In the present work we address the problem of approximately realizing quantum spin ice in two dimensions with cold atoms in optical lattices. The relevant interactions are obtained by weakly admixing van der Waals interactions between laser admixed Rydberg states to the atomic ground state atoms, exploiting the strong angular dependence of interactions between Rydberg p-states together with the possibility of designing step-like potentials. This allows us to implement Abelian gauge theories in a series of geometries, which could be demonstrated within state of the art atomic Rydberg experiments. We numerically analyze the family of resulting microscopic Hamiltonians and find that they exhibit both classical and quantum order by disorder, the latter yielding a quantum plaquette valence bond solid. We also present strategies to implement Abelian gauge theories using both s- and p-Rydberg states in exotic geometries, e.g. on a 4-8 lattice.
  • It has been known since long time that many NP-hard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results to the quantum setting. We show that given a quantum circuit $C$ with $n$ uninitialized inputs, $poly(n)$ gates and treewidth $t$, one can compute in time $(\frac{n}{\delta})^{\exp(O(t))}$ a classical witness $y\in \{0,1\}^n$ that maximizes the acceptance probability of $C$ up to a $\delta$ additive factor. In particular our algorithm runs in polynomial time if $t$ is constant and $1/poly(n) \leq \delta < 1$. For unrestricted values of $t$ this problem is known to be hard for the complexity class QCMA, a quantum generalization of NP. In contrast, we show that the same problem is already NP-hard if $t=O(\log n)$ even when $\delta$ is constant. Finally, we show that for $t=O(\log n)$ and constant $\delta$, it is QMA-hard to find a quantum witness $\ket{\varphi}$ that maximizes the acceptance probability of a quantum circuit of treewidth $t$ up to a $\delta$ additive factor.
  • We show how two distrustful parties, "Bob" and "Charlie", can share a secret key with the help of a mutually trusted "Alice", counterfactually - that is with no information-carrying particles travelling between any of the three parties.
  • Unphysical particles are commonly ruled out from the solution of physical equations, as they fundamentally cannot exist in any real system and, hence, cannot be examined experimentally in a direct fashion. One of the most celebrated equations that allows unphysical solutions is the relativistic Majorana equation\citeMajorana which might describe neutrinos and other exotic particles beyond the Standard Model. The equation's physical solutions, the Majorana fermions, are predicted to be their own anti-particles and as a consequence they have to be neutrally charged; the charged version however (called Majoranon) is, due to charge non-conservation, unphysical and cannot exist. On the other hand, charge conservation violation has been contemplated in alternative theories associated with higher spacetime dimensions or a non-vanishing photon mass; theories whose exotic nature makes experimental testing with current technology an impossible task. In our work, we present an experimental scheme based on optics with which we simulate the dynamics of a Majoranon, involving the implementation of unphysical charge conjugation and complex conjugation. We show that the internal dynamics of the Majoranon is fundamentally different from that of its close cousin, the Dirac particle, to illustrate the nature of the unphysical operations. For this we exploit the fact that in quantum mechanics the wave function itself is not a measurable quantity. Therefore, wave functions of real physical particles, in our case Dirac particles with opposite masses, can be superposed to a wave function of an unphysical particle, the Majoranon. Our results open a new front in the field of quantum simulations of exotic phenomena, with possible applications in condensed matter physics, topological quantum computing, and testing theories within and beyond the Standard Model with existing technology.
  • We study holographic entanglement entropy of non-local field theories both at extremality and finite temperature. The gravity duals, constructed in arXiv:1208.3469 [hep-th], are characterized by a parameter $w$. Both the zero temperature backgrounds and the finite temperature counterparts are exact solutions of Einstein-Maxwell-dilaton theory. For the extremal case we consider the examples with the entangling regions being a strip and a sphere. We find that the leading order behavior of the entanglement entropy always exhibits a volume law when the size of the entangling region is sufficiently small. We also clarify the condition under which the next-to-leading order result is universal. For the finite temperature case we obtain the analytic expressions both in the high temperature limit and in the low temperature limit. In the former case the leading order result approaches the thermal entropy, while the finite contribution to the entanglement entropy at extremality can be extracted by taking the zero temperature limit in the latter case. Moreover, we observe some peculiar properties of the holographic entanglement entropy when $w=1$.
  • We present the calculation of all non-planar master integrals that are needed to describe production of two off-shell vector bosons in collisions of two massless partons through NNLO in perturbative QCD. The integrals are computed analytically using differential equations in external kinematic variables and expressed in terms of Goncharov polylogarithms. These results provide the last missing ingredient needed for the computation of two-loop amplitudes that describe the production of two gauge bosons with different invariant masses in hadron collisions.
  • The microscopic modeling of spin-orbit entangled $j=1/2$ Mott insulators such as the layered hexagonal Iridates Na$_2$IrO$_3$ and Li$_2$IrO$_3$ has spurred an interest in the physics of Heisenberg-Kitaev models. Here we explore the effect of lattice distortions on the formation of the collective spin-orbital states which include not only conventionally ordered phases but also gapped and gapless spin-orbital liquids. In particular, we demonstrate that in the presence of spatial anisotropies of the exchange couplings conventionally ordered states are formed through an order-by-disorder selection which is not only sensitive to the type of exchange anisotropy but also to the relative strength of the Heisenberg and Kitaev couplings. The spin-orbital liquid phases of the Kitaev limit -- a gapless phase in the vicinity of spatially isotropic couplings and a gapped Z$_2$ phase for a dominant spatial anisotropy of the exchange couplings -- show vastly different sensitivities to the inclusion of a Heisenberg exchange. While the gapless phase is remarkably stable, the gapped Z$_2$ phase quickly breaks down in what might be a rather unconventional phase transition driven by the simultaneous condensation of its elementary excitations.
  • Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions, one of the most robust continuous transitions known. We present a very brief overview of more than 60 years of work in this area and discuss several open questions for a variety of models, including classical, explosive, invasion, bootstrap, and correlated percolation.
  • We harness general relativistic effects to gain quantum control on a stationary qubit in an optical cavity by controlling the non-inertial motion of a different probe atom. Furthermore, we show that by considering relativistic trajectories of the probe, we enhance the efficiency of the quantum control. We explore the possible use of these relativistic techniques to build universal quantum gates.
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Recent comments

Piotr Migdał 5 days ago
A podcast summarizing this paper, by Geoff Engelstein: [The Dice Tower # 351 - Dealing with the Mockers (43:55 - 50:36)](, and [an alternative link on the BoardGameGeek]( ...(continued)
Matt Hastings 15 days ago
Glad the coarse-graining is clear now. Regarding separating out a qubit, my claim is not just that if sites 1,N are in a pure state one can separate out a qubit. I also claim that even if sites 1,N are in a mixed state of the form $\sum_{\text{correctable errors} E_1 \text{and} E_2} p(E_1,E_2) E_1 ...(continued)
Ari Mizel 15 days ago
Thanks for clearing things up about the definition of coarse-graining; I guess I thought the name suggested some kind of real-space renormalization. About separating out a qubit: I wrote that one expects "the result to be close to a mixed state like $∑_{\text{correctable errors } E_1 \text{ and } ...(continued)
Matt Hastings 16 days ago
Hi Ari, let me reply to your second point first, since I think there may be a misunderstanding about "coarse-graining". If we mistakenly treated the polylog chains as a single spin-1/2 chain, this would give an incorrect result, but I certainly did not suggest doing anything like that. Instead,if ...(continued)
Ari Mizel 16 days ago
Matt, I still take issue with the coarse-graining approach. 1) You wrote "When we say "close to maximal entanglement", we mean we can separate out a qubit from coarse-grained spin 1 and a qubit from coarse-grained spin N (let me stick to my notation) and those two qubits are close to maximally enta ...(continued)
Matt Hastings 19 days ago
One can indeed always ask this coarse-graining question, and one important issue is how strong the resulting interactions are. The coarse-graining itself is definitely well-defined, the question is whether one correctly treats the resulting 1d system. In this case, there is a variational argument ...(continued)
Ari Mizel 19 days ago
You raise an interesting question. It can perhaps be simplified slightly by imagining a quantum circuit that initializes 2 qubits to |0>, generates an EPR pair between qubits 1 and 2, then applies N-1 identity gates to qubit 2. The circuit can be turned into a fault-tolerant version of itself, and ...(continued)
Matt Hastings 20 days ago
I am curious about the following setting. Consider a quantum circuit that initializes N qubits to |0>, then generates an EPR pair in qubits 1 and 2, and then applies SWAPs to move the qubit from 2 to 3 to 4 to ... to N, leaving ultimately an EPR pair between 1 and N. This can be turned into some f ...(continued)
Jarrod McClean 21 days ago
Ryan is exactly correct. The method would work with any of the clock constructions, however we decided that the machinery they developed to make sure it was implementable in qubits was unnecessary overhead for a classical implementation, where having a qudit with large d does not present a great ch ...(continued)
Ari Mizel 21 days ago
Thanks for the remark, Steve. I do not have additional numerics, but I don't think that the translational invariance plays an important role in the spin-wave form of the excitations. I think that the local excitations approximately satisfy a tight-binding Hamiltonian with hopping between adjacent ...(continued)