Direct certification of a class of quantum simulations

One of the main challenges in the field of quantum simulation and computation is to identify ways to certify the correct functioning of a device when a classical efficient simulation is not available. Important cases are situations in which one cannot classically calculate local expectation values of state preparations efficiently. In this work, we develop weak-membership formulations of the certification of ground state preparations. We provide a non-interactive protocol for certifying ground states of frustration-free Hamiltonians based on simple energy measurements of local Hamiltonian terms. This certification protocol can be applied to classically intractable analog quantum simulations: For example, using Feynman-Kitaev Hamiltonians, one can encode universal quantum computation in such ground states. Moreover, our certification protocol is applicable to ground states encodings of IQP circuits demonstration of quantum supremacy. These can be certified efficiently when the error is polynomially bounded.Comment: 10 pages, corrected a small error in Eqs. (2) and (5

Reliable quantum certification for photonic quantum technologies

A major roadblock for large-scale photonic quantum technologies is the lack of practical reliable certification tools. We introduce an experimentally friendly - yet mathematically rigorous - certification test for experimental preparations of arbitrary m-mode pure Gaussian states, pure non-Gaussian states generated by linear-optical circuits with n-boson Fock-basis states as inputs, and states of these two classes subsequently post-selected with local measurements on ancillary modes. The protocol is efficient in m and the inverse post-selection success probability for all Gaussian states and all mentioned non-Gaussian states with constant n. We follow the mindset of an untrusted prover, who prepares the state, and a skeptic certifier, with classical computing and single-mode homodyne-detection capabilities only. No assumptions are made on the type of noise or capabilities of the prover. Our technique exploits an extremality-based fidelity bound whose estimation relies on non-Gaussian state nullifiers, which we introduce on the way as a byproduct result. The certification of many-mode photonic networks, as those used for photonic quantum simulations, boson samplers, and quantum metrology, is now within reach.Comment: 8 pages + 20 pages appendix, 2 figures, results generalized to scenarios with post-selection, presentation improve

Locality of temperature

This work is concerned with thermal quantum states of Hamiltonians on spin and fermionic lattice systems with short range interactions. We provide results leading to a local definition of temperature, thereby extending the notion of "intensivity of temperature" to interacting quantum models. More precisely, we derive a perturbation formula for thermal states. The influence of the perturbation is exactly given in terms of a generalized covariance. For this covariance, we prove exponential clustering of correlations above a universal critical temperature that upper bounds physical critical temperatures such as the Curie temperature. As a corollary, we obtain that above the critical temperature, thermal states are stable against distant Hamiltonian perturbations. Moreover, our results imply that above the critical temperature, local expectation values can be approximated efficiently in the error and the system size.Comment: 11 pages + 6 pages appendix, 6 figures; proof of the clustering theorem corrected, improved presentatio

Fidelity Witnesses for Fermionic Quantum Simulations

The experimental interest and developments in quantum spin-1/2 chains has increased uninterruptedly over the past decade. In many instances, the target quantum simulation belongs to the broader class of noninteracting fermionic models, constituting an important benchmark. In spite of this class being analytically efficiently tractable, no direct certification tool has yet been reported for it. In fact, in experiments, certification has almost exclusively relied on notions of quantum state tomography scaling very unfavorably with the system size. Here, we develop experimentally friendly fidelity witnesses for all pure fermionic Gaussian target states. Their expectation value yields a tight lower bound to the fidelity and can be measured efficiently. We derive witnesses in full generality in the Majorana-fermion representation and apply them to experimentally relevant spin-1/2 chains. Among others, we show how to efficiently certify strongly out-of-equilibrium dynamics in critical Ising chains. At the heart of the measurement scheme is a variant of importance sampling specially tailored to overlaps between covariance matrices. The method is shown to be robust against finite experimental-state infidelities

NP-Hardness and Undecidability

Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed- matter physics, as well as in mathematical physics. This is specifically true for finitely correlated states or matrix-product operators, designed to capture mixed states of one-dimensional quantum systems. It is a well-known open problem to find an efficient algorithm that decides whether a given matrix-product operator actually represents a physical state that in particular has no negative eigenvalues. We address and answer this question by showing that the problem is provably undecidable in the thermodynamic limit and that the bounded version of the problem is NP-hard (nondeterministic- polynomial-time hard) in the system size. Furthermore, we discuss numerous connections between tensor network methods and (seemingly) different concepts treated before in the literature, such as hidden Markov models and tensor trains

Immunohistochemical characterization of the anti-Müllerian hormone receptor type 2 (AMHR-2) in human testes

Purpose In males, AMH is secreted by immature Sertoli cells; following exposure to endogenous androgens, Sertoli cells undergo a process of maturation which ultimately inhibits AMH expression to undetectable levels in the serum. However, expression of AMH receptor (AMHR-2) has never been studied in human testes, and high intratubular concentrations of AMH have been reported in recent literature. We therefore assessed expression of AMHR-2 in several testicular tissue samples by immunohistochemistry (IHC). Methods The IHC method was first validated on tissue samples from healthy human testis (n = 2) and from marmoset ovary (n = 1). The same method was then used for assessment on testicular histopathology specimens from patients with mixed atrophy (MA, n = 2), spermatogenetic arrest (SA, n = 2), Sertoli cell-only syndrome (SCO, n = 1), Klinefelter syndrome (KS, n = 1), and nonseminomatous germ cell tumors (NSGCT, n = 1). Tissue samples from two subjects at different pubertal stages (AndroProtect (AP), aged 5 and 14 years) with hematological malignancies were also retrieved. Results In adult men, AMHR-2 was expressed on peritubular mesenchymal cells, with patterns closely mirroring alpha-smooth muscle actin expression. Similar patterns were preserved in almost all conditions; however, in nonseminomatous germ cell tumors the tissue architecture was lost, including AMHR-2 expression. More positive and diffuse staining was observed in tissue samples from prepubertal testes. Conclusions In specimens from both healthy and affected testes, AMHR-2 expression appears weaker in adult than in prepubertal tissue sections. The persistence of AMHR-2 expression seemingly hints at a possible effect of intratesticular AMH on the tubular walls

Serum concentrations of dihydrotestosterone are associated with symptoms of hypogonadism in biochemically eugonadal men

Purpose Symptoms of hypogonadism are often reported by subjects with normal serum testosterone (T) levels. We aimed to assess the association between clinical symptoms in andrological outpatients and sex steroids levels. Methods This is a retrospective cross-sectional cohort study in an Academic clinic and research unit. International Index of Erectile Function (IIEF, EF domain) and Aging Males Symptoms scale (AMS) questionnaires were completed by 635 and 574 men, respectively (mean age: 47.3 ± 13.9 and 47.4 ± 13.8 years, p = 0.829), free of interfering medications with complaints possibly related to hypogonadism. Results Serum total/free T as well as dihydro-T (DHT) was associated with IIEF-EF and AMS scores in the overall population using univariate analyses. Multivariate approaches revealed DHT concentrations in subjects with normal T levels (n = 416, Total T > 12 nmol/L) to be significant predictors of AMS scores. A 0.1 nmol/l serum DHT increase within the eugonadal range was associated with a 4.67% decrease in odds of having worse symptoms (p = 0.011). In men with biochemical hypogonadism (Total T < 12 nmol/L), total and free T rather than DHT were associated with AMS results. This association was not found for IIEF-EF scores. Indirect effects of age and BMI were seen for relations with hormone concentrations but not questionnaire scores. Conclusion DHT can be associated with symptoms of hypogonadism in biochemically eugonadal men. Serum DHT measurement might be helpful once the diagnosis of hypogonadism has been ruled out but should not be routinely included in the primary diagnostic process