Quantum error mitigation via quantum-noise-effect circuit groups.

Near-term quantum computers have been built as intermediate-scale quantum devices and are fragile against quantum noise effects, namely, NISQ devices. Traditional quantum-error-correcting codes are not implemented on such devices and to perform quantum computation in good accuracy with these machines we need to develop alternative approaches for mitigating quantum computational errors. In this work, we propose quantum error mitigation (QEM) scheme for quantum computational errors which occur due to couplings with environments during gate operations, i.e., decoherence. To establish our QEM scheme, first we estimate the quantum noise effects on single-qubit states and represent them as groups of quantum circuits, namely, quantum-noise-effect circuit groups. Then our QEM scheme is conducted by subtracting expectation values generated by the quantum-noise-effect circuit groups from those obtained by the quantum circuits for the quantum algorithms under consideration. As a result, the quantum noise effects are reduced, and we obtain approximately the ideal expectation values via the quantum-noise-effect circuit groups and the numbers of elementary quantum circuits composing them scale polynomial with respect to the products of the depths of quantum algorithms and the numbers of register bits. To numerically demonstrate the validity of our QEM scheme, we run noisy quantum simulations of qubits under amplitude damping effects for four types of quantum algorithms. Furthermore, we implement our QEM scheme on IBM Q Experience processors and examine its efficacy. Consequently, the validity of our scheme is verified via both the quantum simulations and the quantum computations on the real quantum devices. Our QEM scheme is solely composed of quantum-computational operations (quantum gates and measurements), and thus, it can be conducted by any type of quantum device. In addition, it can be applied to error mitigation for many other types of quantum noise effects as well as noisy quantum computing of long-depth quantum algorithms.

Systematic study on the dependence of the warm-start quantum approximate optimization algorithm on approximate solutions.

Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm to solve combinatorial optimization problems in the era of noisy intermediate-scale quantum computers. Recently it has been revealed that warm-start approaches can improve the performance of QAOA, where approximate solutions are obtained by classical algorithms in advance and incorporated into the initial state and/or unitary ansatz. In this work, we study in detail how the accuracy of approximate solutions affects the performance of the warm-start QAOA (WS-QAOA). We numerically find that in typical MAX-CUT problems, WS-QAOA achieves higher fidelity (probability that exact solutions are observed) and approximation ratio than QAOA as the Hamming distance of approximate solutions to the exact ones becomes smaller. We reveal that this could be quantitatively attributed to the initial state of the ansatz. We also solve MAX-CUT problems by WS-QAOA with approximate solutions obtained via QAOA, having higher fidelity and approximation ratio than QAOA especially when the circuit is relatively shallow. We believe that our study may deepen understanding of the performance of WS-QAOA and also provide a guide as to the necessary quality of approximate solutions.

Quasiparticle energy spectra of isolated atoms from coupled-cluster singles and doubles (CCSD): Comparison with exact CI calculations.

In this study, we have calculated single-electron energy spectra via the Green's function based on the coupled-cluster singles and doubles (GFCCSD) method for isolated atoms from H to Ne. In order to check the accuracy of the GFCCSD method, we compared the results with the exact ones calculated from the full-configuration interaction. Consequently, we have found that the GFCCSD method reproduces not only the correct quasiparticle peaks but also satellite ones by comparing the exact spectra with the 6-31G basis set. It is also found that open-shell atoms such as C atom exhibit Mott gaps at the Fermi level, which the exact density-functional theory fails to describe. The GFCCSD successfully reproduces the Mott highest-occupied molecular orbital and lowest-unoccupied molecular orbital gaps even quantitatively. We also discussed the origin of satellite peaks as shake-up effects by checking the components of wave function of the satellite peaks. The GFCCSD is a novel cutting edge to investigate the electronic states in detail.

Comparison of Green's functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD).

We demonstrate in the present study that self-consistent calculations based on the self-energy functional theory (SFT) are possible for the electronic structure of realistic systems in the context of quantum chemistry. We describe the procedure of a self-consistent SFT calculation in detail and perform the calculations for isolated 3d transition metal atoms from V to Cu as a preliminary study. We compare the one-particle Green's functions obtained in this way and those obtained from the coupled-cluster singles and doubles method. Although the SFT calculation starts from the spin-unpolarized Hartree-Fock state for each of the target systems, the self-consistency loop correctly leads to degenerate spin-polarized ground states. We examine the spectral functions in detail to find their commonalities and differences among the atoms by paying attention to the characteristics of the two approaches. It is demonstrated via the two approaches that calculations based on the density functional theory (DFT) can fail in predicting the orbital energy spectra for spherically symmetric systems. It is found that the two methods are quite reliable and useful beyond DFT.

Band structures in coupled-cluster singles-and-doubles Green's function (GFCCSD).

We demonstrate that the coupled-cluster singles-and-doubles Green's function (GFCCSD) method is a powerful and prominent tool drawing the electronic band structures and the total energies, which many theoretical techniques struggle to reproduce. We have calculated single-electron energy spectra via the GFCCSD method for various kinds of systems, ranging from ionic to covalent and van der Waals, for the first time: the one-dimensional LiH chain, one-dimensional C chain, and one-dimensional Be chain. We have found that the bandgap becomes narrower than in HF due to the correlation effect. We also show that the band structures obtained from the GFCCSD method include both quasiparticle and satellite peaks successfully. Besides, taking one-dimensional LiH as an example, we discuss the validity of restricting the active space to suppress the computational cost of the GFCCSD method. We show that the calculated results without bands that do not contribute to the chemical bonds are in good agreement with full-band calculations. With the GFCCSD method, we can calculate the total energies and spectral functions for periodic systems in an explicitly correlated manner.

Phenotypic expression of a novel desmin gene mutation: hypertrophic cardiomyopathy followed by systemic myopathy.

Hypertrophic cardiomyopathy is a heterogeneous disease caused by gene mutations. Most of the disease-causing mutations were found in the genes for sarcomeric proteins, but there are several cases carrying mutations in genes for extra-sarcomeric cytoskeletons. Desmin is a member of extra-sarcomeric cytoskeletons and plays an important role in muscle contraction. Mutations in the desmin gene cause various type of general myopathy and/or cardiomyopathy, known as desmin-related myopathies. We identified a novel desmin missense mutation, Thr219Pro, in the homozygous state in a patient, who first manifested with hypertrophic cardiomyopathy and later progressed to general myopathy. His parents were heterozygous for the mutation, but showed no clinical abnormality, suggesting the recessive inheritance of the mutation. We here report a severe phenotype of hypertrophic cardiomyopathy preceded the onset of general myopathy caused by a novel homozygous missense mutation in the 1B α-helix domain of desmin.

Cardiac ankyrin repeat protein gene (ANKRD1) mutations in hypertrophic cardiomyopathy.

OBJECTIVES: The purpose of this study was to explore a novel disease gene for hypertrophic cardiomyopathy (HCM) and to evaluate functional alterations caused by mutations. BACKGROUND: Mutations in genes encoding myofilaments or Z-disc proteins of the cardiac sarcomere cause HCM, but the disease-causing mutations can be found in one-half of the patients, indicating that novel HCM-susceptibility genes await discovery. We studied a candidate gene, ankyrin repeat domain 1 (ANKRD1), encoding for the cardiac ankyrin repeat protein (CARP) that is a Z-disc component interacting with N2A domain of titin/connectin and N-terminal domain of myopalladin. METHODS: We analyzed 384 HCM patients for mutations in ANKRD1 and in the N2A domain of titin/connectin gene (TTN). Interaction of CARP with titin/connectin or myopalladin was investigated using coimmunoprecipitation assay to demonstrate the functional alteration caused by ANKRD1 or TTN mutations. Functional abnormalities caused by the ANKRD1 mutations were also examined at the cellular level in neonatal rat cardiomyocytes. RESULTS: Three ANKRD1 missense mutations, Pro52Ala, Thr123Met, and Ile280Val, were found in 3 patients. All mutations increased binding of CARP to both titin/connectin and myopalladin. In addition, TTN mutations, Arg8500His, and Arg8604Gln in the N2A domain were found in 2 patients, and these mutations increased binding of titin/connectin to CARP. Myc-tagged CARP showed that the mutations resulted in abnormal localization of CARP in cardiomyocytes. CONCLUSIONS: CARP abnormalities may be involved in the pathogenesis of HCM.

L-Maf regulates p27kip1 expression during chick lens fiber differentiation.

Organ formation requires spatio-temporal proliferation and differentiation of precursor cells. During lens development, placodal cells in the posterior lens vesicle exit from the cell cycle and enter into the process of differentiation. Cyclin-dependent kinase inhibitors play critical roles in cell cycle exit and promote differentiation in several tissues. We have found that p27kip1 is expressed in the posterior lens cells that undergo differentiation to form the differentiated fiber cells. The transcription factor L-Maf is expressed in these cells earlier than p27kip1. From in ovo gain- or loss-of-function experiments, we have found that L-Maf can, respectively, induce or inhibit the expression of p27kip1 in lens cells. Promoter assays using the 5' upstream sequences of the human p27kip1 gene indicate that L-Maf can activate p27kip1 transcription through the basal regulatory region. We suggest that L-Maf regulates cell cycle exit of the posterior lens cells by activating p27kip1, and thus directs fiber cell differentiation during lens formation in chick.

Tcap gene mutations in hypertrophic cardiomyopathy and dilated cardiomyopathy.

OBJECTIVES: We sought to explore the relationship between a Tcap gene (TCAP) abnormality and cardiomyopathy. BACKGROUND: Hypertrophic cardiomyopathy (HCM) and dilated cardiomyopathy (DCM) cause severe heart failure and sudden death. Recent genetic investigations have revealed that mutations of genes encoding Z-disc components, including titin and muscle LIM protein (MLP), are the primary cause of both HCM and DCM. The Z-disc plays a role in establishing the mechanical coupling of sarcomeric contraction and stretching, with the titin/Tcap/MLP complex serving as a mechanical stretch sensor. Tcap interacts with the calsarcin, which tethers the calcineurin to the Z-disc. METHODS: The TCAP was analyzed in 346 patients with HCM (236 familial and 110 sporadic cases) and 136 patients with DCM (34 familial and 102 sporadic cases). Two different in vitro qualitative assays-yeast two-hybrid and glutathion S-transferase pull-down competition-were performed in order to investigate functional changes in Tcap's interaction with MLP, titin, and calsarcin-1 caused by the identified mutations and a reported DCM-associated mutation, R87Q. RESULTS: Two TCAP mutations, T137I and R153H, were found in patients with HCM, and another TCAP mutation, E132Q, was identified in a patient with DCM. It was demonstrated by the qualitative assays that the HCM-associated mutations augment the ability of Tcap to interact with titin and calsarcin-1, whereas the DCM-associated mutations impair the interaction of Tcap with MLP, titin, and calsarcin-1. CONCLUSIONS: These observations suggest that the difference in clinical phenotype (HCM or DCM) may be correlated with the property of altered binding among the Z-disc components.

Genomic structure and eight novel exonic polymorphisms of the human N-cadherin gene.

Analysis of the detailed genomic structure of human N-cadherin revealed that the 16-exon gene is more than 72 kb in length and that it consists of a mosaic of exons. Five repeated cadherin domains, a transmembrane domain, and a cytoplasmic domain are encoded by exons 4 to 13, 13 and 14, and 14 to 16, respectively. A search for molecular variants in the entire coding region in 96 Japanese individuals resulted in the identification of eight sequence polymorphisms including three CCT- or GCC-type trinucleotide repeat polymorphisms adjacent to the initiation codon and five other novel single-nucleoticle polymorphisms (SNPs) in the coding region. Three of the five SNPs accompanied an amino acid substitution: Ala118Thr, Ala826Thr, and Asn845Ser. Knowlege of the fine gene structure and eight novel polymorphisms will be useful for the genetic study of the role of N-cadherin in diseases involving cell adhesion in the brain and in cardiomyocytes.

Titin mutations as the molecular basis for dilated cardiomyopathy.

Dilated cardiomyopathy (DCM) is a heterogeneous cardiac disease characterized by ventricular dilatation and systolic dysfunction. Recent genetic studies have revealed that mutations in genes for cardiac sarcomere components lead to DCM. The cardiac sarcomere consists of thick and thin filaments and a giant protein, titin. Because one of the loci of familial DCM was mapped to the region of the titin gene, we searched for titin mutations in the patients and identified four possible disease-associated mutations. Two mutations, Val54Met and Ala743Val, were found in the Z-line region of titin and decreased binding affinities of titin to Z-line proteins T-cap/telethonin and alpha-actinin, respectively, in yeast two-hybrid assays. The other two mutations were found in the cardiac-specific N2-B region of titin and one of them was a nonsense mutation, Glu4053ter, presumably encoding for a truncated nonfunctional molecule. These observations suggest that titin mutations may cause DCM in a subset of the patients.