Phase transitions in random circuit sampling.

Undesired coupling to the surrounding environment destroys long-range correlations in quantum processors and hinders coherent evolution in the nominally available computational space. This noise is an outstanding challenge when leveraging the computation power of near-term quantum processors1. It has been shown that benchmarking random circuit sampling with cross-entropy benchmarking can provide an estimate of the effective size of the Hilbert space coherently available2-8. Nevertheless, quantum algorithms' outputs can be trivialized by noise, making them susceptible to classical computation spoofing. Here, by implementing an algorithm for random circuit sampling, we demonstrate experimentally that two phase transitions are observable with cross-entropy benchmarking, which we explain theoretically with a statistical model. The first is a dynamical transition as a function of the number of cycles and is the continuation of the anti-concentration point in the noiseless case. The second is a quantum phase transition controlled by the error per cycle; to identify it analytically and experimentally, we create a weak-link model, which allows us to vary the strength of the noise versus coherent evolution. Furthermore, by presenting a random circuit sampling experiment in the weak-noise phase with 67 qubits at 32 cycles, we demonstrate that the computational cost of our experiment is beyond the capabilities of existing classical supercomputers. Our experimental and theoretical work establishes the existence of transitions to a stable, computationally complex phase that is reachable with current quantum processors.

Formation of robust bound states of interacting microwave photons.

Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2-9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

Stable quantum-correlated many-body states through engineered dissipation.

Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.

Dynamics of magnetization at infinite temperature in a Heisenberg spin chain.

Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain's center, [Formula: see text]. The first two moments of [Formula: see text] show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments ruled out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide insights into universal behavior in quantum systems.

Noise-resilient edge modes on a chain of superconducting qubits.

Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model, which exhibits nonlocal Majorana edge modes (MEMs) with [Formula: see text] parity symmetry. We find that any multiqubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment.

Magnetic resonance spectroscopy of an atomically thin material using a single-spin qubit.

Two-dimensional (2D) materials offer a promising platform for exploring condensed matter phenomena and developing technological applications. However, the reduction of material dimensions to the atomic scale poses a challenge for traditional measurement and interfacing techniques that typically couple to macroscopic observables. We demonstrate a method for probing the properties of 2D materials via nanometer-scale nuclear quadrupole resonance (NQR) spectroscopy using individual atomlike impurities in diamond. Coherent manipulation of shallow nitrogen-vacancy (NV) color centers enables the probing of nanoscale ensembles down to approximately 30 nuclear spins in atomically thin hexagonal boron nitride (h-BN). The characterization of low-dimensional nanoscale materials could enable the development of new quantum hybrid systems, combining atomlike systems coherently coupled with individual atoms in 2D materials.

Screening for germ line TP53 mutations in breast cancer patients.

The constant denaturant gel electrophoresis technique was used to screen for TP53 germ line mutations in 237 women with breast carcinoma (167 unselected patients, 30 patients with at least one first-degree relative with breast cancer, and 40 women diagnosed with breast cancer before age 35). A germ line mutation at codon 181 was noted in one of the unselected patients and a codon 245 mutation in one of the early-onset patients. Both had a family history of breast cancer and other malignancies suggestive of Li-Fraumeni syndrome. The codon 245 mutation was also present in this patient's affected mother.

Genomic instability in colorectal cancer: relationship to clinicopathological variables and family history.

Recent reports have suggested that one or more genes may cause replication errors (RER) during colorectal tumorigenesis. Additional alleles are seen in the tumors when analyzing random microsatellite loci. We have studied seven dinucleotide repeat loci, located on seven different chromosomes, by use of polymerase chain reaction amplification and denaturing polyacrylamide gel electrophoresis. We found that 16.5% (40 of 243) colorectal cancers showed RER at one or several loci (RER+). This includes 31% (4 of 13) among cases with a strong positive family history according to previously published criteria and 17% (35 of 207) among cases with no history of familial cancer. Interestingly, no significant association was found between RER+ tumors and a general familial clustering of cancer. Microsatellite instability was significantly associated with DNA diploid status of the tumor (P < 0.001), with the location of the tumor in the proximal colon (P < 0.001), and with poorly differentiated tumor phenotype (P < 0.001). Patients with RER+ at > or = 2 loci tumors had an increased survival (P = 0.05). We further analyzed 84 breast cancers and 86 male germ cell cancers using the same seven markers. None of the tumors were RER+, indicating that this phenomenon may be specific to certain types of tumors.

The APC gene I1307K variant is rare in Norwegian patients with familial and sporadic colorectal or breast cancer.

Recently, a T-to-A transversion creating an 8-base mononucleotide tract in the APC gene, resulting in substitution of lysine for isoleucine at codon 1307 (I1307K), was found in a subset of Ashkenazi Jews. This sequence variant was most frequent in colorectal cancer patients with a positive family history of colorectal cancer. To determine whether the I1307K variant plays a role in colorectal or breast cancer predisposition in the Norwegian population, we have analyzed blood samples from 210 colorectal cancer patients and 183 breast cancer patients by PCR and direct sequencing. Thirty-seven of the colorectal cancer patients had a positive family history of cancer. Among the breast cancer patients, 24 had a family history of colorectal cancer and 75 a family history of breast and/or ovarian cancer. Only one colorectal cancer patient who belonged to a Jewish family was found to carry the A variant. Our data show that the I1307K variant is rare in the Norwegian population and should not be viewed as a candidate for susceptibility testing for colorectal cancer.

A screening for BRCA1 mutations in breast and breast-ovarian cancer families from the Stockholm region.

To identify BRCA1 germ-line mutations in the breast and breast-ovarian cancer families in the Stockholm region, a total of 127 families were screened. DNA from 174 patients from these families were studied using various mutation screening techniques, followed by direct DNA sequencing. Mutations were identified in 7 of 20 families with breast and ovarian cancer and in one family with ovarian cancer only, whereas only 1 family of 106 with breast cancer showed a mutation. Thus, germ-line mutations in BRCA1 were found in one-third of the families with both breast and ovarian cancer, but in only 1% of the breast cancer families. The low frequency of germ-line mutations in the site-specific breast cancer families means that other genes are likely to segregate in these families.

Consortium study on 1280 breast carcinomas: allelic loss on chromosome 17 targets subregions associated with family history and clinical parameters.

The pattern of loss of heterozygosity (LOH) on chromosome 17 in human breast cancer is complicated and shows many different regions of loss. In an attempt to narrow down the relevant regions of LOH on chromosome 17, we have studied the deletion pattern and its association with clinical parameters in 1280 breast carcinoma-venous blood lymphocyte pairs. In total, 42 different chromosome 17 loci were investigated, and between 25 and 625 cases were analyzed at each locus. The frequency of LOH observed on the p arm was much higher than that observed on the q arm. The opposite effect was observed in 52 ovarian cancer cases investigated, with less LOH on 17p than on 17q. Patterns of loss consistent with interstitial and terminal deletions, as well as loss of either the p or q arm or monosomy 17 were observed. To determine whether loss at particular loci may be associated with biological features of breast tumors, clinical data including age of onset, family history of breast cancer, tumor histopathology, tumor size, estrogen receptor (ER) status, and occurrence of lymph node or distant metastases were collected for each case. Overall, large-sized, ER-negative, lymph node-positive ductal tumors showed the highest frequencies of LOH, with ER-negative and ductal tumors showing LOH for markers along the majority of the chromosome. Eight regions of chromosome 17 appear to be associated with human breast cancer, two on 17p and six on 17q. These regions were not necessarily in the areas exhibiting the highest frequencies of LOH but were defined by interstitial and terminal deletions in multiple independent cases. Seven of these regions showed statistically significant differences in LOH associated with clinical parameters. These data strongly suggest that loci on chromosome 17 may determine aspects of tumor presentation and disease behavior in human breast cancer and pinpoint candidate tumor suppressor gene loci.

Enhanced detection of mutations in BRCA1 exon 11 using restriction endonuclease fingerprinting-single-strand conformation polymorphism.

A novel approach to mutation screening in the large exon 11 (comprising 3427 bp) of the human BRCA1 gene is presented. Restriction endonuclease fingerprinting single-strand conformation polymorphism (REF-SSCP) is based on repeated detection of DNA sequence variants in different restriction endonuclease fragments, and we evaluated the method using blood samples from 25 Norwegian patients with hereditary breast/ovarian cancer. We compared REF-SSCP to constant denaturant gel electrophoresis (CDGE) and to the protein truncation test (PTT). REF-SSCP detected 12 different DNA variants. Four of these were not detected by CDGE, and only one variant detected by CDGE was missed by REF-SSCP. PTT detected 4 of these 13 variants. REF-SSCP was subsequently applied to a second patient series (Swedish, n=20). A total of 14 different DNA variants were detected by REF-SSCP, 6 of which were truncating mutations (PTT detected only 4). Nonsense and frameshift mutations that are putative breast/ovarian cancer mutations, were detected in 7 of the 25 Norwegian and 9 of the 20 Swedish patients.

A rare CYP19 (aromatase) variant may increase the risk of breast cancer.

The aromatase P450 (coded by the CYP19 gene) is responsible for the rate limiting step in the metabolism of C19 steroids to estrogens and is expressed in most breast carcinomas. A polymorphic tetranucleotide repeat (TTTA)n in intron 5, about 80 nucleotides downstream of exon 4 has previously been described. The allele frequencies of the polymorphic repeat were studied in series of 182 sporadic and 185 familial breast cancer patients as well as in 252 healthy control individuals. Five different alleles containing 7, 8, 9, 11 and 12-TTTA-repeats were detected. A relatively rare allele (A1) containing the longest repeat (TTTA)12 was found significantly more frequently in breast cancer patients than in control individuals. This indicates that individuals carrying the A1 allele of CYP19 may have an increased risk of developing breast cancer, OR 2.42 (95% confidence interval [CI] 1.03-5.80). The higher frequency was observed in both sporadic and familial patients, although when each of the groups was compared to the control group only a borderline significance was seen. A higher frequency of A1 allele carriers was also found in the group of patients with positive estrogen receptor and progesterone receptor positive tumors. These data suggest that the CYP19 gene may be involved as a low penetrance gene in breast cancer susceptibility.

Single tube multiplex polymerase chain reaction genotype analysis of GSTM1, GSTT1 and GSTP1: relation of genotypes to TP53 tumor status and clinicopathological variables in breast cancer patients.

Glutathione S-transferases are involved in the conjugation of a number of human carcinogens. The frequencies of the deletion alleles coding for GSTM1, and GSTT1, related to deficient conjugation of xenobiotics, as well as a recently reported variant in the exon 5 of GSTP1 were investigated in this study. A multiplex polymerase chain reaction based method for a rapid and high throughput genotype analysis of all three GSTM1, GSTT1 and GSTP1 genes in a single tube was developed. Leukocyte DNA from two hundred and thirty-nine (n = 239) breast cancer patients were genotyped. Tumors from a subset of these breast cancer patients (n = 131) have previously been investigated for mutations in the TP53 gene, levels of p53 protein accumulation and loss of heterozygosity at several loci on chromosome 17. When genetic alterations in the tumors were analyzed with respect to glutathione S-transferase genotypes, a significantly higher proportion of the patients with a G allele (GG + AG) of the GSTP1 had loss of heterozygosity at the TP53 gene locus mapping to 17p, compared with non-G allele carriers (74% versus 29%) (P = 0.018). The patients carrying the G allele of GSTP1 also had more frequently mutations in the TP53 gene in their tumor (38%), compared with patients with the AA genotype (21%) (P = 0.055). G allele carriers had predominantly deletion or transversion mutations in the TP53 gene (5 of 7 and 5 of 6 respectively). A higher frequency of the G allele carriers was observed among patients with negative lymph node status (P = 0.0004). A higher proportion of the patients with positive lymph node status at the time of diagnosis had a combined GSTM1 null/GSTT1 null genotype (P = 0.05). Patients who were homozygous for the deleted GSTM1 allele were found to have a significantly shorter overall survival (P = 0.036).

Association studies of estrogen receptor polymorphisms in a Norwegian testicular cancer population.

To examine a possible influence of estrogen receptor variants on the genetic susceptibility to germ cell cancer we have analyzed the allelic frequencies of three polymorphisms within the estrogen receptor gene in testicular cancer (n = 454) and control populations (n = 672). There were no differences in allelic frequencies in cancer patients compared to controls. Subgroup analyses did not indicate differences in allele frequencies for any of the polymorphisms in those individuals most likely to be predisposed to testicular cancer (patients with a history of maldescent of testicles and/or infertility, patients suffering from bilateral testicular cancer, and patients with familial testicular cancer). The data do not indicate that variation in the 5' end of the estrogen receptor gene confers susceptibility to testicular cancer.

Alterations of the TP53 gene as a potential prognostic marker in breast carcinomas. Advantages of using constant denaturant gel electrophoresis in mutation detection.

Reviewing studies of alterations of the TP53 tumor suppressor gene in human breast carcinomas gives cautious optimism about TP53 alterations as a prognostic marker in this disease. For the time being, breast carcinomas should be screened for TP53 alterations at both the protein and gene levels. Improved mutational screening techniques are needed for this purpose. We consider constant denaturant gel electrophoresis, a modification of denaturing gradient gel electrophoresis, to represent such an improvement. With the recent development of the BioRad D GENE system, constant denaturant gel electrophoresis screening for TP53 mutations can easily be performed on large series of breast carcinomas.

Genetic alterations of chromosome 17 in human breast carcinoma studied by fluorescence in situ hybridization and molecular DNA techniques.

Fluorescence in situ hybridization (FISH) with a chromosome 17 centromere-specific probe was used together with Southern blot analyses and PCR amplification of a polymorphic segment to characterize 13 breast carcinomas. Cells with an abnormal number of chromosome 17 centromeres were found mixed with disomic cells in nine of the 13 tumors studied. Three of the four cases found to have a normal number of chromosome 17 centromeres had DNA alterations restricted to allelic imbalance of the two most distal markers on 17p; the fourth had no detectable alterations. In contrast, of the seven tumors found to have genetic alterations elsewhere on chromosome 17, all had more than one cell population when examined for numerical chromosome 17 alterations. The present data support the hypothesis that alterations at the distal short arm of chromosome 17 represent earlier events in the tumorigenic process than do the other chromosome 17 abnormalities observed. The results of molecular DNA studies interpreted as allelic imbalance of distal 17p markers in most cases probably reflect chromosomal rearrangements like loss of specific loci, rather than monosomies and large deletions. The report illustrates the usefulness of FISH when added to current molecular DNA techniques.

[Telomeres, telomerase and development of cancer]. / Telomerer, telomerase og kreftutvikling.

The chromosome ends, telomeres, shorten during each cell division due to the inability of DNA polymerase to replicate the ends of linear chromosomes. The telomere length serves as a clock determining the remaining replicative capacity of the cell. After 50-100 doublings, the cell becomes senescent. Rarely, a cell overcomes the senescence blockade, and eventually becomes immortal. Cellular immortalisation is almost always accompanied by the expression of the enzyme telomerase, which synthesises telomeric DNA. Telomerase is present in approximately 85% of malignancies. The detection of telomerase activity in cancer cells represents a possible cancer diagnostic and prognostic tool, and telomerase inhibition may become a novel therapeutic strategy in cancer patients.

[Diagnostic molecular biology in prostatic cancer]. / Diagnostisk molekylaerbiologi ved prostatacancer.

Studies of molecular genetic changes in prostate carcinomas are slowly improving our understanding of the biological process which leads to a normal prostate epithelial cell becoming an adenocarcinoma cell with invasive and metastatic properties. Carriers of germ-line mutations in still unidentified prostate cancer susceptibility genes, one of which has been localised to chromosome arm lq, seem to be particularly prone to develop the disease. The susceptibility genes have to be identified and the effects of carrier detection evaluated before genetic testing for prostate cancer predisposition can be performed in a clinical setting. The identification of specific molecular genetic changes in prostate carcinomas may become clinically useful diagnostic and prognostic tools. An improved understanding of the molecular genetic mechanisms underlying the development of prostate cancer may eventually yield novel therapeutic strategies, attacking specific genetic changes in the prostate carcinomas.