Power of Quantum Computation with Few Clean Qubits

This paper investigates the power of polynomial-time quantum computation in which only a very limited number of qubits are initially clean in the |0> state, and all the remaining qubits are initially in the totally mixed state. No initializations of qubits are allowed during the computation, nor intermediate measurements. The main results of this paper are unexpectedly strong error-reducible properties of such quantum computations. It is proved that any problem solvable by a polynomial-time quantum computation with one-sided bounded error that uses logarithmically many clean qubits can also be solvable with exponentially small one-sided error using just two clean qubits, and with polynomially small one-sided error using just one clean qubit. It is further proved in the case of two-sided bounded error that any problem solvable by such a computation with a constant gap between completeness and soundness using logarithmically many clean qubits can also be solvable with exponentially small two-sided error using just two clean qubits. If only one clean qubit is available, the problem is again still solvable with exponentially small error in one of the completeness and soundness and polynomially small error in the other. As an immediate consequence of the above result for the two-sided-error case, it follows that the TRACE ESTIMATION problem defined with fixed constant threshold parameters is complete for the classes of problems solvable by polynomial-time quantum computations with completeness 2/3 and soundness 1/3 using logarithmically many clean qubits and just one clean qubit. The techniques used for proving the error-reduction results may be of independent interest in themselves, and one of the technical tools can also be used to show the hardness of weak classical simulations of one-clean-qubit computations (i.e., DQC1 computations).Comment: 44 pages + cover page; the results in Section 8 are overlapping with the main results in arXiv:1409.677

Sumcheck-based delegation of quantum computing to rational server

Delegated quantum computing enables a client with a weak computational power to delegate quantum computing to a remote quantum server in such a way that the integrity of the server is efficiently verified by the client. Recently, a new model of delegated quantum computing has been proposed, namely, rational delegated quantum computing. In this model, after the client interacts with the server, the client pays a reward to the server. The rational server sends messages that maximize the expected value of the reward. It is known that the classical client can delegate universal quantum computing to the rational quantum server in one round. In this paper, we propose novel one-round rational delegated quantum computing protocols by generalizing the classical rational sumcheck protocol. The construction of the previous rational protocols depends on gate sets, while our sumcheck technique can be easily realized with any local gate set. Furthermore, as with the previous protocols, our reward function satisfies natural requirements. We also discuss the reward gap. Simply speaking, the reward gap is a minimum loss on the expected value of the server's reward incurred by the server's behavior that makes the client accept an incorrect answer. Although our sumcheck-based protocols have only exponentially small reward gaps as with the previous protocols, we show that a constant reward gap can be achieved if two non-communicating but entangled rational servers are allowed. We also discuss that a single rational server is sufficient under the (widely-believed) assumption that the learning-with-errors problem is hard for polynomial-time quantum computing. Apart from these results, we show, under a certain condition, the equivalence between $rational$ and $ordinary$ delegated quantum computing protocols. Based on this equivalence, we give a reward-gap amplification method.Comment: 28 pages, 1 figure, Because of the character limitation, the abstract was shortened compared with the PDF fil

Divide-and-conquer verification method for noisy intermediate-scale quantum computation

Several noisy intermediate-scale quantum computations can be regarded as logarithmic-depth quantum circuits on a sparse quantum computing chip, where two-qubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediate-scale quantum computation. To this end, we first characterize small-scale quantum operations with respect to the diamond norm. Then by using these characterized quantum operations, we estimate the fidelity $\langle\psi_t|\hat{\rho}_{\rm out}|\psi_t\rangle$ between an actual $n$-qubit output state $\hat{\rho}_{\rm out}$ obtained from the noisy intermediate-scale quantum computation and the ideal output state (i.e., the target state) $|\psi_t\rangle$. Although the direct fidelity estimation method requires $O(2^n)$ copies of $\hat{\rho}_{\rm out}$ on average, our method requires only $O(D^32^{12D})$ copies even in the worst case, where $D$ is the denseness of $|\psi_t\rangle$. For logarithmic-depth quantum circuits on a sparse chip, $D$ is at most $O(\log{n})$, and thus $O(D^32^{12D})$ is a polynomial in $n$. By using the IBM Manila 5-qubit chip, we also perform a proof-of-principle experiment to observe the practical performance of our method.Comment: 17 pages, 7 figures, v3: Added a proof-of-principle experiment (Sec. IV) and improved Sec. V, Accepted for publication in Quantu

Successful treatment with positive airway pressure ventilation for tension pneumopericardium after pericardiocentesis in a neonate: a case report

Background Pneumopericardium in neonates is often associated with respiratory diseases, of which positive pressure ventilation (PPV) is an exacerbating factor. Here, we present a neonate case of pneumopericardium after cardiac surgery which was resolved after applying PPV. Case presentation A 28-day-old neonate with left recurrent nerve palsy after aortic reconstruction for interrupted aortic arch developed pericardial effusion. Pericardiocentesis was performed under general anesthesia, and a drainage tube was left in the pericardium. After extubation, stridor gradually exacerbated, following hemodynamic deterioration. A chest X-ray demonstrated pneumopericardium. Upper airway stenosis due to recurrent nerve palsy developed excessive negative pleural pressure, and air was drawn into pericardium via the insertion site of the drainage tube. After tracheal intubation and applying PPV, the pneumopericardium improved. Conclusion PPV does not always exacerbate pneumopericardium. In a patient with pericardial-atmosphere communication, increased inspiration effort can cause pneumopericardium, and PPV is a therapeutic option to alleviate the pneumopericardium

Two cases of intraoperative hemodynamic instability during combined thoracoscopic-laparoscopic surgery for esophagogastric junction carcinoma

Background Intraoperative complications during combined thoracoscopic-laparoscopic surgery for esophagogastric junction (EGJ) carcinoma have not been reported as compared to those during surgery for esophageal carcinoma. We present two cases which had surgery-related hemodynamic instability during laparoscopic proximal gastrectomy and intra-mediastinal valvuloplastic esophagogastrostomy (vEG) with thoracoscopic mediastinal lymphadenectomy for EGJ carcinoma. Case presentation In case 1, the patient fell into hypotension with hypoxemia during laparoscopic vEG due to pneumothorax caused by entry of intraabdominal carbon dioxide. In case 2, ventricular arrythmia and ST elevation occurred during laparoscopic vEG. Pericardium retraction to secure surgical field during reconstruction compressed the coronary artery, which caused coronary malperfusion. These two events were induced by the surgical procedure, characterized by the following: (1) connection of the thoracic and abdominal cavities and (2) cardiac displacement during vEG. Conclusion These cases indicated tension pneumothorax and coronary ischemia are possible intraoperative complications specific to combined thoracoscopic-laparoscopic surgery for EGJ carcinoma

A Catalytic Role of XoxF1 as La3+-Dependent Methanol Dehydrogenase in Methylobacterium extorquens Strain AM1

In the methylotrophic bacterium Methylobacterium extorquens strain AM1, MxaF, a Ca2+-dependent methanol dehydrogenase (MDH), is the main enzyme catalyzing methanol oxidation during growth on methanol. The genome of strain AM1 contains another MDH gene homologue, xoxF1, whose function in methanol metabolism has remained unclear. In this work, we show that XoxF1 also functions as an MDH and is La3+-dependent. Despite the absence of Ca2+ in the medium strain AM1 was able to grow on methanol in the presence of La3+. Addition of La3+ increased MDH activity but the addition had no effect on mxaF or xoxF1 expression level. We purified MDH from strain AM1 grown on methanol in the presence of La3+, and its N-terminal amino acid sequence corresponded to that of XoxF1. The enzyme contained La3+ as a cofactor. The ΔmxaF mutant strain could not grow on methanol in the presence of Ca2+, but was able to grow after supplementation with La3+. Taken together, these results show that XoxF1 participates in methanol metabolism as a La3+-dependent MDH in strain AM1

Lanthanide-Dependent Methanol and Formaldehyde Oxidation inMethylobacterium aquaticumStrain 22A

Lanthanides (Ln) are an essential cofactor for XoxF-type methanol dehydrogenases (MDHs) in Gram-negative methylotrophs. The Ln(3+)dependency of XoxF has expanded knowledge and raised new questions in methylotrophy, including the differences in characteristics of XoxF-type MDHs, their regulation, and the methylotrophic metabolism including formaldehyde oxidation. In this study, we genetically identified one set of Ln(3+)- and Ca2+-dependent MDHs (XoxF1 and MxaFI), that are involved in methylotrophy, and an ExaF-type Ln(3+)-dependent ethanol dehydrogenase, among six MDH-like genes inMethylobacterium aquaticumstrain 22A. We also identified the causative mutations in MxbD, a sensor kinase necessary formxaFexpression andxoxF1repression, for suppressive phenotypes inxoxF1mutants defective in methanol growth even in the absence of Ln(3+). Furthermore, we examined the phenotypes of a series of formaldehyde oxidation-pathway mutants (fae1,fae2,mchin the tetrahydromethanopterin (H4MPT) pathway andhgdin the glutathione-dependent formaldehyde dehydrogenase (GSH) pathway). We found that MxaF produces formaldehyde to a toxic level in the absence of the formaldehyde oxidation pathways and that either XoxF1 or ExaF can oxidize formaldehyde to alleviate formaldehyde toxicity in vivo. Furthermore, the GSH pathway has a supportive role for the net formaldehyde oxidation in addition to the H4MPT pathway that has primary importance. Studies on methylotrophy inMethylobacteriumspecies have a long history, and this study provides further insights into genetic and physiological diversity and the differences in methylotrophy within the plant-colonizing methylotrophs