scholarly journals Impossibility of blind quantum sampling for classical client

2019 ◽  
Vol 19 (9&10) ◽  
pp. 793-806
Author(s):  
Tomoyuki Morimae ◽  
Harumichi Nishimura ◽  
Yuki Takeuch ◽  
Seiichiro Tani
Keyword(s):  
Quantum Computing ◽  
Polynomial Time ◽  
Open Problem ◽  
Input Output ◽  
Information Theoretic ◽  
Single Qubit ◽  
The Third ◽  
The One ◽  
Qubit States ◽  
Polynomial Time Hierarchy

Blind quantum computing enables a client, who can only generate or measure single-qubit states, to delegate quantum computing to a remote quantum server in such a way that the input, output, and program are hidden from the server. It is an open problem whether a completely classical client can delegate quantum computing blindly (in the information theoretic sense). In this paper, we show that if a completely classical client can blindly delegate sampling of subuniversal models, such as the DQC1 model and the IQP model, then the polynomial-time hierarchy collapses to the third level. Our delegation protocol is the one where the client first sends a polynomial-length bit string to the server and then the server returns a single bit to the client. Generalizing the no-go result to more general setups is an open problem.

scholarly journals Rational proofs for quantum computing

2020 ◽  
Vol 20 (3&4) ◽  
pp. 181-193
Author(s):  
Tomoyuki Morimae ◽  
Harumichi Harumichi Nishimura
Keyword(s):  
Quantum Computing ◽  
Polynomial Time ◽  
Open Problem ◽  
Correct Solution ◽  
Expectation Value ◽  
Reward Function ◽  
Single Qubit ◽  
Quantum Technology ◽  
Qubit States ◽  
Probabilistic Polynomial Time

It is an open problem whether a classical client can delegate quantum computing to an efficient remote quantum server in such a way that the correctness of quantum computing is somehow guaranteed. Several protocols for verifiable delegated quantum computing have been proposed, but the client is not completely free from any quantum technology: the client has to generate or measure single-qubit states. In this paper, we show that the client can be completely classical if the server is rational (i.e., economically motivated), following the ``rational proofs" framework of Azar and Micali. More precisely, we consider the following protocol. The server first sends the client a message allegedly equal to the solution of the problem that the client wants to solve. The client then gives the server a monetary reward whose amount is calculated in classical probabilistic polynomial-time by using the server's message as an input. The reward function is constructed in such a way that the expectation value of the reward (the expectation over the client's probabilistic computing) is maximum when the server's message is the correct solution to the problem. The rational server who wants to maximize his/her profit therefore has to send the correct solution to the client.

scholarly journals Impossibility of perfectly-secure one-round delegated quantum computing for classical client

2019 ◽  
Vol 19 (3&4) ◽  
pp. 214-221
Author(s):  
Tomoyuki Morimae ◽  
Takeshi Koshiba
Keyword(s):  
Quantum Computing ◽  
Correct Result ◽  
Input Output ◽  
Single Qubit ◽  
The One ◽  
Qubit States

Blind quantum computing protocols enable a client, who can generate or measure single-qubit states, to delegate quantum computing to a remote quantum server protecting the client's privacy (i.e., input, output, and program). With current technologies, generations or measurements of single-qubit states are not too much burden for the client. In other words, secure delegated quantum computing is possible for ``almost classical" clients. However, is it possible for a ``completely classical" client? Here we consider a one-round perfectly-secure delegated quantum computing, and show that the protocol cannot satisfy both the correctness (i.e., the correct result is obtained when the server is honest) and the perfect blindness (i.e., the client's privacy is completely protected) simultaneously unless BQP is in NP. Since BQP is not believed to be in NP, the result suggests the impossibility of the one-round perfectly-secure delegated quantum computing.

scholarly journals Additive-error fine-grained quantum supremacy

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 329
Author(s):  
Tomoyuki Morimae ◽  
Suguru Tamaki
Keyword(s):  
Quantum Computing ◽  
Complexity Theory ◽  
Polynomial Time ◽  
Boolean Circuits ◽  
Exponential Time ◽  
Fine Grained ◽  
Additive Error ◽  
Universal Quantum ◽  
The One ◽  
Computing Models

It is known that several sub-universal quantum computing models, such as the IQP model, the Boson sampling model, the one-clean qubit model, and the random circuit model, cannot be classically simulated in polynomial time under certain conjectures in classical complexity theory. Recently, these results have been improved to ``fine-grained" versions where even exponential-time classical simulations are excluded assuming certain classical fine-grained complexity conjectures. All these fine-grained results are, however, about the hardness of strong simulations or multiplicative-error sampling. It was open whether any fine-grained quantum supremacy result can be shown for a more realistic setup, namely, additive-error sampling. In this paper, we show the additive-error fine-grained quantum supremacy (under certain complexity assumptions). As examples, we consider the IQP model, a mixture of the IQP model and log-depth Boolean circuits, and Clifford+T circuits. Similar results should hold for other sub-universal models.

Quantum Merlin-Arthur with Clifford Arthur

2015 ◽  
Vol 15 (15&16) ◽  
pp. 1420-1430 ◽  
Author(s):  
Tomoyuki Morimae ◽  
Masahito Hayashi ◽  
Harumichi Nishimura ◽  
Keisuke Fujii
Keyword(s):  
Quantum Computing ◽  
Computational Power ◽  
Xor Gate ◽  
Single Qubit ◽  
Qubit States

We show that the class QMA does not change even if we restrict Arthur’s computing ability to only Clifford gate operations (plus classical XOR gate). The idea is to use the fact that the preparation of certain single-qubit states, so called magic states, plus any Clifford gate operations are universal for quantum computing. If Merlin is honest, he sends the witness plus magic states to Arthur. If Merlin is malicious, he might send other states to Arthur, but Arthur can verify the correctness of magic states by himself. We also generalize the result to QIP(3): we show that the class QIP(3) does not change even if the computational power of the verifier is restricted to only Clifford gate operations (plus classical XOR gate).

scholarly journals Fine-grained quantum computational supremacy

2019 ◽  
Vol 19 (13&14) ◽  
pp. 1089-1115
Author(s):  
Tomoyuki Morimae ◽  
Suguru Tamaki
Keyword(s):  
Quantum Computing ◽  
Complexity Theory ◽  
Polynomial Time ◽  
Probability Distributions ◽  
Fine Grained ◽  
Multiplicative Error ◽  
Universal Quantum ◽  
The One ◽  
Output Probability ◽  
Computing Models

(pp1089-1115) Tomoyuki Morimae and Suguru Tamaki doi: https://doi.org/10.26421/QIC19.13-14-2 Abstracts: Output probability distributions of several sub-universal quantum computing models cannot be classically efficiently sampled unless some unlikely consequences occur in classical complexity theory, such as the collapse of the polynomial-time hierarchy. These results, so called quantum supremacy, however, do not rule out possibilities of super-polynomial-time classical simulations. In this paper, we study ``fine-grained" version of quantum supremacy that excludes some exponential-time classical simulations. First, we focus on two sub-universal models, namely, the one-clean-qubit model (or the DQC1 model) and the HC1Q model. Assuming certain conjectures in fine-grained complexity theory, we show that for any a>0 output probability distributions of these models cannot be classically sampled within a constant multiplicative error and in 2^{(1-a)N+o(N)} time, where N is the number of qubits. Next, we consider universal quantum computing. For example, we consider quantum computing over Clifford and T gates, and show that under another fine-grained complexity conjecture, output probability distributions of Clifford-T quantum computing cannot be classically sampled in 2^{o(t)} time within a constant multiplicative error, where t is the number of T gates.

scholarly journals Polynomial-Time Random Oracles and Separating Complexity Classes

2021 ◽  
Vol 13 (1) ◽  
pp. 11-16
Author(s):  
John M. Hitchcock ◽  
Adewale Sekoni ◽  
Hadi Shafei
Keyword(s):  
Polynomial Time ◽  
Open Problem ◽  
Random Oracle ◽  
Complexity Class ◽  
Complexity Classes ◽  
Random Oracles ◽  
Class Separation ◽  
Polynomial Time Hierarchy

Bennett and Gill [1981] showed that P A ≠ NP A ≠ coNP A for a random oracle A , with probability 1. We investigate whether this result extends to individual polynomial-time random oracles. We consider two notions of random oracles: p-random oracles in the sense of martingales and resource-bounded measure [Lutz 1992; Ambos-Spies et al. 1997], and p-betting-game random oracles using the betting games generalization of resource-bounded measure [Buhrman et al. 2000]. Every p-betting-game random oracle is also p-random; whether the two notions are equivalent is an open problem. (1) We first show that P A ≠ NP A for every oracle A that is p-betting-game random. Ideally, we would extend (1) to p-random oracles. We show that answering this either way would imply an unrelativized complexity class separation: (2) If P A ≠ NP A relative to every p-random oracle A , then BPP ≠ EXP. (3) If P A ≠ NP A relative to some p-random oracle A , then P ≠ PSPACE. Rossman, Servedio, and Tan [2015] showed that the polynomial-time hierarchy is infinite relative to a random oracle, solving a longstanding open problem. We consider whether we can extend (1) to show that PH A is infinite relative to oracles A that are p-betting-game random. Showing that PH A separates at even its first level would also imply an unrelativized complexity class separation: (4) If NP A ≠ coNP A for a p-betting-game measure 1 class of oracles A , then NP ≠ EXP. (5) If PH A is infinite relative to every p-random oracle A , then PH ≠ EXP. We also consider random oracles for time versus space, for example: (6) L A ≠ P A relative to every oracle A that is p-betting-game random.

scholarly journals On statistically-secure quantum homomorphic encryption

2018 ◽  
Vol 18 (9&10) ◽  
pp. 785-794
Author(s):  
Ching-Yi Lai ◽  
Kai-Min Chung
Keyword(s):  
Polynomial Time ◽  
Homomorphic Encryption ◽  
Quantum Circuits ◽  
It Security ◽  
Encryption Scheme ◽  
Information Theoretic ◽  
Information Theoretic Security ◽  
Quantum Polynomial ◽  
The One

Homomorphic encryption is an encryption scheme that allows computations to be evaluated on encrypted inputs without knowledge of their raw messages. Recently Ouyang et al. constructed a quantum homomorphic encryption (QHE) scheme for Clifford circuits with statistical security (or information-theoretic security (IT-security)). It is desired to see whether an information-theoretically-secure (ITS) quantum FHE exists. If not, what other nontrivial class of quantum circuits can be homomorphically evaluated with IT-security? We provide a limitation for the first question that an ITS quantum FHE necessarily incurs exponential overhead. As for the second one, we propose a QHE scheme for the instantaneous quantum polynomial-time (IQP) circuits. Our QHE scheme for IQP circuits follows from the one-time pad.

Alkohol im Tank – Bio-Kraftstoffe und die Grenzen moderner Mobilität

2004 ◽  
Vol 34 (136) ◽  
pp. 455-468
Author(s):  
Hartwig Berger
Keyword(s):  
Third World ◽  
Fossil Fuel ◽  
Energy Resources ◽  
The Third ◽  
Political Conflicts ◽  
The Future ◽  
Long Time ◽  
Food Market ◽  
The One ◽  
The Third World

The article discusses the future of mobility in the light of energy resources. Fossil fuel will not be available for a long time - not to mention its growing environmental and political conflicts. In analysing the potential of biofuel it is argued that the high demands of modern mobility can hardly be fulfilled in the future. Furthermore, the change into using biofuel will probably lead to increasing conflicts between the fuel market and the food market, as well as to conflicts with regional agricultural networks in the third world. Petrol imperialism might be replaced by bio imperialism. Therefore, mobility on a solar base pursues a double strategy of raising efficiency on the one hand and strongly reducing mobility itself on the other.

Al-Rasm al-ʿUthmānī: Towards Correct Pronunciation and the Preclusion of Ambiguity

2011 ◽  
Vol 13 (2) ◽  
pp. 201-171
Author(s):  
Nāṣir Al-Dīn Abū Khaḍīr
Keyword(s):  
Specific Pattern ◽  
Writing Style ◽  
The Third ◽  
The Past ◽  
Different Ages ◽  
Correct Pronunciation ◽  
The One ◽  
The Mind

The ʿUthmānic way of writing (al-rasm al-ʿUthmānī) is a science that specialises in the writing of Qur'anic words in accordance with a specific ‘pattern’. It follows the writing style of the Companions at the time of the third caliph, ʿUthmān b. ʿAffān, and was attributed to ʿUthmān on the basis that he was the one who ordered the collection and copying of the Qur'an into the actual muṣḥaf. This article aims to expound on the two fundamental functions of al-rasm al-ʿUthmānī: that of paying regard to the ‘correct’ pronunciation of the words in the muṣḥaf, and the pursuit of the preclusion of ambiguity which may arise in the mind of the reader and his auditor. There is a further practical aim for this study: to show the connection between modern orthography and the ʿUthmānic rasm in order that we, nowadays, are thereby able to overcome the problems faced by calligraphers and writers of the past in their different ages and cultures.

Detection and representation of the basic peculiarities of vegetation cover by the mapping method (experience based on a research of goltsy-taiga territories)

2013 ◽  
pp. 32-47
Author(s):  
S. V. Osipov
Keyword(s):  
Vegetation Cover ◽  
Mapping Method ◽  
Vegetation Changes ◽  
Large Classes ◽  
High Rise ◽  
The Third ◽  
Altitudinal Belts ◽  
The One ◽  
Dynamic Series ◽  
River Valleys

Geobotanical mapping of the territory in riverheads Bureya of 4500 sq.km is carried out and the map of a actual vegetation cover of scale 1 : 200 000 is prepared. The legend of the map is presented in the form of the text with three-level hierarchy of classes. At the heart of structure of a legend of the map such regularities of a vegetation cover, as its latitudinal zonality / altitudinal belts, situation in a relief and dynamic series lie. The largest divisions of the legend reflect, first, change of large classes of mesocombinations of vegetation at the level of belts and, secondly, distinction in a boreal - forestry belt between a vegetation cover of tops and slopes of mountains, on the one hand, and the bottoms of river valleys, with another. Divisions of the legend of the second level reflect, first, vegetation changes in the form of high-rise and barrier changes of subbelts, secondly, distinctions of a vegetation cover in different geomorphological conditions (small and average river valleys, northern slopes, etc.). Divisions of the legend of the second level correspond to dynamic series of units of the third level. Essential addition to it are block diagrams of dynamics of a vegetation cover.

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