scholarly journals Estimating expectation values using approximate quantum states

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 413
Author(s):  
Marco Paini ◽  
Amir Kalev ◽  
Dan Padilha ◽  
Brendan Ruck

We introduce an approximate description of an N-qubit state, which contains sufficient information to estimate the expectation value of any observable to a precision that is upper bounded by the ratio of a suitably-defined seminorm of the observable to the square root of the number of the system's identical preparations M, with no explicit dependence on N. We describe an operational procedure for constructing the approximate description of the state that requires, besides the quantum state preparation, only single-qubit rotations followed by single-qubit measurements. We show that following this procedure, the cardinality of the resulting description of the state grows as 3MN. We test the proposed method on Rigetti's quantum processor unit with 12, 16 and 25 qubits for random states and random observables, and find an excellent agreement with the theory, despite experimental errors.

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Michal Gulka ◽  
Daniel Wirtitsch ◽  
Viktor Ivády ◽  
Jelle Vodnik ◽  
Jaroslav Hruby ◽  
...  

AbstractNuclear spins in semiconductors are leading candidates for future quantum technologies, including quantum computation, communication, and sensing. Nuclear spins in diamond are particularly attractive due to their long coherence time. With the nitrogen-vacancy (NV) centre, such nuclear qubits benefit from an auxiliary electronic qubit, which, at cryogenic temperatures, enables probabilistic entanglement mediated optically by photonic links. Here, we demonstrate a concept of a microelectronic quantum device at ambient conditions using diamond as wide bandgap semiconductor. The basic quantum processor unit – a single 14N nuclear spin coupled to the NV electron – is read photoelectrically and thus operates in a manner compatible with nanoscale electronics. The underlying theory provides the key ingredients for photoelectric quantum gate operations and readout of nuclear qubit registers. This demonstration is, therefore, a step towards diamond quantum devices with a readout area limited by inter-electrode distance rather than by the diffraction limit. Such scalability could enable the development of electronic quantum processors based on the dipolar interaction of spin-qubits placed at nanoscopic proximity.


Author(s):  
Vladimir Myslivyy ◽  
Angelina Mykyta

Problem setting. According to Art. 27 of the Constitution of Ukraine, everyone has an inalienable right to life, no one can be arbitrarily deprived of life, and the state, in turn, is obliged to protect human life. Protection of a person’s life, as a duty of the state, is manifested in the establishment of criminal liability, enshrined in Section II “Criminal offenses against life and health of a person” of the Criminal Code of Ukraine, who commit socially dangerous acts. whether there are criminal offenses and what punishments they should be committed. The distinction between crimes such as premeditated murder and negligent deprivation of another’s life is important, as criminal law theory still does not have sufficient information on this issue and does not have a complete list of features of the above crimes, but we tried to identify them in our article. Target of research. Deepening their knowledge on the caution of a person’s life due to inconsistency and drawing the line between possible offenses and conditional authority, clarifying the special characteristics of the perpetrator and the victim, outlining the essential features of the perpetrator and the victim, and researching the regulation of negligent proposal of a new version of the Criminal Code of Ukraine. Analysis of resent researches and publications. The theoretical basis for the study of the problem of murder through negligence are the works of legal scholars, in particular, M. Bazhanov, V. Borisov, S. Borodin, V. Glushkov, O. Gorokhovskaya, I. Zinchenko , V. Tyutyugin, O. Us, E. Kisilyuk, V. Kuts, M. Yefimov, S. Likhova, V. Stashis, V. Shablisty and others. Article’s main body. According to Art. 3 of the Constitution of Ukraine, man, his life and health, honor and dignity, inviolability and security are recognized in Ukraine as the highest social value. Given this constitutional provision, the legislator should pay special attention to the criminal law protection of human life and health as the most important public relations. So it is no coincidence that considering such encroachments as one of the most dangerous in the criminal law dimension, the legislator established criminal liability for their commission in Section II “Criminal offenses against life and health” of the Special Part of the Criminal Code of Ukraine. Due to the high public danger and the high prevalence of criminal offenses against human life and health, criminal law theory and law enforcement practice are under increasing scrutiny. Thus, the analysis of judicial practice in recent years shows that, for example, among all murders (Articles 117-119 of the Criminal Code of Ukraine) the number of persons convicted of deprivation of life due to negligence is about 15 percent annually. In our opinion, it is also advisable to analyze the concept of “murder” by comparing the common and distinctive features of the offenses referred to in Art. Art. 115 and 119 of the Criminal Code of Ukraine. According to scientific results, we can conclude that these offenses have many common features. It is possible to understand the common features and preconditions for the spread of these types of offenses. Conclusions and prospects for the development. A study of issues related to the criminal law analysis of murder through negligence and its difference from other types of murder, shows that these acts encroach on the identical object, which is “human life as a set of social relations.” Unfortunately, nowadays the dynamics of offenses committed in Art. Art. 115 and 119 is intensifying, so consideration of their delimitation and characterization of their features is very important. The study examines the main features of these types of crimes, as well as analyzes some provisions of national law and proposes some adjustments to them.


Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 436 ◽  
Author(s):  
Adrián Pérez-Salinas ◽  
Diego García-Martín ◽  
Carlos Bravo-Prieto ◽  
José Latorre

We present a quantum circuit that transforms an unknown three-qubit state into its canonical form, up to relative phases, given many copies of the original state. The circuit is made of three single-qubit parametrized quantum gates, and the optimal values for the parameters are learned in a variational fashion. Once this transformation is achieved, direct measurement of outcome probabilities in the computational basis provides an estimate of the tangle, which quantifies genuine tripartite entanglement. We perform simulations on a set of random states under different noise conditions to asses the validity of the method.


Author(s):  
Akshay Gaikwad ◽  
Krishna Shende ◽  
Kavita Dorai

We experimentally performed complete and optimized quantum process tomography of quantum gates implemented on superconducting qubit-based IBM QX2 quantum processor via two constrained convex optimization (CCO) techniques: least squares optimization and compressed sensing optimization. We studied the performance of these methods by comparing the experimental complexity involved and the experimental fidelities obtained. We experimentally characterized several two-qubit quantum gates: identity gate, a controlled-NOT gate, and a SWAP gate. The general quantum circuit is efficient in the sense that the data needed to perform CCO-based process tomography can be directly acquired by measuring only a single qubit. The quantum circuit can be extended to higher dimensions and is also valid for other experimental platforms.


2021 ◽  
pp. 2150034
Author(s):  
Zhanjun Zhang

A three-party scheme for sharing an arbitrary single-qubit operation on a distant target qubit is proposed by first utilizing a six-qubit genuinely entangled state presented by [Borras et al., J. Phys. A 40, 13407 (2007)]. The security of the scheme is simply analyzed and ensured. The essential role which the state in the given qubit distribution plays in the QOS task is revealed. The important features including the sharing determinacy and the sharer symmetry are identified. Moreover, the experimental implementation feasibility of the scheme is discussed and confirmed.


2013 ◽  
Vol 11 (07) ◽  
pp. 1350062 ◽  
Author(s):  
YOSHIFUMI NAKATA ◽  
MIO MURAO

We study efficient generations of random diagonal-unitary matrices, an ensemble of unitary matrices diagonal in a given basis with randomly distributed phases for their eigenvalues. Despite the simple algebraic structure, they cannot be achieved by quantum circuits composed of a few-qubit diagonal gates. We introduce diagonal-unitaryt-designs and present two quantum circuits that implement diagonal-unitary 2-design with the computational basis in N-qubit systems. One is composed of single-qubit diagonal gates and controlled-phase gates with randomized phases, which achieves an exact diagonal-unitary 2-design after applying the gates on all pairs of qubits. The number of required gates is N(N - 1)/2. If the controlled-Z gates are used instead of the controlled-phase gates, the circuit cannot achieve an exact 2-design, but achieves an ϵ-approximate 2-design by applying gates on randomly selected pairs of qubits. Due to the random choice of pairs, the circuit obtains extra randomness and the required number of gates is at most O(N2(N + log 1/∊)). We also provide an application of the circuits, a protocol of generating an exact 2-design of random states by combining the circuits with a simple classical procedure requiring O(N) random classical bits.


2006 ◽  
Vol 13 (01) ◽  
pp. 1-16 ◽  
Author(s):  
Konrad Banaszek

The trade-off between the information gain and the state disturbance is derived for quantum operations on a single qubit prepared in a uniformly distributed pure state. The derivation is valid for a class of measures quantifying the state disturbance and the information gain which satisfy certain invariance conditions. This class includes in particular the Shannon entropy versus the operation fidelity. The central role in the derivation is played by efficient quantum operations, which leave the system in a pure output state for any measurement outcome. It is pointed out that the optimality of efficient quantum operations among those inducing a given operator-valued measure is related to Davies' characterization of convex invariant functions on hermitian operators.


2021 ◽  
Vol 77 (4) ◽  
pp. 39-50
Author(s):  
Galyna Utkina ◽  
◽  
Tetiana Datsiuk ◽  

The authors note the existence of significant changes in the legal field of Ukraine on gender equality, awareness of the majority of the society of the importance of this issue for achieving equal opportunities and realization of women in the field of career and socio-political life. It is proved that the state pays more and more attention to specific mechanisms of gender transformation and takes into account international agreements signed and ratified by Ukraine. It is becaming a part of the world gender technologies. The state recognizes the main directions of gender democracy, restrictions which are based on the grounds of sex and aimed at the weakening, recognition, usage or exercising by women on the basis of equality between men and women, human rights and fundamental freedoms in political, economic, cultural, social or any other field of activity. The article concetrates on the imbalance between the awareness and the real state of gender issues in the labour market, wages and participation in politics. It is concluded that the most perfect laws and decisions of the Government will not be effective without overcoming the existing low level of gender culture in the society, creation of a sufficient information and consultation network in all regions of the country on implementation of equal opportunities of policy for men and women, introduction of equal treatment and equal opportunities for women and men in public policy in the field of labor, social policy, economic policy in order to prevent occupational segregation, eliminate inequality in wages, stimulate the growth of women's entrepreneurship, as well as to assess women's work; cooperation and interaction of various public administration bodies in the implementation of the principle of equal treatment and equal opportunities for women and men; balanced representation of women and men in the lists of candidates in elections and decision-making, improving the actual situation through the implementation of effective and concrete decisions and strategies.


Author(s):  
Gavryliv К.-T. ◽  

In the article, the definitions “castle in a state of long-term ruin” and “architectural revitalization” are given. A list of measures aimed at preserving architectural monuments from the standpoint of their application on castles in a state of long-term ruin is considered. The definitions characterizing permissible activities on architectural monuments specified in the Law of Ukraine “On the Protection of Cultural Heritage” and restoration State Building Standards, however, in theory and practice, much more concepts are used, since the regulated terms do not cover the entire range of possibilities for the preservation and development of architectural monuments. In their works, M. Bevz, A. Rybchynskyi, O. Plamenytska, P. Molski highlight measures for the preservation of architectural monuments. Analyzing the history of the founding of defensive castles, their further restructuring and decline, we form a definition: a castle in a state of long-term ruin is a castle, as a result of destruction during a siege or loss of its defensive functions in the 16th-17th centuries was abandoned without acquiring new owners fell and came to the state of ruin that we can observe today. Looking at conservation measures using the example of castles in a state of long-term ruin, we state the following positions: The conservation method is the main point for keeping castles in a state of long-term ruin. The restoration can only be applied fragmentarily, since a holistic restoration is akin to restoration, which is an unacceptable step, given the lack of sufficient information about the original appearance of the structure. Museumification is excellent, as a method of bringing a castle in ruins to a state suitable for an excursion visit, as well as designation, as a subspecies of museumification, accompanied by both information stands and tracing of foundations reveals the planning structure of the monument. Revitalization measures aimed at revitalizing the degraded space, and renovations, which give an authentic building a touch of novelty and emphasize the period of intervention in the monument are also important. In general, the idea of preserving the castle in a state of long-term ruin should be based on three main positions such as conservation, fragmentary restoration and revitalization, that is, preserving the authentic component and returning life to the object.


2017 ◽  
Vol 13 (1) ◽  
pp. e57-e61 ◽  
Author(s):  
Lee N. Newcomer ◽  
Richard Weininger ◽  
Robert W. Carlson

Purpose: To evaluate a computer-based prior authorization system that was designed to include and test two new concepts for physician review: (1) the tool would minimize denials by providing real-time decision support with alternative options if the original request was noncompliant, and (2) the tool would collect sufficient information to create a patient registry. Methods: A new prior authorization tool incorporating real-time decision support was tested with a large national payer. The tool used the National Comprehensive Cancer Network Clinical Practice Guidelines in Oncology as the content for decision making. Physicians were asked to submit the minimal amount of clinical data necessary to reach a treatment-decision node within the National Comprehensive Cancer Network Guidelines. To minimize denials, all available recommended treatments were displayed for physician consideration and immediate authorization was granted for any compliant selection. Results: During a 1-year pilot in a Florida commercial health plan, 4,272 eligible cases were reviewed with only 42 denials. Chemotherapy drug costs for the prior authorization pilot were compared with a similar time period in the previous year for the state of Florida, as well as for the Southeast region and for the nation, which served as controls. The percentage change between the time periods was −9% in Florida, 10% for the national costs, and 11% for the Southeast region costs. The difference between the regional increase and the Florida decrease represented a savings of $5.3 million dollars for the state of Florida in 1 year. Conclusion: There is significant opportunity to reduce the costs of therapy while being compliant with nationally accepted guidelines for cancer chemotherapy.


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