Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot be explained by non-contextual ontological models, where physical properties are assumed to exist prior to and independently of the act of measurement. However, all such contextuality proofs assume a traditional notion of causal structure, where causal influence flows from past to future according to ordinary dynamical laws. This leaves open the question of whether the apparent contextuality of quantum mechanics is simply the signature of some exotic causal structure, where the future might affect the past or distant systems might get correlated due to non-local constraints. Here we show that quantum predictions require a deeper form of contextuality: even allowing for arbitrary causal structure, no model can explain quantum correlations from non-contextual ontological properties of the world, be they initial states, dynamical laws, or global constraints.

Quantum 2, 63 (2018). https://doi.org/10.22331/q-2018-05-18-63

]]>Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot be explained by non-contextual ontological models, where physical properties are assumed to exist prior to and independently of the act of measurement. However, all such contextuality proofs assume a traditional notion of causal structure, where causal influence flows from past to future according to ordinary dynamical laws. This leaves open the question of whether the apparent contextuality of quantum mechanics is simply the signature of some exotic causal structure, where the future might affect the past or distant systems might get correlated due to non-local constraints. Here we show that quantum predictions require a deeper form of contextuality: even allowing for arbitrary causal structure, no model can explain quantum correlations from non-contextual ontological properties of the world, be they initial states, dynamical laws, or global constraints.

]]>We present a planar surface-code-based scheme for fault-tolerant quantum computation which eliminates the time overhead of single-qubit Clifford gates, and implements long-range multi-target CNOT gates with a time overhead that scales only logarithmically with the control-target separation. This is done by replacing hardware operations for single-qubit Clifford gates with a classical tracking protocol. Inter-qubit communication is added via a modified lattice surgery protocol that employs twist defects of the surface code. The long-range multi-target CNOT gates facilitate magic state distillation, which renders our scheme fault-tolerant and universal.

Quantum 2, 62 (2018). https://doi.org/10.22331/q-2018-05-04-62

]]>We present a planar surface-code-based scheme for fault-tolerant quantum computation which eliminates the time overhead of single-qubit Clifford gates, and implements long-range multi-target CNOT gates with a time overhead that scales only logarithmically with the control-target separation. This is done by replacing hardware operations for single-qubit Clifford gates with a classical tracking protocol. Inter-qubit communication is added via a modified lattice surgery protocol that employs twist defects of the surface code. The long-range multi-target CNOT gates facilitate magic state distillation, which renders our scheme fault-tolerant and universal.

]]>Quantum is now listed in the Web of Science, the possibly most widely used proprietary citation indexing service.

Quantum enters the Emerging Sources Citation Index (ESCI) of the Web of Science Core Collection, this means that it is now possible for users of the Web of Science to track citations to publications in Quantum on the article and journal level. Every paper published in Quantum, including all papers since we began publishing, will be indexed, all references will be captured, and citations to articles in Quantum will be displayed as the times cited count.

The gathered data will, along with other criteria, be used in the Journal Selection Process of Clarivate Analytics (previously part of Thomson Reuters) for the more narrowly defined Science Citation Index Expanded. Journals can enter this more selective index, for which also an official impact factor is calculated, only after at least two years of publication activity. No Journal Impact Factor metrics for journals covered in the Emerging Sources Citation Index are computed.

]]>Quantum is very happy to announce a generous donation from Ilyas Khan’s Stanhill Foundation in London.

The Stanhill Foundation has a primary focus on education. It is sponsoring outstanding individuals and organizations who show promise and potential but lack resources. By supporting Quantum, it is contributing our mission of making publishing in the quantum sciences more open and affordable for all scientists and students. Ilyas Khan is the founder and CEO of Cambridge Quantum Computing.

]]>To test this hypothesis, Quantum started a pilot outreach project, Quantum Leaps, in collaboration with Cherrybrook Technology High School in Sydney, Australia. We encouraged quantum information and computation researchers around the world to **write a popular science article** about their work.

We received thirteen ambitious submissions, and took six to a science class from the Year 8 cohort of the school. These are **13–14 year-old students** that are especially keen to hear about cutting edge science and the process of peer review. Over the course of three sessions, the students learned about peer review, discussed the articles, and wrote their first report, which we have now sent back to the authors. Here are our conclusions from the first round of reviews.

We worked with a class of about thirty students, organised in groups of four to five people. This meant that we had to pick six out of the thirteen submissions received to bring to the students. We picked at random; the remaining articles may be used in the next edition of this project.

So far we had three sessions with the students, facilitated by Chris Ferrie of the University of Technology of Sydney and by Cherrybrook Technology High School teacher Byrne LaGinestra:

- 50 minutes of discussion on peer review in science. Homework: read papers.
- 50 minutes of in-class discussion on topics of papers. Homework: begin report.
- 50 minutes of discussion on final verdict. Homework: complete report.

We received six reports, which we have now sent back to the authors. Once they implement the reports’ suggestions, the original group of referees will write up a final assessment, after which the articles will be published in Quantum Views. The tentative timeline for publication is early June.

The students were very engaged and excited to be a part of this! They enjoyed reading about quantum research, and most said that they want to give a talk explaining the articles to their peers. To encourage the maximum possible engagement, we suggested that the students not hold back any punches in their reviews. Warning: some of the comments are not for the faint of heart!

We ran the articles through an online readability test and found that their **language level was too high** – and this is just referring to the grammatical structure! A randomly chosen article in the New York Times had a reading grade level of 8, which is the average for a US newspaper. The average grade level of the submissions was 10. Not bad, but that also means some of the submissions could only be read by college graduates!

The paper was quite lengthy resulting in lots of information to grasp, causing us to re-read certain parts multiple times, slowly losing a bit of interest.

On the other hand, our referees were gentle on typos and grammar mistakes:

Our group agrees that the paper was explained well, but there were a few faults in terms of English skills and grammar. The few grammar issues that there existed can easily be fixed by editing.

The larger problem (which readability tests do not capture) was technical language. The most common criticism raised by our referees was that the articles were rife with **technical terms unknown to them**. Expressions like superconductor, quantum state, spin, superposition, and entanglement were often not defined and even used in explaining other concepts.

The results were extensive and the scientific explanations were precise however the scientific terms could have been replaced with simpler terms so that the reader could understand the article better. The article was also too long and should be more straightforward when explaining.

The paper was interesting and had a clear concept but sometimes the explanations/other points were not very clear and did not belong at the current point of the report. These areas could have been ordered in a better and satisfying way. That is why we recommend revising it slightly and just tweaking the order of arguments in order for it to flow better. We also would like to recommend to define scientific terms more clearly and precisely due to the fact that we were not able to understand some terms that were defined.

The paper was not interesting to read because it described many terms in a technical and complicated way; hard to understand.

Some attempts at explaining basic concepts were not deemed satisfactory:

Author: In a superposition, it’s like one atom is in two places at once; it feels effects from both of those places at the same time.

Referees: We were not fully clear on the concept of an atom being ‘in two places at once’. Also, you could explain why the particles are not in one place but in two places…

Although some of the terms were explained, the phrasing of those explanations were confusing, and hard to understand to the point where it had to be re-read multiple times to grasp the basic concept.

The students applauded the use of **diagrams and pictures**, and requested them when absent. However, not all visuals aided…

Although there were visual aids to assist understanding of a concept, it was often unclear what the concept being talked about was, or what it meant. For example, Figure 2 is effective in explaining that the “quantum states” flipped abruptly and not gradually, however that could only be understood if the meaning of “quantum states” or “electronic spin flip” was defined clearly – which it unfortunately was not.

Referees also suggested **improved structure** for the articles, including subheadings and a glossary section:

Things like mind maps, highlighted words, explanations of words within the paragraphs etc. would help to further this paper.

Some students were thrilled by purely foundational research:

The research is relevant to society because by proving their idea, they change the way that we view scientific principles, such as Einstein’s Relativity Principle. It makes important findings and that is good because it can change how we view gravity and do cool stuff!

Others felt that the authors had not done enough to motivate their work:

What is a quantum computer and why are we trying to build it? What would we use his findings for and how would it benefit society? We don’t know… Why are we trying to figure out how to build internet quantum computers? How costly is this process?

And for some, the opacity of explanations rendered them unable to assess the relevance of the research:

It probably was important to those who could understand it.

Chris and Lídia found that the articles were well-written, but more suitable for an **older, more knowledgeable audience, like physics undergrads**. Indeed the articles we found the most interesting were the ones struck the hardest by our referees, for having too many technical terms and too opaque explanations for the target audience. Articles that we thought were too simple were lauded by the students as clear and accessible.

We believe that **our student referees model the best of a general audience**: readers with no technical knowledge of the physics involved, but intelligent and motivated to understand the articles.

The articles succeeded at intriguing the readers and spiking their curiosity,** motivating them to learn more** about these topics. However, in most cases the students **did not obtain a good understanding of the concepts** in the articles. This main culprit was an abundance of poorly explained technical terms. Scientists have had difficulty in explaining the concepts of quantum physics since its inception. But we seem to have settled on a few popular metaphorical explanations. For example, superposition is often explained with the simile of being in “two places at once”. We were quite surprised—and, quite frankly, impressed—when we found that the students recognised this as being incomplete and demanded more. Other concrete suggestions included **improved structure and visual aids**: a popular science article is not an academic paper, and our referees were put off by walls of text.

The challenge is now on the authors to try to implement all the referees’ suggestions! We will keep you posted on updates.

*Lídia del Rio and Chris Ferrie*

One of the most fundamental tasks in quantum thermodynamics is extracting energy from one system and subsequently storing this energy in an appropriate battery. Both of these steps, work extraction and charging, can be viewed as cyclic Hamiltonian processes acting on individual quantum systems. Interestingly, so-called passive states exist, whose energy cannot be lowered by unitary operations, but it is safe to assume that the energy of any not fully charged battery may be increased unitarily. However, unitaries raising the average energy by the same amount may differ in qualities such as their precision, fluctuations, and charging power. Moreover, some unitaries may be extremely difficult to realize in practice. It is hence of crucial importance to understand the qualities that can be expected from practically implementable transformations. Here, we consider the limitations on charging batteries when restricting to the feasibly realizable family of Gaussian unitaries. We derive optimal protocols for general unitary operations as well as for the restriction to easier implementable Gaussian unitaries. We find that practical Gaussian battery charging, while performing significantly less well than is possible in principle, still offers asymptotically vanishing relative charge variances and fluctuations.

Quantum 2, 61 (2018). https://doi.org/10.22331/q-2018-04-23-61

]]>One of the most fundamental tasks in quantum thermodynamics is extracting energy from one system and subsequently storing this energy in an appropriate battery. Both of these steps, work extraction and charging, can be viewed as cyclic Hamiltonian processes acting on individual quantum systems. Interestingly, so-called passive states exist, whose energy cannot be lowered by unitary operations, but it is safe to assume that the energy of any not fully charged battery may be increased unitarily. However, unitaries raising the average energy by the same amount may differ in qualities such as their precision, fluctuations, and charging power. Moreover, some unitaries may be extremely difficult to realize in practice. It is hence of crucial importance to understand the qualities that can be expected from practically implementable transformations. Here, we consider the limitations on charging batteries when restricting to the feasibly realizable family of Gaussian unitaries. We derive optimal protocols for general unitary operations as well as for the restriction to easier implementable Gaussian unitaries. We find that practical Gaussian battery charging, while performing significantly less well than is possible in principle, still offers asymptotically vanishing relative charge variances and fluctuations.

]]>Motivated by the gate set tomography we study quantum channels from the perspective of information which is invariant with respect to the gauge realized through similarity of matrices representing channel superoperators. We thus use the complex spectrum of the superoperator to provide necessary conditions relevant for complete positivity of qubit channels and to express various metrics such as average gate fidelity.

Quantum 2, 60 (2018). https://doi.org/10.22331/q-2018-04-11-60

]]>Motivated by the gate set tomography we study quantum channels from the perspective of information which is invariant with respect to the gauge realized through similarity of matrices representing channel superoperators. We thus use the complex spectrum of the superoperator to provide necessary conditions relevant for complete positivity of qubit channels and to express various metrics such as average gate fidelity.

]]>We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive. This directly implies, against naive intuition, that the minimal entropic uncertainty can always be realized by fully separable states. Hence, in contradiction to proposals by other authors, no entanglement witness can be constructed solely by comparing the attainable uncertainties of entangled and separable states. However, our result gives rise to a huge simplification for computing global uncertainty bounds as they now can be deduced from local ones. Furthermore, we provide the natural generalization of the Maassen and Uffink inequality for linear uncertainty relations with arbitrary positive coefficients.

Quantum 2, 59 (2018). https://doi.org/10.22331/q-2018-03-30-59

]]>We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive. This directly implies, against naive intuition, that the minimal entropic uncertainty can always be realized by fully separable states. Hence, in contradiction to proposals by other authors, no entanglement witness can be constructed solely by comparing the attainable uncertainties of entangled and separable states. However, our result gives rise to a huge simplification for computing global uncertainty bounds as they now can be deduced from local ones. Furthermore, we provide the natural generalization of the Maassen and Uffink inequality for linear uncertainty relations with arbitrary positive coefficients.

]]>Quantum has been officially approved by the European Physical Society (EPS) and is now listed among the journals that have received the recognized journal status. Through this, the EPS certifies that Quantum fulfills high standards in physics publishing and that it performs unbiased peer-review based on scientific merit. This is another important step forward in establishing Quantum as a respected publishing venue.

]]>We analyze a modified Bose-Hubbard model, where two cavities having on-site Kerr interactions are subject to two-photon driving and correlated dissipation. We derive an exact solution for the steady state of this interacting driven-dissipative system, and use it show that the system permits the preparation and stabilization of pure entangled non-Gaussian states, so-called entangled cat states. Unlike previous proposals for dissipative stabilization of such states, our approach requires only a linear coupling to a single engineered reservoir (as opposed to nonlinear couplings to two or more reservoirs). Our scheme is within the reach of state-of-the-art experiments in circuit QED.

Quantum 2, 58 (2018). https://doi.org/10.22331/q-2018-03-27-58

]]>We analyze a modified Bose-Hubbard model, where two cavities having on-site Kerr interactions are subject to two-photon driving and correlated dissipation. We derive an exact solution for the steady state of this interacting driven-dissipative system, and use it show that the system permits the preparation and stabilization of pure entangled non-Gaussian states, so-called entangled cat states. Unlike previous proposals for dissipative stabilization of such states, our approach requires only a linear coupling to a single engineered reservoir (as opposed to nonlinear couplings to two or more reservoirs). Our scheme is within the reach of state-of-the-art experiments in circuit QED.

]]>A causal structure is a relationship between observed variables that in general restricts the possible correlations between them. This relationship can be mediated by unobserved systems, modelled by random variables in the classical case or joint quantum systems in the quantum case. One way to differentiate between the correlations realisable by two different causal structures is to use entropy vectors, i.e., vectors whose components correspond to the entropies of each subset of the observed variables. To date, the starting point for deriving entropic constraints within causal structures are the so-called Shannon inequalities (positivity of entropy, conditional entropy and conditional mutual information). In the present work we investigate what happens when non-Shannon entropic inequalities are included as well. We show that in general these lead to tighter outer approximations of the set of realisable entropy vectors and hence enable a sharper distinction of different causal structures. Since non-Shannon inequalities can only be applied amongst classical variables, it might be expected that their use enables an entropic distinction between classical and quantum causal structures. However, this remains an open question. We also introduce techniques for deriving inner approximations to the allowed sets of entropy vectors for a given causal structure. These are useful for proving tightness of outer approximations or for finding interesting regions of entropy space. We illustrate these techniques in several scenarios, including the triangle causal structure.

Quantum 2, 57 (2018). https://doi.org/10.22331/q-2018-03-14-57

]]>A causal structure is a relationship between observed variables that in general restricts the possible correlations between them. This relationship can be mediated by unobserved systems, modelled by random variables in the classical case or joint quantum systems in the quantum case. One way to differentiate between the correlations realisable by two different causal structures is to use entropy vectors, i.e., vectors whose components correspond to the entropies of each subset of the observed variables. To date, the starting point for deriving entropic constraints within causal structures are the so-called Shannon inequalities (positivity of entropy, conditional entropy and conditional mutual information). In the present work we investigate what happens when non-Shannon entropic inequalities are included as well. We show that in general these lead to tighter outer approximations of the set of realisable entropy vectors and hence enable a sharper distinction of different causal structures. Since non-Shannon inequalities can only be applied amongst classical variables, it might be expected that their use enables an entropic distinction between classical and quantum causal structures. However, this remains an open question. We also introduce techniques for deriving inner approximations to the allowed sets of entropy vectors for a given causal structure. These are useful for proving tightness of outer approximations or for finding interesting regions of entropy space. We illustrate these techniques in several scenarios, including the triangle causal structure.

]]>Magic states are eigenstates of non-Pauli operators. One way of suppressing errors present in magic states is to perform parity measurements in their non-Pauli eigenbasis and postselect on even parity. Here we develop new protocols based on non-Pauli parity checking, where the measurements are implemented with the aid of pre-distilled multiqubit resource states. This leads to a two step process: pre-distillation of multiqubit resource states, followed by implementation of the parity check. These protocols can prepare single-qubit magic states that enable direct injection of single-qubit axial rotations without subsequent gate-synthesis and its associated overhead. We show our protocols are more efficient than all previous comparable protocols with quadratic error reduction, including the protocols of Bravyi and Haah.

Quantum 2, 56 (2018). https://doi.org/10.22331/q-2018-03-14-56

]]>Magic states are eigenstates of non-Pauli operators. One way of suppressing errors present in magic states is to perform parity measurements in their non-Pauli eigenbasis and postselect on even parity. Here we develop new protocols based on non-Pauli parity checking, where the measurements are implemented with the aid of pre-distilled multiqubit resource states. This leads to a two step process: pre-distillation of multiqubit resource states, followed by implementation of the parity check. These protocols can prepare single-qubit magic states that enable direct injection of single-qubit axial rotations without subsequent gate-synthesis and its associated overhead. We show our protocols are more efficient than all previous comparable protocols with quadratic error reduction, including the protocols of Bravyi and Haah.

]]>Quantum is now not only indexed but fully recognized by Google Scholar!

The Quantum website has been indexed by Google Scholar for some time, but, up to now, the version of a paper published in Quantum often appeared only in the “All versions” listing (together with the arXiv and university library websites) and was not recognized as the primary, published version.

For new articles this will change with immediate effect (as can be seen for one of our most recently published papers at the time of writing). For older articles, the information will be updated when Google Scholar rebuilds their index in (northern) summer. From then on, all articles in Quantum can be discovered via Google Scholar.

]]>Quantum has joined the Free Journal Network, a recently founded organization that will help coordinate the efforts of scholarly journals run according to the Fair Open Access model, that is journals that are controlled by the scientific community and which publish open-access without mandatory article processing charges.

The network will promote this form of publishing by raising awareness, supporting journals by sharing resources and know how, and work towards their increasing professionalization through the establishment of best practices. You can join the discussion and support the cause by bringing in your ideas, expertise, time, and contacts.

Quantum’s Christian Gogolin will further be joining the Steering Committee of the Free Journal Network, which will be tasked with the selection of further member journals and the development of the initiative.

]]>We study the speed of convergence of a primitive quantum time evolution towards its fixed point in the distance of sandwiched Rényi divergences. For each of these distance measures the convergence is typically exponentially fast and the best exponent is given by a constant (similar to a logarithmic Sobolev constant) depending only on the generator of the time evolution. We establish relations between these constants and the logarithmic Sobolev constants as well as the spectral gap. An important consequence of these relations is the derivation of mixing time bounds for time evolutions directly from logarithmic Sobolev inequalities without relying on notions like lp-regularity. We also derive strong converse bounds for the classical capacity of a quantum time evolution and apply these to obtain bounds on the classical capacity of some examples, including stabilizer Hamiltonians under thermal noise.

Quantum 2, 55 (2018). https://doi.org/10.22331/q-2018-02-27-55

]]>We study the speed of convergence of a primitive quantum time evolution towards its fixed point in the distance of sandwiched Rényi divergences. For each of these distance measures the convergence is typically exponentially fast and the best exponent is given by a constant (similar to a logarithmic Sobolev constant) depending only on the generator of the time evolution. We establish relations between these constants and the logarithmic Sobolev constants as well as the spectral gap. An important consequence of these relations is the derivation of mixing time bounds for time evolutions directly from logarithmic Sobolev inequalities without relying on notions like lp-regularity. We also derive strong converse bounds for the classical capacity of a quantum time evolution and apply these to obtain bounds on the classical capacity of some examples, including stabilizer Hamiltonians under thermal noise.

]]>Interactions of quantum systems with their environment play a crucial role in resource-theoretic approaches to thermodynamics in the microscopic regime. Here, we analyze the possible state transitions in the presence of "small" heat baths of bounded dimension and energy. We show that for operations on quantum systems with fully degenerate Hamiltonian (noisy operations), all possible state transitions can be realized exactly with a bath that is of the same size as the system or smaller, which proves a quantum version of Horn's lemma as conjectured by Bengtsson and Zyczkowski. On the other hand, if the system's Hamiltonian is not fully degenerate (thermal operations), we show that some possible transitions can only be performed with a heat bath that is unbounded in size and energy, which is an instance of the third law of thermodynamics. In both cases, we prove that quantum operations yield an advantage over classical ones for any given finite heat bath, by allowing a larger and more physically realistic set of state transitions.

Quantum 2, 54 (2018). https://doi.org/10.22331/q-2018-02-22-54

]]>Interactions of quantum systems with their environment play a crucial role in resource-theoretic approaches to thermodynamics in the microscopic regime. Here, we analyze the possible state transitions in the presence of "small" heat baths of bounded dimension and energy. We show that for operations on quantum systems with fully degenerate Hamiltonian (noisy operations), all possible state transitions can be realized exactly with a bath that is of the same size as the system or smaller, which proves a quantum version of Horn's lemma as conjectured by Bengtsson and Zyczkowski. On the other hand, if the system's Hamiltonian is not fully degenerate (thermal operations), we show that some possible transitions can only be performed with a heat bath that is unbounded in size and energy, which is an instance of the third law of thermodynamics. In both cases, we prove that quantum operations yield an advantage over classical ones for any given finite heat bath, by allowing a larger and more physically realistic set of state transitions.

]]>Quantum has hired two management assistants to help the executive board in the day-to-day running of the journal. They have been working for Quantum in Vienna since December, and we are very happy with them. Their work allows the executive board (Christian, Lídia and Marcus) to focus on developing Quantum further, and makes the journal more sustainable in the long term. Without further delay, it is a pleasure to introduce Mariana and Lukas.

**Mariana Munárriz** grew up in Madrid, Spain and studied Translation and Interpretation at the University of Salamanca. She has since worked as a freelance translator, a legal secretary and a technical writer in Berlin, Madrid and Vienna. She joined Quantum as a **financial and administrative assistant**, handling the gritty legal details, processing payments and doing most of the backstage work not directly related to the peer-review process.

**Lukas Schalleck**, born and raised in Vienna, Austria, studied political science at the University of Vienna. Since 2011 he has been working as assistant to the editors with the editorial office of Transplant International at the Medical University of Vienna. He has now joined Quantum as an **assistant to the editorial board** at Quantum, ensuring that the peer review process and publication of papers run smoothly.

For now, they are each in a part-time contract of 5h/week, while they receive training. Since Quantum is financially stable, thanks to our generous sponsors and authors, the long-term plan is to increase the hours of our employees and move them to open-ended contracts.

]]>The Quantum Leaps submission deadline has passed and we received 13 articles which attempt to explain cutting-edge quantum science research to teenagers. Great! So how did they do? I don’t know—I’m not a teenager—but that is what we are going to find out in March!

During the first week of March I will join the science class of Year 8 at Cherrybrook Technology High School in Sydney, Australia. I will help facilitate their self-guided learning of the scientific peer review process. During the process, 30 students in groups of 5 will be given the Quantum Leaps submissions and be tasked with writing a referee report for one article.

The articles will be returned to authors, who will make changes accordingly, before publication in Quantum Views. Meanwhile, back in Sydney, the students will present each article and report to their peers. Stay tuned for the conclusion!

]]>Quantum is now listed in the Directory of Open Access Journals (DOAJ) and is also pushing the meta-data of all published articles (future and past) to the DOAJ.

Quantum thereby has joined a club of trusted journals adhering to open-access best practices. Indexing the content of Quantum in the DOAJ means that all works published in Quantum can now be discovered via the DOAJ database.

]]>The award is given yearly by QSIT, the Swiss National Centre of Competence in Research for Quantum Science and Technology, its industry partners, and a representative of the Swiss National Science Foundation.

This year’s two other awardees were ProjectQ, an open source software framework for quantum computing, recently published in Quantum, and Qnami, a tech startup for surface analysis with nanometer resolution.

]]>In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for the first time, our protocol also applies to a broader class of distance-three codes than was previously known. Flag circuits use extra ancilla qubits to signal when errors resulting from $v$ faults in the circuit have weight greater than $v$. The flag error correction protocol is applicable to stabilizer codes of arbitrary distance which satisfy a set of conditions and uses fewer qubits than other schemes such as Shor, Steane and Knill error correction. We give examples of infinite code families which satisfy these conditions and analyze the behaviour of distance-three and -five examples numerically. Requiring fewer resources than Shor error correction, flag error correction could potentially be used in low-overhead fault-tolerant error correction protocols using low density parity check quantum codes of large code length.

Quantum 2, 53 (2018). https://doi.org/10.22331/q-2018-02-08-53

]]>In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for the first time, our protocol also applies to a broader class of distance-three codes than was previously known. Flag circuits use extra ancilla qubits to signal when errors resulting from $v$ faults in the circuit have weight greater than $v$. The flag error correction protocol is applicable to stabilizer codes of arbitrary distance which satisfy a set of conditions and uses fewer qubits than other schemes such as Shor, Steane and Knill error correction. We give examples of infinite code families which satisfy these conditions and analyze the behaviour of distance-three and -five examples numerically. Requiring fewer resources than Shor error correction, flag error correction could potentially be used in low-overhead fault-tolerant error correction protocols using low density parity check quantum codes of large code length.

]]>To what extent do thermodynamic resource theories capture physically relevant constraints? Inspired by quantum computation, we define a set of elementary thermodynamic gates that only act on 2 energy levels of a system at a time. We show that this theory is well reproduced by a Jaynes-Cummings interaction in rotating wave approximation and draw a connection to standard descriptions of thermalisation. We then prove that elementary thermal operations present tighter constraints on the allowed transformations than thermal operations. Mathematically, this illustrates the failure at finite temperature of fundamental theorems by Birkhoff and Muirhead-Hardy-Littlewood-Polya concerning stochastic maps. Physically, this implies that stronger constraints than those imposed by single-shot quantities can be given if we tailor a thermodynamic resource theory to the relevant experimental scenario. We provide new tools to do so, including necessary and sufficient conditions for a given change of the population to be possible. As an example, we describe the resource theory of the Jaynes-Cummings model. Finally, we initiate an investigation into how our resource theories can be applied to Heat Bath Algorithmic Cooling protocols.

Quantum 2, 52 (2018). https://doi.org/10.22331/q-2018-02-08-52

]]>To what extent do thermodynamic resource theories capture physically relevant constraints? Inspired by quantum computation, we define a set of elementary thermodynamic gates that only act on 2 energy levels of a system at a time. We show that this theory is well reproduced by a Jaynes-Cummings interaction in rotating wave approximation and draw a connection to standard descriptions of thermalisation. We then prove that elementary thermal operations present tighter constraints on the allowed transformations than thermal operations. Mathematically, this illustrates the failure at finite temperature of fundamental theorems by Birkhoff and Muirhead-Hardy-Littlewood-Polya concerning stochastic maps. Physically, this implies that stronger constraints than those imposed by single-shot quantities can be given if we tailor a thermodynamic resource theory to the relevant experimental scenario. We provide new tools to do so, including necessary and sufficient conditions for a given change of the population to be possible. As an example, we describe the resource theory of the Jaynes-Cummings model. Finally, we initiate an investigation into how our resource theories can be applied to Heat Bath Algorithmic Cooling protocols.

]]>Given a linear map $\Phi : M_n \rightarrow M_m$, its multiplicity maps are defined as the family of linear maps $\Phi \otimes \textrm{id}_{k} : M_n \otimes M_k \rightarrow M_m \otimes M_k$, where $\textrm{id}_{k}$ denotes the identity on $M_k$. Let $\|\cdot\|_1$ denote the trace-norm on matrices, as well as the induced trace-norm on linear maps of matrices, i.e. $\|\Phi\|_1 = \max\{\|\Phi(X)\|_1 : X \in M_n, \|X\|_1 = 1\}$. A fact of fundamental importance in both operator algebras and quantum information is that $\|\Phi \otimes \textrm{id}_{k}\|_1$ can grow with $k$. In general, the rate of growth is bounded by $\|\Phi \otimes \textrm{id}_{k}\|_1 \leq k \|\Phi\|_1$, and matrix transposition is the canonical example of a map achieving this bound. We prove that, up to an equivalence, the transpose is the unique map achieving this bound. The equivalence is given in terms of complete trace-norm isometries, and the proof relies on a particular characterization of complete trace-norm isometries regarding preservation of certain multiplication relations. We use this result to characterize the set of single-shot quantum channel discrimination games satisfying a norm relation that, operationally, implies that the game can be won with certainty using entanglement, but is hard to win without entanglement. Specifically, we show that the well-known example of such a game, involving the Werner-Holevo channels, is essentially the unique game satisfying this norm relation. This constitutes a step towards a characterization of single-shot quantum channel discrimination games with maximal gap between optimal performance of entangled and unentangled strategies.

Quantum 2, 51 (2018). https://doi.org/10.22331/q-2018-02-05-51

]]>Given a linear map $\Phi : M_n \rightarrow M_m$, its multiplicity maps are defined as the family of linear maps $\Phi \otimes \textrm{id}_{k} : M_n \otimes M_k \rightarrow M_m \otimes M_k$, where $\textrm{id}_{k}$ denotes the identity on $M_k$. Let $\|\cdot\|_1$ denote the trace-norm on matrices, as well as the induced trace-norm on linear maps of matrices, i.e. $\|\Phi\|_1 = \max\{\|\Phi(X)\|_1 : X \in M_n, \|X\|_1 = 1\}$. A fact of fundamental importance in both operator algebras and quantum information is that $\|\Phi \otimes \textrm{id}_{k}\|_1$ can grow with $k$. In general, the rate of growth is bounded by $\|\Phi \otimes \textrm{id}_{k}\|_1 \leq k \|\Phi\|_1$, and matrix transposition is the canonical example of a map achieving this bound. We prove that, up to an equivalence, the transpose is the unique map achieving this bound. The equivalence is given in terms of complete trace-norm isometries, and the proof relies on a particular characterization of complete trace-norm isometries regarding preservation of certain multiplication relations. We use this result to characterize the set of single-shot quantum channel discrimination games satisfying a norm relation that, operationally, implies that the game can be won with certainty using entanglement, but is hard to win without entanglement. Specifically, we show that the well-known example of such a game, involving the Werner-Holevo channels, is essentially the unique game satisfying this norm relation. This constitutes a step towards a characterization of single-shot quantum channel discrimination games with maximal gap between optimal performance of entangled and unentangled strategies.

]]>For the past twenty years, Matrix Product States (MPS) have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via site-independent tensors and a boundary condition. Exploiting a connection with the theory of matrix algebras, we derive two structural properties shared by all hMPS, namely: a) there exist local operators which annihilate all hMPS of a given bond dimension; and b) there exist local operators which, when applied over any hMPS of a given bond dimension, decouple (cut) the particles where they act from the spin chain while at the same time join (glue) the two loose ends back again into a hMPS. Armed with these tools, we show how to systematically derive `bond dimension witnesses', or 2-local operators whose expectation value allows us to lower bound the bond dimension of the underlying hMPS. We extend some of these results to the ansatz of Projected Entangled Pairs States (PEPS). As a bonus, we use our insight on the structure of hMPS to: a) derive some theoretical limitations on the use of hMPS and hPEPS for ground state energy computations; b) show how to decrease the complexity and boost the speed of convergence of the semidefinite programming hierarchies described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of finite-dimensional quantum correlations.

Quantum 2, 50 (2018). https://doi.org/10.22331/q-2018-01-31-50

]]>For the past twenty years, Matrix Product States (MPS) have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via site-independent tensors and a boundary condition. Exploiting a connection with the theory of matrix algebras, we derive two structural properties shared by all hMPS, namely: a) there exist local operators which annihilate all hMPS of a given bond dimension; and b) there exist local operators which, when applied over any hMPS of a given bond dimension, decouple (cut) the particles where they act from the spin chain while at the same time join (glue) the two loose ends back again into a hMPS. Armed with these tools, we show how to systematically derive `bond dimension witnesses', or 2-local operators whose expectation value allows us to lower bound the bond dimension of the underlying hMPS. We extend some of these results to the ansatz of Projected Entangled Pairs States (PEPS). As a bonus, we use our insight on the structure of hMPS to: a) derive some theoretical limitations on the use of hMPS and hPEPS for ground state energy computations; b) show how to decrease the complexity and boost the speed of convergence of the semidefinite programming hierarchies described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of finite-dimensional quantum correlations.

]]>We introduce ProjectQ, an open source software effort for quantum computing. The first release features a compiler framework capable of targeting various types of hardware, a high-performance simulator with emulation capabilities, and compiler plug-ins for circuit drawing and resource estimation. We introduce our Python-embedded domain-specific language, present the features, and provide example implementations for quantum algorithms. The framework allows testing of quantum algorithms through simulation and enables running them on actual quantum hardware using a back-end connecting to the IBM Quantum Experience cloud service. Through extension mechanisms, users can provide back-ends to further quantum hardware, and scientists working on quantum compilation can provide plug-ins for additional compilation, optimization, gate synthesis, and layout strategies.

Quantum 2, 49 (2018). https://doi.org/10.22331/q-2018-01-31-49

]]>We introduce ProjectQ, an open source software effort for quantum computing. The first release features a compiler framework capable of targeting various types of hardware, a high-performance simulator with emulation capabilities, and compiler plug-ins for circuit drawing and resource estimation. We introduce our Python-embedded domain-specific language, present the features, and provide example implementations for quantum algorithms. The framework allows testing of quantum algorithms through simulation and enables running them on actual quantum hardware using a back-end connecting to the IBM Quantum Experience cloud service. Through extension mechanisms, users can provide back-ends to further quantum hardware, and scientists working on quantum compilation can provide plug-ins for additional compilation, optimization, gate synthesis, and layout strategies.

]]>A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error correction. Here we show that a recurrent neural network can be trained, using only experimentally accessible data, to detect errors in a widely used topological code, the surface code, with a performance above that of the established minimum-weight perfect matching (or blossom) decoder. The performance gain is achieved because the neural network decoder can detect correlations between bit-flip (X) and phase-flip (Z) errors. The machine learning algorithm adapts to the physical system, hence no noise model is needed. The long short-term memory layers of the recurrent neural network maintain their performance over a large number of quantum error correction cycles, making it a practical decoder for forthcoming experimental realizations of the surface code.

Quantum 2, 48 (2018). https://doi.org/10.22331/q-2018-01-29-48

]]>A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error correction. Here we show that a recurrent neural network can be trained, using only experimentally accessible data, to detect errors in a widely used topological code, the surface code, with a performance above that of the established minimum-weight perfect matching (or blossom) decoder. The performance gain is achieved because the neural network decoder can detect correlations between bit-flip (X) and phase-flip (Z) errors. The machine learning algorithm adapts to the physical system, hence no noise model is needed. The long short-term memory layers of the recurrent neural network maintain their performance over a large number of quantum error correction cycles, making it a practical decoder for forthcoming experimental realizations of the surface code.

]]>We analyze randomized benchmarking for arbitrary gate-dependent noise and prove that the exact impact of gate-dependent noise can be described by a single perturbation term that decays exponentially with the sequence length. That is, the exact behavior of randomized benchmarking under general gate-dependent noise converges exponentially to a true exponential decay of exactly the same form as that predicted by previous analysis for gate-independent noise. Moreover, we show that the operational meaning of the decay parameter for gate-dependent noise is essentially unchanged, that is, we show that it quantifies the average fidelity of the noise between ideal gates. We numerically demonstrate that our analysis is valid for strongly gate-dependent noise models. We also show why alternative analyses do not provide a rigorous justification for the empirical success of randomized benchmarking with gate-dependent noise.

Quantum 2, 47 (2018). https://doi.org/10.22331/q-2018-01-29-47

]]>We analyze randomized benchmarking for arbitrary gate-dependent noise and prove that the exact impact of gate-dependent noise can be described by a single perturbation term that decays exponentially with the sequence length. That is, the exact behavior of randomized benchmarking under general gate-dependent noise converges exponentially to a true exponential decay of exactly the same form as that predicted by previous analysis for gate-independent noise. Moreover, we show that the operational meaning of the decay parameter for gate-dependent noise is essentially unchanged, that is, we show that it quantifies the average fidelity of the noise between ideal gates. We numerically demonstrate that our analysis is valid for strongly gate-dependent noise models. We also show why alternative analyses do not provide a rigorous justification for the empirical success of randomized benchmarking with gate-dependent noise.

]]>The solution to the wave equation as a Cauchy problem with prescribed fields at an initial time $t=0$ is purely retarded. Similarly, in the quantum theory of radiation the specification of Heisenberg picture photon annihilation and creation operators at time $t \gt 0$ in terms of operators at $t=0$ automatically yields purely retarded source-fields. However, we show that two-time quantum correlations between the retarded source-fields of a stationary dipole and the quantum vacuum-field possess advanced wave-like contributions. Despite their advanced nature, these correlations are perfectly consistent with Einstein causality. It is shown that while they do not significantly contribute to photo-detection amplitudes in the vacuum state, they do effect the statistics of measurements involving the radiative force experienced by a point charge in the field of the dipole. Specifically, the dispersion in the charge's momentum is found to increase with time. This entails the possibility of obtaining direct experimental evidence for the existence of advanced waves in physical reality, and provides yet another signature of the quantum nature of the vacuum.

Quantum 2, 46 (2018). https://doi.org/10.22331/q-2018-01-18-46

]]>The solution to the wave equation as a Cauchy problem with prescribed fields at an initial time $t=0$ is purely retarded. Similarly, in the quantum theory of radiation the specification of Heisenberg picture photon annihilation and creation operators at time $t \gt 0$ in terms of operators at $t=0$ automatically yields purely retarded source-fields. However, we show that two-time quantum correlations between the retarded source-fields of a stationary dipole and the quantum vacuum-field possess advanced wave-like contributions. Despite their advanced nature, these correlations are perfectly consistent with Einstein causality. It is shown that while they do not significantly contribute to photo-detection amplitudes in the vacuum state, they do effect the statistics of measurements involving the radiative force experienced by a point charge in the field of the dipole. Specifically, the dispersion in the charge's momentum is found to increase with time. This entails the possibility of obtaining direct experimental evidence for the existence of advanced waves in physical reality, and provides yet another signature of the quantum nature of the vacuum.

]]>We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS) states. First, we show that separability in the case of DS in $C^d\otimes C^d$ (symmetric qudits) can be reformulated as a quadratic conic optimization problem. This connection allows us to exchange concepts and ideas between quantum information and this field of mathematics. For instance, copositive matrices can be understood as indecomposable entanglement witnesses for DS states. As a consequence, we show that positivity of the partial transposition (PPT) is sufficient and necessary for separability of DS states for $d \leq 4$. Furthermore, for $d \geq 5$, we provide analytic examples of PPT-entangled states. Second, we develop new sufficient separability conditions beyond the PPT criterion for bipartite DS states. Finally, we focus on $N$-partite DS qubits, where PPT is known to be necessary and sufficient for separability. In this case, we present a family of almost DS states that are PPT with respect to each partition but nevertheless entangled.

Quantum 2, 45 (2018). https://doi.org/10.22331/q-2018-01-12-45

]]>We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS) states. First, we show that separability in the case of DS in $C^d\otimes C^d$ (symmetric qudits) can be reformulated as a quadratic conic optimization problem. This connection allows us to exchange concepts and ideas between quantum information and this field of mathematics. For instance, copositive matrices can be understood as indecomposable entanglement witnesses for DS states. As a consequence, we show that positivity of the partial transposition (PPT) is sufficient and necessary for separability of DS states for $d \leq 4$. Furthermore, for $d \geq 5$, we provide analytic examples of PPT-entangled states. Second, we develop new sufficient separability conditions beyond the PPT criterion for bipartite DS states. Finally, we focus on $N$-partite DS qubits, where PPT is known to be necessary and sufficient for separability. In this case, we present a family of almost DS states that are PPT with respect to each partition but nevertheless entangled.

]]>Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.

Quantum 2, 44 (2018). https://doi.org/10.22331/q-2018-01-08-44

]]>Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.

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