SciPost‘s Jean-Sébastien Caux and Quantum’s Christian Gogolin were both invited to speak about “the future of scientific publishing” at a dedicated session on that topic during YRM 2017 in Tarragona.

SciPost and Quantum, while independent endeavors, share many of their core values and have many common goals. Together with the participants of YRM, topics such as the opportunities and dangers of open-access publishing, the relevance of new technologies for publishing, and the influence of funding policies on publishing were discussed.

We thank the participants of YRM 2017 for the very interesting discussions and the organizers for the opportunity to participate!

]]>Quantum has been assigned an International Standard Serial Number (ISSN) by the ISSN International Centre.

The ISSN is similar to the more widely known ISBN, which is used to uniquely identify books. The ISSN achieves the same, but for periodically appearing publications, like journals. Quantum is thus from now on uniquely identified by its ISSN **2521-327X**.

Having obtained an ISSN enables us to proceed with developing Quantum further and will allow us to apply for inclusion in the Web of Science and the Directory of Open Access Journals.

Papers already published in Quantum (and the respective .bib files) have been updated to include the ISSN.

]]>We investigate an approach to universal quantum computation based on the modulation of longitudinal qubit-oscillator coupling. We show how to realize a controlled-phase gate by simultaneously modulating the longitudinal coupling of two qubits to a common oscillator mode. In contrast to the more familiar transversal qubit-oscillator coupling, the magnitude of the effective qubit-qubit interaction does not rely on a small perturbative parameter. As a result, this effective interaction strength can be made large, leading to short gate times and high gate fidelities. We moreover show how the gate infidelity can be exponentially suppressed with squeezing and how the entangling gate can be generalized to qubits coupled to separate oscillators. Our proposal can be realized in multiple physical platforms for quantum computing, including superconducting and spin qubits.

Quantum 1, 11 (2017). https://doi.org/10.22331/q-2017-05-11-11

]]>We investigate an approach to universal quantum computation based on the modulation of longitudinal qubit-oscillator coupling. We show how to realize a controlled-phase gate by simultaneously modulating the longitudinal coupling of two qubits to a common oscillator mode. In contrast to the more familiar transversal qubit-oscillator coupling, the magnitude of the effective qubit-qubit interaction does not rely on a small perturbative parameter. As a result, this effective interaction strength can be made large, leading to short gate times and high gate fidelities. We moreover show how the gate infidelity can be exponentially suppressed with squeezing and how the entangling gate can be generalized to qubits coupled to separate oscillators. Our proposal can be realized in multiple physical platforms for quantum computing, including superconducting and spin qubits.

]]>**By Bill Fefferman, University of Maryland, US.**

One of the most active areas of research in quantum information is “quantum supremacy”. The central goal is to exhibit a provable quantum speedup over classical computation using the restrictive resources of existing or near-term quantum experiments. Starting with work of Bremner, Jozsa, and Shepherd it has been established that even non-universal commuting classes of quantum computations known as “Instantaneous Quantum Polynomial-time” (or IQP) circuits are capable of sampling from distributions that cannot be exactly sampled classically, under mild complexity assumptions.

As quantum supremacy leaps from the domain of theory to experiment, the major open questions involve understanding which intermediate models are capable of demonstrating supremacy, and how to account for experimentally realistic noise in these models. As a starting point, a primary objective has been to strengthen these sampling separations to hold even if the classical sampler is not required to sample exactly from the quantum outcome distribution but instead samples from a distribution close in total variation distance.

Follow-up work of Bremner, Montanaro and Shepherd addressed this stronger scenario. They show that the outcome distribution of IQP circuits cannot be approximately sampled classically, assuming a conjecture concerning the hardness of estimating the complex-temperature partition function of certain random instances of the Ising model. Understanding the feasibility and implications of this conjecture, as well as related conjectures of Aaronson and Arkhipov regarding estimating the permanent of random matrices, has since become one of the most important challenges in quantum complexity theory.

While not settling these conjectures, the present paper makes important contributions to our understanding of approximate sampling hardness results. The first main result extends the prior work to give similar conjectural evidence that approximate sampling from the output distribution of so-called “sparse” IQP circuits is classically hard. A randomly chosen “sparse” IQP circuit on n qubits consists of $O(n \log(n) )$ 2-qubit gates and can be implemented on a square lattice with a shallow depth circuit, with high probability. These structural properties reduce the experimental barrier of implementing such supremacy results and bring the proposal closer to the realm of currently implementable experiments.

The second result studies IQP sampling under a natural noise model, in which independent depolarizing noise is applied to every qubit at the end of the circuit. It is proven that the resulting output distribution becomes easy to sample from classically, illuminating the fragile nature of supremacy results. However, the authors develop new means for protecting against this depolarizing noise model, using ideas from classical error-correcting codes. Crucially, this result is achieved without the full overhead required by traditional quantum fault tolerance. It is very likely that these error-correcting tools will find use in future results on noise-tolerant quantum supremacy proposals.

Taken as a whole, these results give a fresh perspective to some of the most foundational questions in quantum computation—where quantum speedups come from, and under which experimentally motivated settings we can hope to observe these speedups. As such, this work offers a solid contribution to the quantum supremacy literature, and develops useful tools for analyzing candidates for future supremacy experiments.

]]>To study which are the most general causal structures which are compatible with local quantum mechanics, Oreshkov et al. introduced the notion of a process: a resource shared between some parties that allows for quantum communication between them without a predetermined causal order. These processes can be used to perform several tasks that are impossible in standard quantum mechanics: they allow for the violation of causal inequalities, and provide an advantage for computational and communication complexity. Nonetheless, no process that can be used to violate a causal inequality is known to be physically implementable. There is therefore considerable interest in determining which processes are physical and which are just mathematical artefacts of the framework. Here we make the first step in this direction, by proposing a purification postulate: processes are physical only if they are purifiable. We derive necessary conditions for a process to be purifiable, and show that several known processes do not satisfy them.

Quantum 1, 10 (2017). https://doi.org/10.22331/q-2017-04-26-10

]]>To study which are the most general causal structures which are compatible with local quantum mechanics, Oreshkov et al. introduced the notion of a process: a resource shared between some parties that allows for quantum communication between them without a predetermined causal order. These processes can be used to perform several tasks that are impossible in standard quantum mechanics: they allow for the violation of causal inequalities, and provide an advantage for computational and communication complexity. Nonetheless, no process that can be used to violate a causal inequality is known to be physically implementable. There is therefore considerable interest in determining which processes are physical and which are just mathematical artefacts of the framework. Here we make the first step in this direction, by proposing a purification postulate: processes are physical only if they are purifiable. We derive necessary conditions for a process to be purifiable, and show that several known processes do not satisfy them.

]]>We investigate the finite-density phase diagram of a non-abelian $SU(2)$ lattice gauge theory in $(1+1)$-dimensions using tensor network methods. We numerically characterise the phase diagram as a function of the matter filling and of the matter-field coupling, identifying different phases, some of them appearing only at finite densities. For weak matter-field coupling we find a meson BCS liquid phase, which is confirmed by second-order analytical perturbation theory. At unit filling and for strong coupling, the system undergoes a phase transition to a charge density wave of single-site (spin-0) mesons via spontaneous chiral symmetry breaking. At finite densities, the chiral symmetry is restored almost everywhere, and the meson BCS liquid becomes a simple liquid at strong couplings, with the exception of filling two-thirds, where a charge density wave of mesons spreading over neighbouring sites appears. Finally, we identify two tri-critical points between the chiral and the two liquid phases which are compatible with a $SU(2)_2$ Wess-Zumino-Novikov-Witten model. Here we do not perform the continuum limit but we explicitly address the global $U(1)$ charge conservation symmetry.

Quantum 1, 9 (2017). https://doi.org/10.22331/q-2017-04-25-9

]]>We investigate the finite-density phase diagram of a non-abelian $SU(2)$ lattice gauge theory in $(1+1)$-dimensions using tensor network methods. We numerically characterise the phase diagram as a function of the matter filling and of the matter-field coupling, identifying different phases, some of them appearing only at finite densities. For weak matter-field coupling we find a meson BCS liquid phase, which is confirmed by second-order analytical perturbation theory. At unit filling and for strong coupling, the system undergoes a phase transition to a charge density wave of single-site (spin-0) mesons via spontaneous chiral symmetry breaking. At finite densities, the chiral symmetry is restored almost everywhere, and the meson BCS liquid becomes a simple liquid at strong couplings, with the exception of filling two-thirds, where a charge density wave of mesons spreading over neighbouring sites appears. Finally, we identify two tri-critical points between the chiral and the two liquid phases which are compatible with a $SU(2)_2$ Wess-Zumino-Novikov-Witten model. Here we do not perform the continuum limit but we explicitly address the global $U(1)$ charge conservation symmetry.

]]>The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in the presence of physically motivated constraints. First, we show that there is a family of sparse IQP circuits that can be implemented on a square lattice of n qubits in depth O(sqrt(n) log n), and which is likely hard to simulate classically. Next, we show that, if an arbitrarily small constant amount of noise is applied to each qubit at the end of any IQP circuit whose output probability distribution is sufficiently anticoncentrated, there is a polynomial-time classical algorithm that simulates sampling from the resulting distribution, up to constant accuracy in total variation distance. However, we show that purely classical error-correction techniques can be used to design IQP circuits which remain hard to simulate classically, even in the presence of arbitrary amounts of noise of this form. These results demonstrate the challenges faced by experiments designed to demonstrate quantum supremacy over classical computation, and how these challenges can be overcome.

Quantum 1, 8 (2017). https://doi.org/10.22331/q-2017-04-25-8

]]>The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in the presence of physically motivated constraints. First, we show that there is a family of sparse IQP circuits that can be implemented on a square lattice of n qubits in depth O(sqrt(n) log n), and which is likely hard to simulate classically. Next, we show that, if an arbitrarily small constant amount of noise is applied to each qubit at the end of any IQP circuit whose output probability distribution is sufficiently anticoncentrated, there is a polynomial-time classical algorithm that simulates sampling from the resulting distribution, up to constant accuracy in total variation distance. However, we show that purely classical error-correction techniques can be used to design IQP circuits which remain hard to simulate classically, even in the presence of arbitrary amounts of noise of this form. These results demonstrate the challenges faced by experiments designed to demonstrate quantum supremacy over classical computation, and how these challenges can be overcome.

]]>We give a complete proposal showing how to detect the non-classical nature of photonic states with naked eyes as detectors. The enabling technology is a sub-Poissonian photonic state that is obtained from single photons, displacement operations in phase space and basic non-photon-number-resolving detectors. We present a detailed statistical analysis of our proposal including imperfect photon creation and detection and a realistic model of the human eye. We conclude that a few tens of hours are sufficient to certify non-classical light with the human eye with a p-value of 10%.

Quantum 1, 7 (2017). https://doi.org/10.22331/q-2017-04-25-7

]]>We give a complete proposal showing how to detect the non-classical nature of photonic states with naked eyes as detectors. The enabling technology is a sub-Poissonian photonic state that is obtained from single photons, displacement operations in phase space and basic non-photon-number-resolving detectors. We present a detailed statistical analysis of our proposal including imperfect photon creation and detection and a realistic model of the human eye. We conclude that a few tens of hours are sufficient to certify non-classical light with the human eye with a p-value of 10%.

]]>We apply classical algorithms for approximately solving constraint satisfaction problems to find bounds on extremal eigenvalues of local Hamiltonians. We consider spin Hamiltonians for which we have an upper bound on the number of terms in which each spin participates, and find extensive bounds for the operator norm and ground-state energy of such Hamiltonians under this constraint. In each case the bound is achieved by a product state which can be found efficiently using a classical algorithm.

Quantum 1, 6 (2017). https://doi.org/10.22331/q-2017-04-25-6

]]>We apply classical algorithms for approximately solving constraint satisfaction problems to find bounds on extremal eigenvalues of local Hamiltonians. We consider spin Hamiltonians for which we have an upper bound on the number of terms in which each spin participates, and find extensive bounds for the operator norm and ground-state energy of such Hamiltonians under this constraint. In each case the bound is achieved by a product state which can be found efficiently using a classical algorithm.

]]>Characterizing quantum systems through experimental data is critical to applications as diverse as metrology and quantum computing. Analyzing this experimental data in a robust and reproducible manner is made challenging, however, by the lack of readily-available software for performing principled statistical analysis. We improve the robustness and reproducibility of characterization by introducing an open-source library, QInfer, to address this need. Our library makes it easy to analyze data from tomography, randomized benchmarking, and Hamiltonian learning experiments either in post-processing, or online as data is acquired. QInfer also provides functionality for predicting the performance of proposed experimental protocols from simulated runs. By delivering easy-to-use characterization tools based on principled statistical analysis, QInfer helps address many outstanding challenges facing quantum technology.

Quantum 1, 5 (2017). https://doi.org/10.22331/q-2017-04-25-5

]]>Characterizing quantum systems through experimental data is critical to applications as diverse as metrology and quantum computing. Analyzing this experimental data in a robust and reproducible manner is made challenging, however, by the lack of readily-available software for performing principled statistical analysis. We improve the robustness and reproducibility of characterization by introducing an open-source library, QInfer, to address this need. Our library makes it easy to analyze data from tomography, randomized benchmarking, and Hamiltonian learning experiments either in post-processing, or online as data is acquired. QInfer also provides functionality for predicting the performance of proposed experimental protocols from simulated runs. By delivering easy-to-use characterization tools based on principled statistical analysis, QInfer helps address many outstanding challenges facing quantum technology.

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