Catálogo de publicaciones - revistas

<jats:title>Abstract</jats:title> <jats:p>We consider the sensing of scalar valued fields with specific spatial dependence using a network of sensors, e.g. multiple atoms located at different positions within a trap. We show how to harness the spatial correlations to sense only a specific signal, and be insensitive to others at different positions or with unequal spatial dependence by constructing a decoherence-free subspace for noise sources at fixed, known positions. This can be extended to noise sources lying on certain surfaces, where we encounter a connection to mirror charges and equipotential surfaces in classical electrostatics. For general situations, we introduce the notion of an approximate decoherence-free subspace, where noise for all sources within some volume is significantly suppressed, at the cost of reducing the signal strength in a controlled way. We show that one can use this approach to maintain Heisenberg-scaling over long times and for a large number of sensors, despite the presence of multiple noise sources in large volumes. We introduce an efficient formalism to construct internal states and sensor configurations, and apply it to several examples to demonstrate the usefulness and wide applicability of our approach.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Coherent errors in quantum operations are ubiquitous. Whether arising from spurious environmental couplings or errors in control fields, such errors can accumulate rapidly and degrade the performance of a quantum circuit significantly more than an average gate fidelity may indicate. As Hastings (2017 <jats:italic>Quantum Inf. Comput.</jats:italic> <jats:bold>17</jats:bold> 488) and Campbell (2017 <jats:italic>Phys. Rev.</jats:italic> A <jats:bold>95</jats:bold> 042306) have recently shown, by replacing the deterministic implementation of a quantum gate with a randomized ensemble of implementations, one can dramatically suppress coherent errors. Our work begins by reformulating the results of Hastings and Campbell as a quantum optimal control problem. We then discuss a family of convex programs able to solve this problem, as well as a set of secondary objectives designed to improve the performance, implementability, and robustness of the resulting mixed quantum gates. Finally, we implement these mixed quantum gates on a superconducting qubit and discuss randomized benchmarking results consistent with a marked reduction in the coherent error.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The non-Markovianity of an arbitrary open quantum system is analyzed in reference to the multi-time statistics given by its monitoring at discrete times. On the one hand, we exploit the hierarchy of inhomogeneous transfer tensors (TTs), which provides us with relevant information about the role of correlations between the system and the environment in the dynamics. The connection between the TT hierarchy and the CP-divisibility property is then investigated, by showing to what extent quantum Markovianity can be linked to a description of the open-system dynamics by means of the composition of one-step TTs only. On the other hand, we introduce the set of stochastic TT transformations associated with local measurements on the open system at different times and conditioned on the measurement outcomes. The use of the TT formalism accounts for different kinds of memory effects in the multi-time statistics and allows us to compare them on a similar footing with the memory effects present in non-monitored non-Markovian dynamics, as we illustrate on a spin-boson case study.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum systems and phenomena. However, for interacting many-body quantum systems, its calculation generally involves summing over an exponential number of terms and can thus quickly grow to be intractable. Accurately and efficiently estimating the partition function of its corresponding system Hamiltonian then becomes the key in solving quantum many-body problems. In this paper we develop a hybrid quantum–classical algorithm to estimate the partition function, utilising a novel quantum Clifford sampling technique. Note that previous works on the estimation of partition functions require <jats:inline-formula> <jats:tex-math><?CDATA $\mathcal{O}(1/{\epsilon}\sqrt{{\Delta}})$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">O</mml:mi> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mi>ϵ</mml:mi> <mml:msqrt> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> </mml:mrow> </mml:msqrt> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstac47f0ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>-depth quantum circuits (Srinivasan <jats:italic>et al</jats:italic> 2021 <jats:italic>IEEE Int. Conf. on Quantum Computing and Engineering (QCE)</jats:italic> pp 112–22; Montanaro 2015 <jats:italic>Proc. R. Soc.</jats:italic> A <jats:bold>471</jats:bold> 20150301), where Δ is the minimum spectral gap of stochastic matrices and <jats:italic>ϵ</jats:italic> is the multiplicative error. Our algorithm requires only a shallow <jats:inline-formula> <jats:tex-math><?CDATA $\mathcal{O}(1)$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">O</mml:mi> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstac47f0ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>-depth quantum circuit, repeated <jats:inline-formula> <jats:tex-math><?CDATA $\mathcal{O}(n/{{\epsilon}}^{2})$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">O</mml:mi> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mi>ϵ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstac47f0ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> times, to provide a comparable <jats:italic>ϵ</jats:italic> approximation. Shallow-depth quantum circuits are considered vitally important for currently available noisy intermediate-scale quantum devices.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>A <jats:italic>while</jats:italic> loop tests a termination condition on every iteration. On a quantum computer, such measurements perturb the evolution of the algorithm. We define a while loop primitive using weak measurements, offering a trade-off between the perturbation caused and the amount of information gained per iteration. This trade-off is adjusted with a parameter set by the programmer. We provide sufficient conditions that let us determine, with arbitrarily high probability, a worst-case estimate of the number of iterations the loop will run for. As an example, we solve Grover’s search problem using a while loop and prove the quadratic quantum speed-up is maintained.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving quadratic unconstrained binary optimization problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a specific class of linear equations whose solutions can be found efficiently, to a hard constraint satisfaction problem (three-regular three-XORSAT, or an Ising spin glass) with a ‘golf-course’ shaped energy landscape, to benchmark several of these different approaches. We perform a scaling and prefactor analysis of the performance of Fujitsu’s digital annealer unit (DAU), the D-Wave advantage quantum annealer, a virtual MemComputing machine, Toshiba’s simulated bifurcation machine (SBM), the SATonGPU algorithm from Bernaschi <jats:italic>et al</jats:italic>, and our implementation of parallel tempering. We identify the SATonGPU and DAU as currently having the smallest scaling exponent for this benchmark, with SATonGPU having a small scaling advantage and in addition having by far the smallest prefactor thanks to its use of massive parallelism. Our work provides an objective assessment and a snapshot of the promise and limitations of dedicated optimization hardware relative to a particular class of optimization problems.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Noisy linear problems have been studied in various science and engineering disciplines. A class of ‘hard’ noisy linear problems can be formulated as follows: Given a matrix <jats:inline-formula> <jats:tex-math><?CDATA $\hat{A}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>A</mml:mi> </mml:mrow> <mml:mo stretchy="false">^</mml:mo> </mml:mover> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstac51b0ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> and a vector <jats:bold>b</jats:bold> constructed using a finite set of samples, a hidden vector or structure involved in <jats:bold>b</jats:bold> is obtained by solving a noise-corrupted linear equation <jats:inline-formula> <jats:tex-math><?CDATA $\hat{A}\mathbf{x}\approx \mathbf{b}+\boldsymbol{\eta }$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>A</mml:mi> </mml:mrow> <mml:mo stretchy="false">^</mml:mo> </mml:mover> </mml:mrow> <mml:mi mathvariant="bold">x</mml:mi> <mml:mo>≈</mml:mo> <mml:mi mathvariant="bold">b</mml:mi> <mml:mo>+</mml:mo> <mml:mi mathvariant="bold-italic">η</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstac51b0ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>, where <jats:bold> <jats:italic>η</jats:italic> </jats:bold> is a noise vector that cannot be identified. For solving such a noisy linear problem, we consider a quantum algorithm based on a divide-and-conquer strategy, wherein a large core process is divided into smaller subprocesses. The algorithm appropriately reduces both the computational complexities and size of a quantum sample. More specifically, if a quantum computer can access a particular reduced form of the quantum samples, polynomial quantum-sample and time complexities are achieved in the main computation. The size of a quantum sample and its executing system can be reduced, e.g., from exponential to sub-exponential with respect to the problem length, which is better than other results we are aware. We analyse the noise model conditions for such a quantum advantage, and show when the divide-and-conquer strategy can be beneficial for quantum noisy linear problems.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Entanglement is one of the key ingredients for enhancing the measurement precision of quantum sensors. Generally, there is a trade-off between state preparation and sensing within a limited coherence time. To fully exploit temporal resources, concurrent entanglement generation and sensing with designed sequence of rotations are proposed. Based on twist-and-turn dynamics, modulated rotations along only one axis may be sufficient to drive the state to the optimal one for tiny estimated parameter. However, when the estimated parameter is not tiny, it may impact the evolved state and hence degrade the final measurement precision. Here, we introduce another modulated rotations along different axis and find out the optimal control sequences by means of machine optimization. The optimal measurement precision bounds become independent on the estimated parameter, which improves the dynamic range of the machine designed sensors. Particularly, by optimizing the interaction strength for different particle number and the time-modulated rotations along two different axes via machine optimization, the Heisenberg-limited precision scaling can be attained. Our work points out a way for designing optimized quantum-enhanced metrology protocols, which is promising for developing practical quantum sensors.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact and relevance, too. In this respect, Bayesian methods have emerged as an effective and elegant solution, with the perk of incorporating naturally the availability of <jats:italic>a priori</jats:italic> information. In this article we present an evaluation of Bayesian methods for multiple phase estimation, assessed based on bounds that work beyond the usual limit of large samples assumed in parameter estimation. Importantly, such methods are applied to experimental data generated from the output statistics of a three-arm interferometer seeded by single photons. Our studies provide a blueprint for a more comprehensive data analysis in quantum metrology.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Weak-value amplification employs postselection to enhance the measurement of small parameters of interest. The amplification comes at the expense of reduced success probability, hindering the utility of this technique as a tool for practical metrology. Following other quantum technologies that display a quantum advantage, we formalize a quantum advantage in the success probability and present a scheme based on non-linear collective Hamiltonians that shows a super-extensive growth in success probability while simultaneously displaying an extensive growth in the weak value. We propose an experimental implementation of our scheme.</jats:p>