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Register a new userOperational, gauge-free quantum tomography
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As increasingly impressive quantum information processors are realized in laboratories around the world, robust and reliable characterization of these devices is now more urgent than ever. These diagnostics can take many forms, but one of the most popular categories is tomography, where an underlying parameterized model is proposed for a device and inferred by experiments. Here, we introduce and implement efficient operational tomography, which uses experimental observables as these model parameters. This addresses a problem of ambiguity in representation that arises in current tomographic approaches (the gauge problem). Solving the gauge problem enables us to efficiently implement operational tomography in a Bayesian framework computationally, and hence gives us a natural way to include prior information and discuss uncertainty in fit parameters. We demonstrate this new tomography in a variety of different experimentally-relevant scenarios, including standard process tomography, Ramsey interferometry, randomized benchmarking, and gate set tomography.
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The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally probabilistic in character. Here, we propose a generalized formulation of quantum theory without predefined time or causal structure, building upon a recently introduced operationally time-symmetric approach to quantum theory. The key idea is a novel isomorphism between transformations and states which depends on the symmetry transformation of time reversal. This allows us to express the time-symmetric formulation in a time-neutral form with a clear physical interpretation, and ultimately drop the assumption of time. In the resultant generalized formulation, operations are associated with regions that can be connected in networks with no directionality assumed for the connections, generalizing the standard circuit framework and the process matrix framework for operations without global causal order. The possible events in a given region are described by positive semidefinite operators on a Hilbert space at the boundary, while the connections between regions are described by entangled states that encode a nontrivial symmetry and could be tested in principle. We discuss how the causal structure of space-time could be understood as emergent from properties of the operators on the boundaries of compact space-time regions. The framework is compatible with indefinite causal order, timelike loops, and other acausal structures.
We introduce a framework for simulating quantum measurements based on classical processing of a set of accessible measurements. Well-known concepts such as joint measurability and projective simulability naturally emerge as particular cases of our framework, but our study also leads to novel results and questions. First, a generalisation of joint measurability is derived, which yields a hierarchy for the incompatibility of sets of measurements. A similar hierarchy is defined based on the number of outcomes used to perform the simulation of a given measurement. This general approach also allows us to identify connections between different types of simulability and, in particular, we characterise the qubit measurements that are projective-simulable in terms of joint measurability. Finally, we discuss how our framework can be interpreted in the context of resource theories.
We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states, a complete set of variational states grasping states in quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on low-order correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomised continuous matrix product states from their correlation data and study the robustness of the reconstruction for different noise models. We also apply the method to data generated by simulations based on continuous matrix product states and using the time-dependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as encountered in experiments with ultra-cold atoms on top of atom chips. By virtue of the analogy with the input-output formalism in quantum optics, it also allows for studying open quantum systems.
Recent advances in quantum computers and simulators are steadily leading us towards full-scale quantum computing devices. Due to the fact that debugging is necessary to create any computing device, quantum tomography (QT) is a critical milestone on this path. In practice, the choice between different QT methods faces the lack of comparison methodology. Modern research provides a wide range of QT methods, which differ in their application areas, as well as experimental and computational complexity. Testing such methods is also being made under different conditions, and various efficiency measures are being applied. Moreover, many methods have complex programming implementations; thus, comparison becomes extremely difficult. In this study, we have developed a general methodology for comparing quantum state tomography methods. The methodology is based on an estimate of the resources needed to achieve the required accuracy. We have developed a software library (in MATLAB and Python) that makes it easy to analyze any QT method implementation through a series of numerical experiments. The conditions for such a simulation are set by the number of tests corresponding to real physical experiments. As a validation of the proposed methodology and software, we analyzed and compared a set of QT methods. The analysis revealed some method-specific features and provided estimates of the relative efficiency of the methods.
Quantum memory -- the capacity to store and faithfully recover unknown quantum states -- is essential for quantum-enhanced technology. There is thus a pressing need for operationally meaningful means to benchmark candidate memories across diverse physical platforms. Here we introduce a universal benchmark distinguished by its relevance across multiple key operational settings, exactly quantifying (1) the memorys robustness to noise, (2) the number of noiseless qubits needed for its synthesis, (3) its potential to speed up statistical sampling tasks, and (4) performance advantage in non-local games beyond classical limits. The measure is analytically computable for low-dimensional systems and can be efficiently bounded in experiment without tomography. We thus illustrate quantum memory as a meaningful resource, with our benchmark reflecting both its cost of creation and what it can accomplish. We demonstrate the benchmark on the five-qubit IBM Q hardware, and apply it to witness efficacy of error-suppression techniques and quantify non-Markovian noise. We thus present an experimentally accessible, practically meaningful, and universally relevant quantifier of a memorys capability to preserve quantum advantage.
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