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Prabha Mandayam
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Prabha Mandayam
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Prabha Mandayam
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Mandayam, Prabha
Mandayam, P.
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9 results
Now showing 1 - 9 of 9
- PublicationQuantum Error Correction: Noise-Adapted Techniques and Applications(01-04-2023)
;Jayashankar, AkshayaThe quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects of such noise on quantum states can be mitigated, paving the way for realising robust, scalable quantum computers. In this article we survey the current landscape of quantum error correcting (QEC) codes, focusing on recent theoretical advances in the domain of noise-adapted QEC, and highlighting some key open questions. We also discuss the interesting connections that have emerged between such adaptive QEC techniques and fundamental physics, especially in the areas of many-body physics and cosmology. We conclude with a brief review of the theory of quantum fault tolerance which gives a quantitative estimate of the physical noise threshold below which error-resilient quantum computation is possible. - PublicationTime-Bin Superposition Methods for DPS-QKD(01-10-2022)
;Shaw, Gautam ;Sridharan, Shyam ;Ranu, Shashank ;Shingala, Foram; Key generation efficiency, and security, in differential phase-shift quantum key distribution (DPS-QKD) improve with an increase in the number of optical delays or time-bin superpositions. We demonstrate the implementation of superposition states using time-bins, with two different approaches. In Type-A, we use an optical pulse and create superposition states with optical splitters and path delays. Similar superposition states are created, in Type-B, by applying direct phase modulation within a single weak coherent pulse. We establish the equivalence between both the approaches, and note that higher-order superposition states of Type-B are easier to generate for DPS-QKD. We set up DPS-QKD, over 105 km of single mode optical fiber, with a quantum bit error rate of less than 15% at a secure key rate of 2 kbps. With temporal guard bands, the QBER reduced to less than 10%, but with a 20% reduction in the key rate. - PublicationOn optimal cloning and incompatibility(08-10-2021)
;Mitra, ArindamWe investigate the role of symmetric quantum cloning machines (QCMs) in quantifying the mutual incompatibility of quantum observables. Specifically, we identify a cloning-based incompatibility measure whereby the incompatibility of a set of observables maybe quantified in terms of how well a uniform ensemble of their eigenstates can be cloned via a symmetric QCM. We show that this new incompatibility measure Qc is faithful since it vanishes only for commuting observables.We prove an upper bound forQc for any set of observables in a finite-dimensional system and show that the upper bound is attained if and only if the observables are mutually unbiased. Finally, we use our formalism to obtain the optimal quantum cloner for a pair of qubit observables. Our work marks an important step in formalising the connection between two fundamental concepts in quantum information theory, namely, the no-cloning principle and the existence of incompatible observables in quantum theory. - PublicationAchieving fault tolerance against amplitude-damping noise(01-06-2022)
;Jayashankar, Akshaya ;Long, My Duy Hoang ;Ng, Hui KhoonWith the intense interest in small, noisy quantum computing devices comes the push for larger, more accurate - and hence more useful - quantum computers. While fully fault-tolerant quantum computers are, in principle, capable of achieving arbitrarily accurate calculations using devices subjected to general noise, they require immense resources far beyond our current reach. An intermediate step would be to construct quantum computers of limited accuracy enhanced by lower-level, and hence lower-cost, noise-removal techniques. This is the motivation for our paper, which looks into fault-tolerant encoded quantum computation targeted at the dominant noise afflicting the quantum device. Specifically, we develop a protocol for fault-tolerant encoded quantum computing components in the presence of amplitude-damping noise, using a 4-qubit code and a recovery procedure tailored to such noise. We describe a universal set of fault-tolerant encoded gadgets and compute the pseudothreshold for the noise, below which our scheme leads to more accurate computation. Our paper demonstrates the possibility of applying the ideas of quantum fault tolerance to targeted noise models, generalizing the recent pursuit of biased-noise fault tolerance beyond the usual Pauli noise models. We also illustrate how certain aspects of the standard fault tolerance intuition, largely acquired through Pauli-noise considerations, can fail in the face of more general noise. - PublicationEntanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength(23-10-2020)
;Jonnadula, Bhargavi; ;Życzkowski, KarolEntanglement properties of bipartite unitary operators are studied via their local invariants, namely the entangling power ep and a complementary quantity, the gate typicality gt. We characterize the boundaries of the set K2 representing all two-qubit gates projected onto the plane (ep,gt) showing that the fractional powers of the swap operator form a parabolic boundary of K2, while the other bounds are formed by two straight lines. In this way, a family of gates with extreme properties is identified and analyzed. We also show that the parabolic curve representing powers of swap persists in the set KN for gates of higher dimensions (N>2). Furthermore, we study entanglement of bipartite quantum gates applied sequentially n times, and we analyze the influence of interlacing local unitary operations, which model generic Hamiltonian dynamics. An explicit formula for the entangling power of a gate applied n times averaged over random local unitary dynamics is derived for an arbitrary dimension of each subsystem. This quantity shows an exponential saturation to the value predicted by the random matrix theory, indicating "thermalization"in the entanglement properties of sequentially applied quantum gates that can have arbitrarily small, but nonzero, entanglement to begin with. The thermalization is further characterized by the spectral properties of the reshuffled and partially transposed unitary matrices. - PublicationFinding good quantum codes using the Cartan form(01-04-2020)
;Jayashankar, Akshaya ;Babu, Anjala M. ;Ng, Hui KhoonWe present a simple and fast numerical procedure to search for good quantum codes for storing logical qubits in the presence of independent per-qubit noise. In a key departure from past work, we use the worst-case fidelity as the figure of merit for quantifying code performance, a much better indicator of code quality than, say, entanglement fidelity. Yet our algorithm does not suffer from inefficiencies usually associated with the use of worst-case fidelity. Specifically, using a near-optimal recovery map, we are able to reduce the triple numerical optimization needed for the search to a single optimization over the encoding map. We can further reduce the search space by using the Cartan decomposition, focusing our search over the nonlocal degrees of freedom resilient against independent per-qubit noise, while not suffering much in code performance. - PublicationHolographic spacetime, black holes and quantum error correcting codes: a review(01-05-2022)
;Kibe, Tanay; This article reviews the progress in our understanding of the reconstruction of the bulk spacetime in the holographic correspondence from the dual field theory including an account of how these developments have led to the reproduction of the Page curve of the Hawking radiation from black holes. We review quantum error correction and relevant recovery maps with toy examples based on tensor networks, and discuss how it provides the desired framework for bulk reconstruction in which apparent inconsistencies with properties of the operator algebra in the dual field theory are naturally resolved. The importance of understanding the modular flow in the dual field theory has been emphasized. We discuss how the state-dependence of reconstruction of black hole microstates can be formulated in the framework of quantum error correction with inputs from extremal surfaces along with a quantification of the complexity of encoding of bulk operators. Finally, we motivate and discuss a class of tractable microstate models of black holes which can illuminate how the black hole complementarity principle can emerge operationally without encountering information paradoxes, and provide new insights into generation of desirable features of encoding into the Hawking radiation. - PublicationDifferential phase encoded measurement-device-independent quantum key distribution(01-02-2021)
;Ranu, Shashank Kumar; We present a measurement-device-independent quantum key distribution (MDI-QKD) using single photons in a linear superposition of three orthogonal time-bin states, for generating the key. The orthogonal states correspond to three distinct paths in the delay line interferometers used by two (trusted) sources. The key information is decoded based on the measurement outcomes obtained by an untrusted third party Charles, who uses a beamsplitter to measure the phase difference between pulses traveling through different paths of the two delay lines. The proposed scheme combines the best of both differential-phase-shift (DPS) QKD and MDI-QKD. It is more robust against phase fluctuations, and also ensures protection against detector side-channel attacks. We prove unconditional security by demonstrating an equivalent protocol involving shared entanglement between the two trusted parties. We show that the secure key rate for our protocol compares well to existing protocols in the asymptotic regime. For the decoy-state variant of our protocol, we evaluate the secure key rate by using a phase-post-selection technique. Finally, we estimate the bit error rate and the phase error rate, in the finite key regime. - PublicationPretty good measurement for bosonic Gaussian ensembles(2024-01-01)
;Mishra, Hemant K. ;Lami, Ludovico; Wilde, Mark M.The pretty good measurement is a fundamental analytical tool in quantum information theory, giving a method for inferring the classical label that identifies a quantum state chosen probabilistically from an ensemble. Identifying and constructing the pretty good measurement for the class of bosonic Gaussian states is of immediate practical relevance in quantum information processing tasks. Holevo recently showed that the pretty good measurement for a bosonic Gaussian ensemble is a bosonic Gaussian measurement that attains the accessible information of the ensemble [IEEE Trans. Inf. Theory 66(9) (2020) 5634]. In this paper, we provide an alternate proof of Gaussianity of the pretty good measurement for a Gaussian ensemble of multimode bosonic states, with a focus on establishing an explicit and efficiently computable Gaussian description of the measurement. We also compute an explicit form of the mean square error of the pretty good measurement, which is relevant when using it for parameter estimation. Generalizing the pretty good measurement is a quantum instrument, called the pretty good instrument. We prove that the post-measurement state of the pretty good instrument is a faithful Gaussian state if the input state is a faithful Gaussian state whose covariance matrix satisfies a certain condition. Combined with our previous finding for the pretty good measurement and provided that the same condition holds, it follows that the expected output state is a faithful Gaussian state as well. In this case, we compute an explicit Gaussian description of the post-measurement and expected output states. Our findings imply that the pretty good instrument for bosonic Gaussian ensembles is no longer merely an analytical tool, but that it can also be implemented experimentally in quantum optics laboratories.