The development of graduate work speech in the United States

Gray, Giles Wilkeson

doi:10.1080/03634525309376624

Cited by 3 publications

(4 citation statements)

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“…We show that in the qubit case both these measures coincide. The encoding by Alice utilises the roots of the generalised Pauli matrices, as well as Gray codes [20] and its non-Boolean generalisations [21,22], which is an example of a single distance code. We also present an analysis for higher dimensions, d = 3, 4 and show that the two measures of efficiency differ (in contrast to d = 2)-the interpretation of this fact is also discussed.…”

Section: Summary Of the Resultsmentioning

confidence: 99%

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Two instances of random access code in the quantum regime

et al. 2023

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We consider two classes of quantum generalisations of Random Access Code (RAC) and study the bounds for probabilities of success for such tasks. It provides a useful framework for the study of certain information processing tasks with constrained resources. The first class is based on a random access code with quantum inputs and output known as the No-Signalling Quantum RAC (NS-QRAC) box [A. Grudka et al., Phys. Rev. A 92, 052312 (2015)], where unbounded entanglement and constrained classical communication are allowed. We show that it can be seen as quantum teleportation with constrained classical communication and provide a lower quantum bound for the success probability. We consider two modifications to the NS-QRAC scenario, first where unbounded entanglement and constrained quantum communication is allowed and, second where bounded entanglement and unconstrained classical communication are allowed. We find a monogamy relation for the transmission fidelities, which --- in contrast to the usual communication schemes --- involves multiple senders and a single receiver. We provide an upper bounds for the latter and a lower one for the former. The second class is based on a RAC with a quantum channel and shared entanglement [A. Tavakoli et al., PRX Quantum 2, 040357 (2021)]. We study the set of tasks where two inputs made of two digits of d-base are encoded over a qudit and a maximally entangled state. We show that such tasks can be seen as quantum dense coding with constrained quantum communication and explicit protocols, which give lower quantum bounds for the tasks' efficiency, in dimensions d=2,3,4. The employed encoding utilises Gray codes.

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Section: Summary Of the Resultsmentioning

confidence: 99%

“…1 . The proposed encoding scheme to be employed by Alice for the general problem from equation (20) involves a map between the two strings a (0) and a (1) and two encoding strings e 0 and e (4)…”

Section: Higher Dimensionsmentioning

confidence: 99%

Two instances of random access code in the quantum regime

et al. 2023

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“…For Hamiltonian simulations on a quantum computer, a more efficient encoding than the SB is the Gray code (GC) [60,61], which effectively uses less gates and a lower circuit depth. The Gray code is defined to be an ordering of binary values where any two adjacent entries differ by only a single bit [62]. For example, consider the eight states of three binary bits, which can be ordered sequentially as…”

Section: Efficient Encoding Schemementioning

confidence: 99%

Simulating excited states of the Lipkin model on a quantum computer

Hlatshwayo

Zhang²,

Wibowo³

et al. 2022

Phys. Rev. C

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We simulate the excited states of the Lipkin model using the recently proposed Quantum Equation of Motion (qEOM) method. The qEOM generalizes the EOM on classical computers and gives access to collective excitations based on quasi-boson operators Ô † n (α) of increasing configuration complexity α. We show, in particular, that the accuracy strongly depends on the fermion to qubit encoding. Standard encoding leads to large errors, but the use of symmetries and the Gray code reduces the quantum resources and improves significantly the results on current noisy quantum devices. With this encoding scheme, we use IBM quantum machines to compute the energy spectrum for a system of N = 2, 3 and 4 particles, and compare the accuracy against the exact solution. We found that the results of the approach with α = 2, an analog of the second random phase approximation (SRPA), are, in principle, more accurate than with α = 1, which corresponds to the random phase approximation (RPA), but the SRPA is more amenable to noise for large coupling strengths. Thus, the proposed scheme shows potential for achieving higher spectroscopic accuracy by implementations with higher configuration complexity, if a proper error mitigation method is applied.

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“…In order to further validate bit-to-symbol mappings provided by our simulated annealing algorithm, we ran benchmarking tests on constellations that admit Gray coding [98] (e.g., M-PSK and M-QAM). Our implementation of the simulated annealing algorithm displayed strong performance in these tests, often finding the global minimum for small constellation sizes.…”

Section: A Constellation Designmentioning

confidence: 99%