arXiv subjects

Subhash Kak

Publications and source records attributed to Subhash Kak.

124 records · Page 7Linked to original sources

arXiv2002

Statistical Constraints on State Preparation for a Quantum Computer

Quantum computing algorithms require that the quantum register be initially present in a superposition state. To achieve this, we consider the practical problem of creating a coherent superposition state of several qubits. Owing to considerations of quantum statistics, this requires that the entropy of the system go down. This, in turn, has two practical implications: (i) the initial state cannot be controlled; (ii) the temperature of the system must be reduced. These factors, in addition to decoherence and sensitivity to errors, must be considered in the implementation of quantum computers.

quant-ph↗

arXiv2002

The Initialization Problem in Quantum Computing

The problem of initializing phase in a quantum computing system is considered. The initialization of phases is a problem when the system is initially present in an entangled state and also in the application of the quantum gate transformations since each gate will introduce phase uncertainty. The accumulation of these random phases will reduce the effectiveness of the recently proposed quantum computing schemes. The paper also presents general observations on the nonlocal nature of quantum errors and the expected performance of the proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or phase-flip or both. It is argued that these codes cannot directly solve the initialization problem of quantum computing.

quant-ph↗

arXiv2002

Uncertainty In Quantum Computation

We examine the effect of previous history on starting a computation on a quantum computer. Specifically, we assume that the quantum register has some unknown state on it, and it is required that this state be cleared and replaced by a specific superposition state without any phase uncertainty, as needed by quantum algorithms. We show that, in general, this task is computationally impossible.

quant-ph↗

arXiv2001

On Aryabhata's Planetary Constants

This paper examines the theory of a Babylonian origin of Aryabhata's planetary constants. It shows that Aryabhata's basic constant is closer to the Indian counterpart than to the Babylonian one. Sketching connections between Aryabhata's framework and earlier Indic astronomical ideas on yugas and cyclic calendar systems, it is argued that Aryabhata's system is an outgrowth of an earlier Indic tradition.

physics.gen-ph↗

arXiv2001

Collapse, Expansion, and a Variable Speed of Light

This paper presents an information-theoretic view of how an observer within a quantum system will perceive his world. It is argued that because of the indistinguishability of quantum particles, a coherent state will appear to an observer within the system like a singularity. As superposition is lost, space appears to expand, although to the outsider it is merely the collapse of the wave function. Implications of these ideas to cosmology are considered. The superluminal expansion of space provides a basis to understand inflationary cosmologies. This expansion may be taken to be equivalent to a much faster speed of light during the inflationary period. These ideas can be tested by checking for `higher' speed of light from photons emitted by decohering atoms.

astro-ph↗

arXiv2001

Birth and Early Development of Indian Astronomy

This paper provides an overview of the birth and early development of Indian astronomy. Taking account of significant new findings from archaeology and literary analysis, it is shown that early mathematical astronomy arose in India in the second millennium BC. The paper reviews the astronomy of the period of the Vedas, the Brahmanas, and the Vedanga Jyotisha. The origins of Puranic cosmology are also explained.

physics.hist-ph↗

arXiv2001

The Speed of Light and Puranic Cosmology

We survey early Indian ideas on the speed of light and the size of the universe. A context is provided for Sayana's statement (14th century)that the speed is 2,202 yojanas per half nimesha (186,000 miles per second!). It is shown how this statement may have emerged from early Puranic notions regarding the size of the universe. Although this value can only be considered to be an amazing coincidence, the Puranic cosmology at the basis of this assertion illuminates many ancient ideas of space and time.

physics.hist-ph↗

arXiv2001

Yajnavalkya and the Origins of Puranic Cosmology

This paper shows that characteristic features of Puranic cosmology, such as alternating cosmic continents and oceans of successively doubling areas, can be traced to Vedic texts. The Rigveda speaks of seven regions of the universe, and Yajnavalkya, in Brihadaranyaka Upanishad, presents a cosmology that has all the essential features of the Puranic system. This discovery solves the old puzzle of the origin of Puranic astronomy.

physics.hist-ph↗

arXiv2000

Quantum Key Distribution Using Three Basis States

This note presents a method of public key distribution using quantum communication of n photons that simultaneously provides a high probability that the bits have not been tampered. It is a three-state variant of the quantum method of Bennett and Brassard (BB84) where the transmission states have been decreased from 4 to 3 and the detector states have been increased from 2 to 3. Under certain assumptions regarding method of attack, it provides superior performance (in terms of the number of usable key bits) for n < 18 m, where m is the number of key bits used to verify the integrity of the process in the BB84-protocol.

quant-ph↗

arXiv1999

On Rotating a Qubit

The state function of a quantum object is undetermined with respect to its phase. This indeterminacy does not matter if it is global, but what if the components of the state have unknown relative phases? Can useful computations be performed in spite of this local indeterminacy? We consider this question in relation to the problem of the rotation of a qubit and examine its broader implications for quantum computing.

quant-ph↗

arXiv1999

Concepts of Space, Time, and Consciousness in Ancient India

This paper describes Indian ideas of the early-Purana/Mahabharata times (centuries BC) on the nature of space, time and consciousness that would be of interest to the physicist. In order to simplify references, we quote mainly from Yoga-Vasistha (YV), which is representative of that period of Indian thought. YV professes to be a book of instruction on the nature of consciousness but it has many fascinating passages on time, space, matter and cognition. This paper presents a random selection that has parallels with recent speculations in physics. It also presents a brief account of the context in which ideas of YV developed.

physics.hist-ph↗

arXiv1999

The Solar Numbers in Angkor Wat

The great Vishnu temple at Angkor Wat in north-central Kampuchea (Cambodia) is known to have been built according to an astronomical plan. In this note we show that the little-understood solar formula of the temple is identical to the one in the 2nd millennium BC Indian text called Shatapatha Brahmana. We propose that the Angkor Wat formula was an expression of the Shatapatha astronomy.

physics.hist-ph↗

arXiv1998

A Formula for the Rotation Periods of the Planets & Asteroids

The note presents a formula for the prediction of the rotation periods of the planets and asteroids. This formula, which is like the Titius-Bode law, gives a good agreement with the rotation periods of most planets, shows that Venus is retrograde, and that there must be five objects between Mars and Jupiter. This formula may be of some relevance in understanding the dynamics of the early solar system.

physics.pop-ph↗

arXiv1998

A Note on Quantum Errors and Their Correction

This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or phase-flip or both.

quant-ph↗

arXiv1998

Early Theories on the Distance to the Sun

According to an ancient Indian text (c. 1700 BC?), the heavens are 1000 earth diameters away from the earth. Other texts took the sun to be halfway to the heavens, so this suggests a distance of the sun about 500 earth diameters from the earth. The confirmation for this supposition comes from the later theories (c. 500 AD) from the same region and from Greek ideas that speak of roughly the same distance. We suggest that this original conception was transformed by the later Indian and Greek theories in different ways to deal with contradictory data related to outer planet periods.

physics.hist-ph↗

arXiv1998

Quantum Information in a Distributed Apparatus

We investigate the information provided about a specified distributed apparatus of n units in the measurement of a quantum state. It is shown that, in contrast to such measurement of a classical state, which is bounded by log (n+1) bits, the information in a quantum measurement is bounded by 3.7 x n^(1/2) bits. This means that the use of quantum apparatus offers an exponential advantage over classical apparatus.

quant-ph↗