Introduction to Quantum Computers

Berman, G. P.; Doolen, Gary D.; Mainieri, Ronnie; Tsifrinovich, V. I.

doi:10.1142/9789812384775

Cited by 88 publications

(88 citation statements)

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“…It is a physical resource, like energy, associated with the peculiar non-classical correlations that are possible between separated quantum systems. Recourse to entanglement is required so as to implement quantum information processes [2,3] such as quantum cryptographic key distribution [4], quantum teleportation [5], superdense coding [6], and quantum computation [7]. Indeed, production of entanglement is a kind of elementary prerequisite for any quantum computation.…”

Section: Introductionmentioning

confidence: 99%

Maximally entangled mixed states and conditional entropies

2005

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The maximally entangled mixed states of Munro, James, White, and Kwiat [Phys. Rev. A 64 (2001) (2000)], whose entanglement-degree can not be increased by acting on them with logic gates. Special types of entangled states that do not violate classical entropic inequalities are seen to exist in the space of two qubits. Special meaning can be assigned to the Munro et al. special participation ratio of 1.8.

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Section: Introductionmentioning

confidence: 99%

Maximally entangled mixed states and conditional entropies

2005

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“…The probability of transition generated by the pulse with the Rabi frequency Ω and detuning ∆ is [20,21] …”

Section: Implementation Of Quantum Logic Gatesmentioning

confidence: 99%

Influence of qubit displacements on quantum logic operations in a silicon-based quantum computer with constant interaction

2006

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The errors caused by qubit displacements from their prescribed locations in an ensemble of spin chains are estimated analytically and calculated numerically for a quantum computer based on phosphorus donors in silicon. We show that it is possible to polarize (initialize) the nuclear spins even with displaced qubits by using Controlled NOT gates between the electron and nuclear spins of the same phosphorus atom. However, a Controlled NOT gate between the displaced electron spins is implemented with large error because of the exponential dependence of exchange interaction constant on the distance between the qubits. If quantum computation is implemented on an ensemble of many spin chains, the errors can be small if the number of chains with displaced qubits is small.

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“…Unitary operations such as XOR can be executed by radio frequency (RF) pulses at resonance frequencies determined in part by this spin-spin coupling between pairs of nuclei (and also by the chemical structure of the molecule). Bulk QC was independently proposed by Cory, Fahmy, Havel [CFH96] and Gershenfeld, Chuang [GC97, GC98] Also see Berman et al [BDL+98] and the proposal of Wei et al [WXM98b] for doing NMR QC on doped crystals rather than in solutions, and see Kane [Kan98] for another solid state NMR architecture using silicon.…”

Section: Enabling Technologies and Experimental Paradigms For Bmcmentioning

confidence: 99%

Alternative Computational Models: A Comparison of Biomolecular and Quantum Computation

Reif

1998

Lecture Notes in Computer Science

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Molecular Computation (MC) is massively parallel computation where data is stored and processed within objects of molecular size. Biomolecular Computation (BMC) is MC using biotechnology techniques, e.g. recombinant DNA operations. In contrast, Quantum Computation (QC) is a type of computation where unitary and measurement operations are executed on linear superpositions of basis states. Both BMC and QC may be executed at the micromolecular scale by a variety of methodologies and technologies. This paper surveys various methods for doing BMC and QC and discusses the considerable theoretical and practical advances in BMC and QC made in the last few years. We compare bounds on key resource such as time, volume (number of molecules times molecular density), energy and error rates achievable, taking particular note of the scalability of these methods with the size of the problem solved. In addition to NP search problems and database search problems, we enumerate a wide variety of further potential practical applications of BMC and QC.We observe that certain problems (e.g., NP search problems), if solved with polynomial time bounds, requires exponentially large volume for BMC, so BMC does not scale well to solve very large NP search problems. However, we describe a number of applications (e.g., search within large data bases and simulation of parallel machines) where the volume grows polynomial.Also, we note that the observation operation of QC, which is a fundamental operation of QC used for obtaining classical output, may potentially suffer from exponentially large volume requirements. Observation operations in quantum physics are generally done by a macroscopic measurement apparatus, and the original formulations of QC implicity assumed that macroscopic measurement apparatus would be used for QC. However, if the measurement apparatus is very small, it will be subject to quantum effects. At this time, no one has demonstrated or proved that the observation operation (for a quantum system with n entangled qubits) can even be approximated within a larger unitary quantum system in volume growing less than exponentially with n. Hence it is unknown whether QC (with the observation operation) scales to even moderate numbers of qubits within small volume. We pose a major open problem in QC: to determine (i.e., provide a formal proof) whether or not observation, in a closed quantum system, can be approximated in small volume: say, growing as a polynomial in the number of qubits.We also discuss techniques for decreasing errors in BMC (e.g., annealing errors) and QC (e.g., decoherence errors), and volume where possible, to insure the scalability of BMC and QC to problems of large input size. In addition, we consider how BMC might be used to assist QC (e.g., to do observation operations for Bulk QC) and also how quantum techniques might be used to assist BMC (e.g., to do exquisite detection of very small quantities of a molecule in solution within a large volume).

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Introduction to Quantum Computers

Cited by 88 publications

References 0 publications

Maximally entangled mixed states and conditional entropies

Maximally entangled mixed states and conditional entropies

Influence of qubit displacements on quantum logic operations in a silicon-based quantum computer with constant interaction

Alternative Computational Models: A Comparison of Biomolecular and Quantum Computation

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