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Knotted Pictures of Hadamard Gate and CNOT Gate

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Communications in Theoretical Physics 2009年第6期51卷 967-972页

作者： gu zhi-yu QIAN Shang-Wu Physics Department Capital Normal University Beijing 100037 China Physics Department Peking University Beijing 100871 China

This paper obtains the knotted pictures of Hadamard gate and CNOT gate in terms of surgical operations described in knot theory.

关键词： two qubit quantum logic gate surgical operations in knot theory knotted picture

Knotted Picture of Unknown Quantum State in Process of Quantum Teleportation

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Communications in Theoretical Physics 2008年第5期49卷 1163-1164页

作者： gu zhi-yu QIAN Shang-Wu Physics Department Capital Normal University Beijing 100037 China Physics Department Peking University Beijing 100871 China

This paper gives the knotted picture of the unknown quantum state in the process of quantum teleportation and the surgical knotted operations of the unitary operators operated on the teleported quantum state.

关键词： Bell bases single particle quantum state knotted picture flip operation inversion operation

A Note on Calculation of Phase Space Path Integral by Means of Invariants

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Communications in Theoretical Physics 2006年第5期45卷 813-814页

作者： QIAN Shang-Wu gu zhi-yu physics Department Peking University Beijing 100871 China physics Department Capital Normal University Beijing 100037 China

In this note we use the method of invariant to calculate the phase space path integral appearing in our previous article.

关键词： phase space path integral invariant propagator

Relationship Between Two Classes of Shape-Invariant Potentials

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Communications in Theoretical Physics 2001年第10期36卷 391-394页

作者： QIAN Shang-Wu gu zhi-yu Department of Physics Peking University Beijing 100871 China Department of Physics Capital Normal University Beijing 100037 China

We show that two classes of shape-invariant potentials are interrelated to each other. For all one-dimensional shape-invariant potentials with parameters related by translation, i.e. the first class of shapc-invariant potentials (SIP1),we can find their multi-parameter deformations with q acting as the deformation parameter, i.e. the second class of shape-invariant potentials (SIP2) with parameters related by scaling. In order to get closed solution of SIP2, we consider two infinitesimal intervals, one is close to q= 0 another close to q = 1, and show that in these intervals we can get separately two first-order approximate solutions in closed form, furthermore we prove that all SIP1 can be obtained by the limiting procedures for corresponding SIP2.

关键词： shape-invariant potential, superpotential, multi-parameter deformation

Knotted Picture of Unitary Transformation Applied to Single Particle Quantum State

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Communications in Theoretical Physics 2008年第1期49卷 65-68页

作者： gu zhi-yu QIAN Shang-Wu Physics Department Capital Normal University Beijing 100037 China Physics Department Peking University Beijing 100871 China

This paper introduces the unified expression of four Bell bases and uses the composition operation in knot theory to obtain the knotted picture of unitary operators based on Pauli operators, and gives the knotted expr... 详细信息

关键词： Bell bases composition operation knotted picture inversion relation

Knotted Picture of Single Qubit Quantum Logic Gate

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Communications in Theoretical Physics 2009年第5期51卷 769-772页

作者： gu zhi-yu QIAN Shang-Wu Physics Department Capital Normal University Beijing 100037 China Physics Department Peking University Beijing 100871 China

This paper briefly introduces the five types of the surgical operations in knot theory and obtains the expression of single qubit quantum logic gate in terms of these surgical operations.

关键词： single qubit quantum logic gate surgical operations in knot theory knotted picture

Evolutions of Yang Phase Under Cyclic Condition and Adiabatic Condition

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Communications in Theoretical Physics 2005年第2X期44卷 243-246页

作者： QIAN Shang-Wu gu zhi-yu Physics Department Peking University Beijing 100871 China Physics Department Capital Normal University Beijing 100037 China

There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the evolutions of Yang phase under the cyclic condition and the adiabatic condition for the generaltime-dependent harmonic oscillator, thus reveals the intimate relations between these three non-integrable phases.

关键词： Berry phase A-A phase Yang phase general time-dependent harmonic oscillator

Correspondence Between GHZ States and Oriented Links in Knot Theory

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Communications in Theoretical Physics 2002年第10期38卷 421-423页

作者： QIAN Shang-Wu gu zhi-yu physics Department Peking University Beijing 100871 China Physics Department Capital Normal University Beijing 100037 China

This article generalizes our previous results for a quantum system of two nodes to a quantum system ofm(m ≥ 2) nodes. It shows that there is a one to one correspondence between 2m GHZ states for a quantum system ofm(m ≥ 2) nodes and 2m oriented links of the linkage N1 in knot theory, where N = 4 C2m = 2m(m - 1) is the numberof crossings of the link with m components, the subscript 1 denotes the order of the unoriented m components link withN crossings, i.e. the first type, actually the simplest type.

关键词： GHZ states, oriented links in knot theory, inversion relations under the action of Pauli matrices

The Homotopic Probability Distribution and the Partition Function for the Entangled System Around a Ribbon Segment Chain

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Communications in Theoretical Physics 2001年第12期36卷 691-694页

作者： QIAN Shang-Wu gu zhi-yu Department of Physics Peking University Beijing 100871 China Department of Physics Capital Normal University Beijing 100037 China

Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution PnL for the winding number n and the partition function PL of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point.

关键词： Feynman's path integral with topological constraints, homotopic probability distribution, parti tion function, entangled system around a ribbon segment chain