Decoherence can be useful in quantum walks

We present a study of the effects of decoherence in the operation of a discrete quantum walk on a line, cycle and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is becoming more delocalised with each step. However, the effect of a small amount of decoherence is to enhance the properties of the quantum walk that are desirable for the development of quantum algorithms. Specifically, we observe a highly uniform distribution on the line, a very fast mixing time on the cycle, and more reliable hitting times across the hypercube.Comment: (Imperial College London) 6 (+epsilon) pages, 6 embedded eps figures, RevTex4. v2 minor changes to correct typos and refs, submitted version. v3 expanded into article format, extra figure, updated refs, Note on "glued trees" adde

Exponential Separation of Quantum and Classical Online Space Complexity

Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, space-bounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentially less work space than a classical computer. More precisely, we introduce a very natural and simple model of a space-bounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the bounded-error setting and for a total language. The language we consider is inspired by a communication problem (the set intersection function) that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical bounded-error communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential.Comment: 13 pages. v3: minor change

Phase Control and Fast Start-Up of a Magnetron Using Modulation of an Addressable Faceted Cathode

The use of an addressable, faceted cathode has been proposed as a method of modulating current injection in a magnetron to improve performance and control phase. To implement the controllable electron emission, five-sided and ten-sided faceted planar cathodes employing gated field emitters are considered as these emitters could be fabricated on flat substrates. For demonstration, the conformal finite-difference time-domain particle-in-cell simulation, as implemented in VORPAL, has been used to model a ten-cavity, rising sun magnetron using the modulated current sources and benchmarked against a typical continuous current source. For the modulated, ten-sided faceted cathode case, the electrons are injected from three emitter elements on each of the ten facets. Each emitter is turned ON and OFF in sequence at the oscillating frequency with five emitters ON at one time to drive the five electron spokes of the π-mode. The emitter duty cycle is then 1/6th the Radio-Frequency (RF) period. Simulations show a fast start-up time as low as 35 ns for the modulated case compared to 100 ns for the continuous current cases. Analysis of the RF phase using the electron spoke locations and the RF magnetic field components shows that the phase is controlled for the modulated case while it is random, as typical, for the continuous current case. Active phase control during oscillation was demonstrated by shifting the phase of the electron injection 180° after oscillations started. The 180° phase shift time was approximately 25 RF cycles

Dynamic Phase-Control of a Rising Sun Magnetron Using Modulated and Continuous Current

Phase-control of a magnetron is studied via simulation using a combination of a continuous current source and a modulated current source. The addressable, modulated current source is turned ON and OFF at the magnetron operating frequency in order to control the electron injection and the spoke phase. Prior simulation work using a 2D model of a Rising Sun magnetron showed that the use of 100% modulated current controlled the magnetron phase and allowed for dynamic phase control. In this work, the minimum fraction of modulated current source needed to achieve a phase control is studied. The current fractions (modulated versus continuous) were varied from 10% modulated current to 100% modulated current to study the effects on phase control. Dynamic phase-control, stability, and start up time of the device were studied for all these cases showing that with 10% modulated current and 90% continuous current, a phase shift of 180˚ can be achieved demonstrating dynamic phase control

Letter from Richard B. Watrous to William F. Bade, 1910 Jul 27.

J. HORACE MCFARLAND, President, Harrisburg, Pa. CLINTON ROGERS WOODRUFF. First Vice-President, PhiladelphiaWILLIAM B. HOWLAND, Treasurer, New YorkRICHARD B. WATROUS. Secretary, Washington, D. C.Vice-President: JAMES R. GARFIELD, Cleveland. OhloJOHN WESLEY HILL. D. D., New YorkW. W. HANNAN. Detroit. Mich.GEORGE W. MARSTON. San Diego, Cal.MRS. EDWARD W. BIDDLB. Carlisle, Pa.American Civic AssociationMAIN OFFICE: WASHINGTON, D.C. Executive BoardDr. JOHN QUINCY ADAMS, New YorkHENRY A. BARKER. Providence, R. I.FRANK CHAPIN BRAY, New YorkMISS MARY MARSHALL BUTLER,Yonkers, N. Y.DR. KRNVON L. BUTTERFIELD, Amherst. Mass.MRS. CAROLINE BARTLETT CRANE, Kalamazoo, Mich.Executive BoardGEORGE OTIS DRAPER. New YorkFREDERICK L. FORD, Hartford, Conn.EDWARD HATCH, JR., New YorkJ. L. HUDSON, Detroit, Mich.MRS. MELVILLE F. JOHNSTON, Richmond, Ind.HARLAN P. KELSEY, Salem, Mass.Executive BoardWARREN H. MANNING. Boston. Mass.MRS. A. E. MCCRRA. Chicago. IH.MRS. EDWIN F. MOULTON, Warren, OhioJOHN NOLEN, CAMBRIDGE. Mass.GRAHAM ROMEVN TAYLOR, Chicago, III.BRAINARD H. WARNER, WASHINGTON. D. COFFICE OF THE SECRETARY913-914 UNION TRUST BUILDINGWASHINGTON, D. C.July 27, 1910.Dr. William F Bade,c/o The Independent,New York City,Dear Dr. Bade:-Thanks for your kind letter of July 26th. I don\u27t think for a moment that Mr, McFarland will think you attacked the San Franciscans too vigorously, for I know he feels strongly on the subject and it was in the belief that he would so cordially approve it that I sent on my proof slip to him.Thank you for interesting yourself in securing for me a few copies of this week\u27s issue.No, I shall not be in Minneapolis, although I may get out to Milwaukee in September, but Mrs. Watrous will leave probably next week from Milwaukee and spend a month in St. Paul and Minneapolis and she will be delighted to see you while there. Her friends in Minneapolis have a little cottage quite a ways out from the city and on one of the main street car lines to Minnetonka. I will give you when she gets there her St. Paul address and her Minneapolis address in the hope that if you happen to be nearby you may be able to call on her.Sincerely yours, [ILLEGIBLE]0628

Local Unitary Quantum Cellular Automata

In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this model is to act as a theoretical model of quantum computation, similar to the quantum circuit model. It is also shown to be an appropriate abstraction for space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains and others. Some results that show the benefits of basing the model on local unitary operators are shown: universality, strong connections to the circuit model, simple implementation on quantum hardware, and a wealth of applications.Comment: To appear in Physical Review

Letter from Richard B. Watrous to William F. Bade, 1910 Jul 25.

J. HORACE, McFARLAND, President, Harrisburg, Pa.CLINTON ROGERS WOODRUFF. First Vice-President, PhiladelphiaWILLIAM B. HOWLAND, Treasurer, New YorkRICHARD B. WATROUS, Secretary, Washington, D. C.Vice-President: JAMES R. GARFIELD, Cleveland, OhioJOHN WESLEY HILL, D. D., New YorkW. W. HANNAN, Detroit, Mich.GEORGE W. MARSTON, San Diego, Cal.MRS. EDWARD W. BIDDLE. Carlisle, Pa.American Civic AssociationMAIN OFFICE: WASHINGTON, D. C.Executive BoardDR. JOHN QUINCY ADAMS, New YorkHENRY A. BARKER, Providence, R. I.FRANK CHAPIN BRAY, New YorkMISS MARY MARSHALL BUTLER, Yonkers. N. Y.DR. KENYON L. BUTTERFIELD, Amherst, Mass.MRS. CAROLINE BARTLETT CRANE, Kalamazoo, Mich.Executive BoardGEORGE OTIS DRAPER, New YorkFREDERICK L. FORD. Hartford, Conn.EDWARD HATCH, JR., New YorkJ. L. HUDSON, Detroit, Mich.MRS. MELVILLE F. JOHNSTON. Richmond, Ind.HARLAN P. KELSEY, Salem, Mass.Executive BoardWARREN H. MANNING, Boston, Mass.MRS. A. E. McCREA, Chicago, III.MRS. EDWIN F. MOULTON, Warren, OhioJOHN NOLEN, Cambridge, Mass.GRAHAM ROMEYN TAYLOR. Chicago, III.BRAINARD H. WARNER, Washington, D. C.OFFFICE OF THE SECRETARY913-914 UNION TRUST BUILDINGWASHINGTON, D. C.July 25, 1910.Dr. William Frederick Bade,c/o The Independent,130 Fulton Street,New York City,Dear Dr. Bade:Thank you sincerely for sending me the galley proof of Ignorant Vandalism , which I have read with very great pleasure. You have stated the case splendidly and by your allusion to the subject of filtration and the further allusion to the importance of recognizing scenic beauty as a material asset to the Nation you have, I am sure, added a very valuable contribution to the general subject of the importance of preserving our present national parks and adding greatly to their number. I am passing on the proof to Mr. McFarland for I know he will be delighted to read it.I have got to confess that I am not taking The Independent. I wish I might have a few copies of the issue of the 28th. I would also suggest that you send a marked copy to Mr. Ballinger, who I understand is now at his home in Seattle, and also send a marked copy to Mr. Alvin P. Kletsch, Republican House, Milwaukee, Wis.So far my pleasant vacation consists of appearing daily at the offices of the Association in the Union Trust Building. I am06284 2. W. F. B.hoping, however, to break away more or less during the month of August. Mrs. Watrous and the children are still out in Milwaukee and I think next week will go on to St. Paul and Minneapolis.With kind regards, I amSincerely yours,[illegible]0628

On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables

In this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization, especially cut polyhedra. Such a relationship was established in Avis, Imai, Ito and Sasaki (2005 J. Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show that several well known bodies related to cut polyhedra are equivalent to bodies such as those defined by Tsirelson (1993 Hadronic J. S. 8 329-45) to represent hidden deterministic behaviors, quantum behaviors, and no-signalling behaviors. Among other things, our results allow a unique representation of these bodies, give a necessary condition for vertices of the no-signalling polytope, and give a method for bounding the quantum violation of Bell inequalities by means of a body that contains the set of quantum behaviors. Optimization over this latter body may be performed efficiently by semidefinite programming. In the second part of the paper we apply these results to the study of classical correlation functions. We provide a complete list of tight inequalities for the two party case with (m,n) dichotomic observables when m=4,n=4 and when min{m,n}<=3, and give a new general family of correlation inequalities.Comment: 17 pages, 2 figure

Letter from Richard B. Watrous to William F. Bade, 1910 Aug 29.

J. HORACE McFARLAND, President, Harrisburg, Pa.CLINTON ROGERS WOODRUFF, First Vice-President, PhiladelphiaWILLIAM B. HOWLAND. Treasurer, New YorkRICHARD B. WATROUS, Secretary, Washington, D. C.Vice-Presidents: JAMES R. GARFIELD, Cleveland, OhioJOHN WESLEY HILL, D. D., New YorkW. W. HANNAN. Detroit, Mich.GEORGE W. MARSTON, San Diego, Cal.MRS. EDWARD W. BIDDLE, Carlisle, Pa.American Civic AssociationMAIN OFFICE: WASHINGTON, D. C.Executive BoardDR. JOHN QUINCY ADAMS, New YorkHENRY A. BARKER, Providence, R. I.FRANK CHAPIN BRAY, New YorkMISS MARY MARSHALL BUTLER, Yonkers, N. Y.DR. KENYON L. BUTTERFIELD, Amherst, Mass.MRS. CAROLINE BARTLETT CRANE, Kalamazoo, Mich.Executive BoardGEORGE OTIS DRAPER, New YorkFREDERICK L. FORD. Hartford. Conn.EDWARD HATCH, JR., New YorkJ. L. HUDSON, Detroit, Mich.MRS. MELVILLE F. JOHNSTON, Richmond, Ind.HARLAN P. KELSEY, Salem, Mass.Executive BoardWARREN H. MANNING, Boston. Mass.MRS. A. E. McCREA, Chicago, III.MRS. EDWIN F. MOULTON, Warren, OhioJOHN NOLEN, Cambridge, Mass.GRAHAM ROMEYN TAYLOR, Chicago, III.BRAINARD H. WARNER, Washington, D. C.OFFFICE OF THE SECRETARY913-914 UNION TRUST BUILDINGWASHINGTON, D. C.August 29, 1910.Dr. William Frederic Bade,Vice-President, Society for the Preservation of National Parks,Mills Building,San Francisco, Cal.Dear Dr. Bade:I am glad to receive your letter even though it comes from far away California and tells me that I can not hope to see you again in the near future unless, of course you happen to be coming east again.I have read with interest your late editorial in the Independent which I did not see in the original publication and I note that you have felt called upon to reprint the letters written by Mr. Pinchot some years ago. I imagine that it has been due to these letters that Mr. Pinchot has been somewhat noncommittal, as you know he has from your correspondence with Mr. McFarland, on the subject of the conservation of the beautiful. How fine it would be if with all his splendid enthusiasm he might throw himself into the recognition of this kind of conservation as some of the rest of us have been doing.I certainly[word?] wish that you might be at the St. Paul meeting. I shall be there the first two days but those are to be so taken up with the addresses of President Taft and Mr. Roosevelt that I imagine there will not be much detail business. We are hoping, however, that some formal recog-06298 Dr. Wm. Frederic Bade. #2-Aug.29, 1910.nition of our ideas may be incorporated in the statements that will be issued by the congress. Mr. McFarland is now preparing a paper which we shall try to have presented at the right time.With sincere regards, and hoping to hear from you, I am,Very truly yours.[illegible]Secretary.RBW/WLC0629

Letter from Richard B. Watrous to William F. Bade, 1910 Jul 11.

J. HORACE McFARLAND, President, Harrisburg, Pa.CLINTON ROGERS WOODRUFF, First Vice-President, PhiladelphiaWILLIAM B. HOWLAND, Treasurer, New YorkRICHARD B. WATROUS, Secretary, Washington, D. C.Vice-Presidents: JAMES R. GARFIELD, Cleveland, OhioJOHN WESLEY HILL, D. D., New YorkW. W. HANNAN. Detroit. Mich.GEORGE W. MARSTON. San Diego. Cal.MRS. EDWARD W. BIDDLE, Carlisle, Pa.American Civic AssociationMAIN OFFICE: WASHINGTON, D. C.Executive BoardDR. JOHN QUINCY ADAMS, New YorkHENRY A.BARKER, Providence, R. I.FRANK CHAPIN BRAY, New YorkMISS MARY MARSHALL BUTLER, Yonkers, N. Y.DR. KENYON L. BUTTERFIELD, Amherst, Mass.MRS. CAROLINA BARTLETT CRANE, Kalananco, Mich.Executive BoardGEORGE OTIS DRAPER, New YorkFREDERICK L. FORD, Hartford, Conn.EDWARD HATCH, JR., New YorkJ. L. HUDSON, Detroit, Mich.MRS. MELVILLE F. JOHNSTON, Richmond, Ind.HARLAN P. KELSEY, Salem, Mass.Executive BoardWARREN H. MANNING, Boston, Mass.MRS. A. H. McCREA, Chicago, III.MRS. EDWIN F. MOULTON, Warren, OhioJOHN NOLEN, Cambridge, Mass.GRAHAM ROMEYN TAYLOR, Chicago, III.BRAINARD H. WARNER, Washington, D. C.OFFICE OF THE SECRETARY913-914 UNION TRUST BUILDINGWASHINGTON, D. C.July 6, 1910.Dr. William F. Bade,c/o The Independent,130 Fulton Street,New York City.My dear Friend:-I was in my office for a little while yesterday - Sunday - morning, of course only to secure and read letters from my wife, but incidentally found yours and enclosed at once a copy of Secretary Ballinger\u27s order, which had come to my office only the day before. I should be glad to read the editorial that you are to have in the Independent.I shall be more than glad to pass on to Mrs. Watrous your kind regards and if I get to New York during the summer, shall hunt you up either at the office or at your residence.Sincerely yours,[illegible]RBW/MS0628