Hasil untuk "quant-ph"

Stephen A. Fenner, Rabins Wosti

It has been shown that, for even $n$, evolving $n$ qubits according to a Hamiltonian that is the sum of pairwise interactions between the particles, can be used to exactly implement an $(n+1)$-qubit fanout gate using a particular constant-depth circuit~[\href{https://arXiv.org/abs/quant-ph/0309163}{arXiv:quant-ph/0309163}]. However, the coupling coefficients in the Hamiltonian considered in that paper are assumed to be all equal. In this paper, we generalize these results and show that for all $n$, including odd $n$, one can exactly implement an $(n+1)$-qubit parity gate and hence, equivalently in constant depth an $(n+1)$-qubit fanout gate, using a similar Hamiltonian but with unequal couplings, and we give an exact characterization of the constraints that the couplings must satisfy in order for them to be adequate to implement fanout via the same circuit.}{In particular, we show the following:Letting $J_{ij}$ be the coupling strength between the $\ordth{i}$ and $\ordth{j}$ qubits, the set of couplings $\{J_{ij}\}$ is adequate to implement fanout via the circuit above if and only if there exists $J>0$ such that 1. each $J_{ij}$ is an odd integer multiple of $J$, and 2. for each $i$, there are an even number of $j\ne i$ such that $J_{ij}/J \equiv 3\pmod{4}$.

Kiryl Pakrouski

We present two 2-body Hamiltonians that approximate the exact PH-Pfaffian wavefunction with their ground states for all the system sizes where this wavefunction has been numerically constructed to date. The approximate wavefunctions have high overlap with the original and reproduce well the low-lying entanglement spectrum and structure factor. The approximate generating Hamiltonians are obtained by an optimisation procedure where three to four pseudopotentials are varied in the neighbourhood of second Landau level Coulomb interaction or of a non-interacting model. They belong to a finite region in the variational space of Hamiltonians where each point approximately generates the PH-Pfaffian. We diagonalize the identified Hamiltonians for up to 20 electrons and find that for them the PH-Pfaffian shift appears energetically more favorable. Possibility to interpret the data in terms of composite fermions is discussed.

Xinyu Wu

After presentations of Raz and Tal's oracle separation of BQP and PH result, several people (e.g. Ryan O'Donnell, James Lee, Avishay Tal) suggested that the proof may be simplified by stochastic calculus. In this short note, we describe such a simplification.

P. Zarzycki, K. Rosso

Goethite is one of the most stable and common iron(III) minerals at the Earth’s near surface. However, recent isotope tracer studies have suggested that goethite continuously recrystallizes in the presence of aqueous Fe(II) ions. Some of these studies indicate the presence of two regimes of atom-exchange kinetics, a rapid stage assigned to reactive defect sites initially available at particle surfaces, followed by slower continuous exchange. An autocatalytic solid-state electron conduction model coupling Fe(II) oxidative adsorption to its reductive release at spatially distinct sites has been proposed, but the thermodynamic driving force has yet to be pinpointed. Here, using a novel hybrid/reactive molecular simulation method, for goethite (110) surfaces at circumneutral pH, we rigorously tested whether surface free energy minimization, including examining the role of structural defects, is sufficient to overcome the activation energy for interfacial electron transfer and conduction. The simulations quant...

Amit Behera, G. Paul

In 2013, Farid and Vasiliev [arXiv:1310.4922 [quant-ph]] for the first time proposed a way to construct a protocol for the realisation of “Classical to Quantum” one-way hash function, a derivative of the quantum one-way function as defined by Gottesman and Chuang [Technical Report arXiv:quant-ph/0105032] and used it for constructing quantum digital signatures. We, on the other hand, for the first time, propose the idea of a different kind of one-way function, which is “quantum-classical” in nature, that is, it takes an n-qubit quantum state of a definite kind as its input and produces a classical output. We formally define such a one-way function and propose a way to construct and realise it. The proposed one-way function turns out to be very useful in authenticating a quantum state in any quantum money scheme, and so we can construct many different quantum money schemes based on such a one-way function. Later in the paper, we also give explicit constructions of some interesting quantum money schemes like quantum bitcoins and quantum currency schemes, solely based on the proposed one-way function. The security of such schemes can be explained on the basis of the security of the underlying one-way functions.

M. Khezri, E. Mlinar, J. Dressel et al.

Measuring a transmon qubit in circuit QED: dressed squeezed states Mostafa Khezri, 1, 2, ∗ Eric Mlinar, 1 Justin Dressel, 3, 4 and Alexander N. Korotkov 1 arXiv:1606.04204v2 [quant-ph] 1 Aug 2016 Department of Electrical and Computer Engineering, University of California, Riverside, California 92521, USA. Department of Physics, University of California, Riverside, California 92521, USA. Institute for Quantum Studies, Chapman University, Orange, California 92866, USA. Schmid College of Science and Technology, Chapman University, Orange, California 92866, USA. (Dated: August 2, 2016) Using circuit QED, we consider the measurement of a superconducting transmon qubit via a coupled microwave resonator. For ideally dispersive coupling, ringing up the resonator produces co- herent states with frequencies matched to transmon energy states. Realistic coupling is not ideally dispersive, however, so transmon-resonator energy levels hybridize into joint eigenstate ladders of the Jaynes-Cummings type. Previous work has shown that ringing up the resonator approximately respects this ladder structure to produce a coherent state in the eigenbasis (a dressed coherent state). We numerically investigate the validity of this coherent state approximation to find two primary de- viations. First, resonator ring-up leaks small stray populations into eigenstate ladders corresponding to different transmon states. Second, within an eigenstate ladder the transmon nonlinearity shears the coherent state as it evolves. We then show that the next natural approximation for this sheared state in the eigenbasis is a dressed squeezed state, and derive simple evolution equations for such states using a hybrid phase-Fock-space description. I. INTRODUCTION Qubit technology using superconducting circuit quan- tum electrodynamics (QED) [1, 2] has rapidly developed over the past decade to become a leading contender for realizing a scalable quantum computer. Most recent qubit designs favor variations of the transmon [3–9] due to its charge-noise insensitivity, which permits long co- herence times while also enabling high-fidelity quantum gates [10–12] and high-fidelity dispersive qubit readout [13–15] via coupled microwave resonators. Transmon- based circuit operation fidelities are now near the thresh- old for quantum error correction protocols, some versions of which have been realized [16–19]. The quantized energy states of a transmon are mea- sured in circuit QED by coupling them to a detuned mi- crowave resonator. For low numbers of photons popu- lating the readout resonator, the coupling is well-studied [1, 3, 20] and approximates an idealized dispersive quan- tum non-demolition (QND) measurement [21]. Each transmon energy level dispersively shifts the frequency of the coupled resonator by a distinct amount, allowing the transmon state to be determined by measurement of the microwave field transmitted through or reflected from the resonator. However, nondispersive effects become im- portant when the number of resonator photons becomes comparable to a characteristic (“critical”) number set by the detuning and coupling strength [1, 22, 23]; present- day experiments often operate in this nondispersive (or nonlinear dispersive) regime [15, 24–26]. In this paper, we analyze and model the nondispersive effects that occur during the ring-up of a readout res- onator coupled to a transmon. These effects arise from email: mostafa.khezri@email.ucr.edu the hybridization of the resonator and transmon states into joint resonator-transmon eigenstates. While ringing up the resonator from its ground state, the joint state remains largely confined to a single Jaynes-Cummings eigenstate ladder that corresponds to the initial transmon state. As pointed out in Refs. [27–29], this joint state can be approximated by a coherent state in the eigenbasis (recently named a dressed coherent state [29]). Here we refine this initial approximation and provide a more accu- rate model for the hybridized resonator-transmon state. We numerically simulate the ring-up process for a res- onator coupled to a transmon, then use this simulation to develop and verify our analytical model. We find two dominant deviations from a dressed coherent state. First, we show that the ring-up process allows a small popula- tion to leak from an initial transmon state into neighbor- ing eigenstate ladders, and find simple expressions that quantify this stray population. Second, we show that the transmon-induced nonlinearity of the resonator distorts the dressed coherent state remaining in the correct eigen- state ladder with a shearing effect as it evolves, and show that this effect closely approximates self-squeezing of the dressed field at higher photon numbers. We then use a hybrid phase-Fock-space method to find equations of mo- tion for the parameters of an effective dressed squeezed state that is formed during the ring-up process. Our im- proved model is satisfyingly simple yet quite accurate. To simplify our analysis and isolate the hybridization effects of interest, we restrict our attention to a trans- mon (modeled as a seven-level nonlinear oscillator) cou- pled to a coherently pumped but non-leaking resonator (using the rotating wave approximation). The simplifi- cation of no resonator leakage may seem artificial, but it is still a reasonable approximation during the resonator ring-up and it is also relevant for at least two known protocols. First, the catch-disperse-release protocol [27]

P. Hayden, D. Leung, D. Mayers

Barnum, Crepeau, Gottesman, Tapp, and Smith (quant-ph/0205128) proposed methods for authentication of quantum messages. The first method is an interactive protocol (TQA') based on teleportation. The second method is a noninteractive protocol (QA) in which the sender first encrypts the message using a protocol QEnc and then encodes the quantum ciphertext with an error correcting code chosen secretly from a set (a purity test code (PTC)). Encryption was shown to be necessary for authentication. We augment the protocol QA with an extra step which recycles the entire encryption key provided QA accepts the message. We analyze the resulting integrated protocol for quantum authentication and key generation, which we call QA+KG. Our main result is a proof that QA+KG is universal composably (UC) secure in the Ben-Or-Mayers model (quant-ph/0409062). More specifically, this implies the UC-security of (a) QA, (b) recycling of the encryption key in QA, and (c) key-recycling of the encryption scheme QEnc by appending PTC. For an m-qubit message, encryption requires 2m bits of key; but PTC can be performed using only O(log m) + O(log e) bits of key for probability of failure e. Thus, we reduce the key required for both QA and QEnc, from linear to logarithmic net consumption, at the expense of one bit of back communication which can happen any time after the conclusion of QA and before reusing the key. UC-security of QA also extends security to settings not obvious from quant-ph/0205128. Our security proof structure is inspired by and similar to that of quant-ph/0205128, reducing the security of QA to that of TQA'. In the process, we define UC-secure entanglement, and prove the UC-security of the entanglement generating protocol given in quant-ph/0205128, which could be of independent interest.

K. W. Chan, M. O’Sullivan, R. Boyd

We compare the performance of high-order thermal ghost imaging with that of conventional (that is, lowest-order) thermal ghost imaging for different data processing methods. Particular attention is given to high-order thermal ghost imaging with background normalization and conventional ghost imaging with background subtraction. The contrast-to-noise ratio (CNR) of the ghost image is used as the figure of merit for the comparison.We find analytically that the CNR of the normalized high-order ghost image is inversely proportional to the square root of the number of transmitting pixels of the object. This scaling law is independent of the exponents used in calculating the high-order correlation and is the same as that of conventional ghost imaging with background subtraction. We find that no data processing procedure performs better than lowest-order ghost imaging with background subtraction. Our results are found to be able to explain the observations of a recent experiment [Chen et al., arXiv:0902.3713v3 [quant-ph]].

A. Mostafazadeh

We study certain linear and antilinear symmetry generators and involution operators associated with pseudo-Hermitian Hamiltonians and show that the theory of pseudo-Hermitian operators provides a simple explanation for the recent results of Bender, Brody and Jones (quant-ph/0208076) on the CPT-symmetry of a class of PT-symmetric non-Hermitian Hamiltonians. We present a natural extension of these results to the class of diagonalizable pseudo-Hermitian Hamiltonians H with a discrete spectrum. In particular, we introduce generalized parity (P), time-reversal (T), and charge-conjugation (C) operators and establish the PT- and CPT-invariance of H.

I. Devetak, T. Berger

An outer bound on the low-entanglement remote state preparation ebits vs bits tradeoff curve [Bennett et al., quant-ph/0006044, 2000] is found using techniques of classical information theory. We show this bound to be optimal among an important class of protocols and conjecture optimality even without this restriction.

David Gross, J. Eisert, N. Schuch et al.

We introduce schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in Gross and Eisert [Phys. Rev. Lett. 98, 220503 (2007); quant-ph/0609149]. Our method makes use of tools from many-body physics--matrix product states, finitely correlated states, or projected entangled pairs states--to show how measurements on entangled states can be viewed as processing quantum information. This work hence constitutes an instance where a quantum information problem--how to realize quantum computation--was approached using tools from many-body theory and not vice versa. We give a more detailed description of the setting and present a large number of examples. We find computational schemes, which differ from the original one-way computer, for example, in the way the randomness of measurement outcomes is handled. Also, schemes are presented where the logical qubits are no longer strictly localized on the resource state. Notably, we find a great flexibility in the properties of the universal resource states: They may, for example, exhibit nonvanishing long-range correlation functions or be locally arbitrarily close to a pure state. We discuss variants of Kitaev's toric code states as universal resources, and contrast this with situations where they can be efficiently classically simulated.more » This framework opens up a way of thinking of tailoring resource states to specific physical systems, such as cold atoms in optical lattices or linear optical systems.« less

S. Heinrich

We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences that satisfy a p-summability condition and for integration of functions from Lebesgue spaces Lp(0, 1]d), and analyze their convergence rates. We also prove lower bounds showing that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of G. Brassard et al. (2000, “Quantum Amplitude Amplification and Estimation,” Technical Report, http://arXiv.org/abs/quant-ph/0005055) on computing the mean for bounded sequences and complements results of E. Novak (2001, J. Complexity17, 2?16) on integration of functions from Holder classes. The analysis requires an appropriate model of quantum computation, capable of covering the typical features of numerical problems such as dealing with real numbers and real-valued functions and with vector and function spaces. We develop and study such a model, which can be viewed as a quantum setting for information-based complexity theory.

C. Fuchs, M. Sasaki

This article is an introduction to quant-ph/0302092. We propose to quantify how "quantum" a set of quantum states is. The quantumness of a set is the worst-case difficulty of transmitting the states through a classical communication channel. Potential applications of this measure arise in quantum cryptography, where one might like to use an alphabet of states most sensitive to quantum eavesdropping, and in lab demonstrations of quantum teleportation, where it is necessary to check that entanglement has indeed been used.

K. A. Kirkpatrick

I reply to Ravon and Vaidman's criticism (quant-ph/0606067) of my classical implementation (quant-ph/0207124) of a three-box system as a card game.

B. Boutten, M. Picard, I. Bouvarel et al.

J. Loyer, J. Susini

Ali Mostafazadeh

In their Erratum [Phys. Rev. Lett. {\bf 92}, 119902 (2004), quant-ph/0208076], written in reaction to [quant-ph/0310164], Bender, Brody and Jones propose a revised definition for a physical observable in PT-symmetric quantum mechanics. We show that although this definition avoids the dynamical inconsistency revealed in quant-ph/0310164, it is still not a physically viable definition. In particular, we point out that a general proof that this definition is consistent with the requirements of the quantum measurement theory is lacking, give such a proof for a class of PT-symmetric systems by establishing the fact that this definition implies that the observables are pseudo-Hermitian operators, and show that for all the cases that this definition is consistent with the requirements of measurement theory it reduces to a special case of a more general definition given in [quant-ph/0310164]. The latter is the unique physically viable definition of observables in PT-symmetric quantum mechanics.

Joseph M. Renes

Quantum key distribution protocols based on equiangular spherical codes are introduced and their behavior under the intercept/resend attack investigated. Such protocols offer a greater range of secure noise tolerance and speed options than protocols based on their cousins, the mutually-unbiased bases, while also enabling the determination of the channel noise rate without the need to sacrifice key bits. For fixed number of signal states in a given dimension, the spherical code protocols offer Alice and Bob more noise tolerance at the price of slower key generation rates.

Toshihiko Ono

This letter proposes a new scenario to solve the structural or conceptual problems remained in quantum mechanics, and gives an overview of the theory proposed in quant-ph/9906130 (including quant-ph/9909025 and quant-ph/0001015).

Gerald Gilbert, Michael Hamrick, F. Javier Thayer et al.

The attempt to equate operator quantum error correction (quant-ph/0504189v1) with the quantum computer condition (quant-ph/0507141) in version two of quant-ph/0504189 is shown to be invalid.