Searcharxiv⌕ Search

arXiv subjects

Andrei Galiautdinov

Publications and source records attributed to Andrei Galiautdinov.

At least 37 records · Page 2Linked to original sources
arXiv2017

Lamb's reconstruction of potentials and spatially localized scattering in nonrelativistic quantum mechanics

We formulate a simple condition for reconstructibility of a certain class of Hamiltonians with real potentials from the knowledge of their complex-valued eigenfunctions. This may be relevant to the question of preparability of quantum states raised by W. Lamb in his 1969 paper on operational interpretation of quantum mechanics. Of particular interest to engineering applications are: (a) an exotic case of an upside-down harmonic-oscillator-type potential (a variation of the inverted "Mexican hat" potential) whose square-integrable complex eigenfunction describes a localized scattering state similar to the "bound state in the continuum" of von Neumann and Wigner, and (b) a spatially confined scattering state of a particle moving in an infinite well with the properly shaped potential bottom.

quant-ph↗
arXiv2017

High-energy cosmic ray production by a neutron star falling into a black hole

We propose a one-shot mechanism for high-energy cosmic ray generation by a neutron star falling into a black hole surrounded by low density plasma. The function of the black hole in this scenario is to accelerate the star to a speed arbitrarily close to that of light. When the star - essentially, a magnetized sphere - approaches the horizon it imparts energy to the ambient plasma charges via the induced electric field. Disregarding radiation losses, for iron nucleus, a simple estimate gives energies on the order of 10^19 eV for stars with magnetic fields as weak as 10^6 teslas. The proposed mechanism should also work in chance encounters between rapidly moving neutron stars and molecular clouds. The rarity of such encounters may explain the apparent randomness and rarity of the high-energy cosmic ray events.

astro-ph.HE↗
arXiv2017

Neutron interference in the Earth's gravitational field

This work relates to the famous experiments, performed in 1975 and 1979 by Werner et al., measuring neutron interference and neutron Sagnac effects in the earth's gravitational field. Employing the method of Stodolsky in its weak field approximation, explicit expressions are derived for the two phase shifts, which turn out to be in agreement with the experiments and with the previously obtained expressions derived from semi-classical arguments: these expressions are simply modified by relativistic correction factors.

gr-qc↗
arXiv2015

Universal quantum simulation with pre-threshold superconducting qubits: Single-excitation subspace method

We propose a method for general-purpose quantum computation and simulation that is well suited for today's pre-threshold-fidelity superconducting qubits. This approach makes use of the $n$-dimensional single-excitation subspace (SES) of a system of $n$ tunably coupled qubits. It can be viewed as a nonscalable special case of the standard gate-based quantum computing model, but allows many operations in the unitary group SU($n$) to be implemented by a single application of the Hamiltonian. Our approach bypasses the need to decompose the evolution operator into elementary gates, making large, nontrivial computations possible without error correction. The method is especially well suited for universal quantum simulation, specifically simulation of the Schrödinger equation with a real but otherwise arbitrary $n \times n$ Hamiltonian. We argue that a 1000-qubit SES processor, which would require no known improvements in superconducting device technology and which could be built today, should be capable of achieving quantum speedup relative to a petaflop supercomputer. We speculate on the utility and practicality of such a universal quantum simulator.

quant-ph↗
arXiv2015

Universal quantum simulation with prethreshold superconducting qubits: Single-excitation subspace method

Current quantum computing architectures lack the size and fidelity required for universal fault-tolerant operation, limiting the practical implementation of key quantum algorithms to all but the smallest problem sizes. In this work we propose an alternative method for general-purpose quantum computation that is ideally suited for such "prethreshold" superconducting hardware. Computations are performed in the n-dimensional single-excitation subspace (SES) of a system of n tunably coupled superconducting qubits. The approach is not scalable, but allows many operations in the unitary group SU(n) to be implemented by a single application of the Hamiltonian, bypassing the need to decompose a desired unitary into elementary gates. This feature makes large, nontrivial quantum computations possible within the available coherence time. We show how to use a programmable SES chip to perform fast amplitude amplification and phase estimation, two versatile quantum subalgorithms. We also show that an SES processor is well suited for Hamiltonian simulation, specifically simulation of the Schrodinger equation with a real but otherwise arbitrary nxn Hamiltonian matrix. We discuss the utility and practicality of such a universal quantum simulator, and propose its application to the study of realistic atomic and molecular collisions.

quant-ph↗
arXiv2013

Catch-Disperse-Release Readout for Superconducting Qubits

We analyze a single-shot readout for superconducting qubits via the controlled catch, dispersion, and release of a microwave field. A tunable coupler is used to decouple the microwave resonator from the transmission line during the dispersive qubit-resonator interaction, thus circumventing damping from the Purcell effect. We show that if the qubit frequency tuning is sufficiently adiabatic, a fast high-fidelity qubit readout is possible, even in the strongly nonlinear dispersive regime. Interestingly, the Jaynes-Cummings nonlinearity leads to the quadrature squeezing of the resonator field below the standard quantum limit, resulting in a significant decrease of the measurement error.

quant-ph↗
arXiv2013

High-fidelity CZ gate for resonator-based superconducting quantum computers

A possible building block for a scalable quantum computer has recently been demonstrated [M. Mariantoni et al., Science 334, 61 (2011)]. This architecture consists of superconducting qubits capacitively coupled both to individual memory resonators as well as a common bus. In this work we study a natural primitive entangling gate for this and related resonator-based architectures, which consists of a CZ operation between a qubit and the bus. The CZ gate is implemented with the aid of the non-computational qubit |2> state [F. W. Strauch et al., Phys. Rev. Lett. 91, 167005 (2003)]. Assuming phase or transmon qubits with 300 MHz anharmonicity, we show that by using only low frequency qubit-bias control it is possible to implement the qubit-bus CZ gate with 99.9% (99.99%) fidelity in about 17ns (23ns) with a realistic two-parameter pulse profile, plus two auxiliary z rotations. The fidelity measure we refer to here is a state-averaged intrinsic process fidelity, which does not include any effects of noise or decoherence. These results apply to a multi-qubit device that includes strongly coupled memory resonators. We investigate the performance of the qubit-bus CZ gate as a function of qubit anharmonicity, indentify the dominant intrinsic error mechanism and derive an associated fidelity estimator, quantify the pulse shape sensitivity and precision requirements, simulate qubit-qubit CZ gates that are mediated by the bus resonator, and also attempt a global optimization of system parameters including resonator frequencies and couplings. Our results are relevant for a wide range of superconducting hardware designs that incorporate resonators and suggest that it should be possible to demonstrate a 99.9% CZ gate with existing transmon qubits, which would constitute an important step towards the development of an error-corrected superconducting quantum computer.

quant-ph↗
arXiv2012

Simple protocol for generating W states in resonator-based quantum computing architectures

We describe a simple, practical scheme for generating multi-qubit W states in resonator-based architectures, in which N Josephson phase qubits are capacitively coupled to a common resonator bus. The entire control sequence consists of three pulses: a local Rabi pulse that excites a single qubit in the circuit; a coupling pulse that transfers the qubit excitation to the resonator bus; and the main, entangling operation that simultaneously couples the bus to all N qubits. If the qubit-resonator coupling strength g is much smaller than the qubit energy splitting, the system initially excited into the near-degenerate single-excitation subspace stays within that subspace, while smoothly evolving toward the fully uniform W state superposition. The duration of the final entangling operation is found to decrease with the total number of the qubits according to t = pi/[2gN^(1/2)], in agreement with some of the previously proposed cavity QED W state generation schemes.

quant-ph↗
arXiv2012

Resonator/zero-Qubit architecture for superconducting qubits

We analyze the performance of the Resonator/zero-Qubit (RezQu) architecture in which the qubits are complemented with memory resonators and coupled via a resonator bus. Separating the stored information from the rest of the processing circuit by at least two coupling steps and the zero qubit state results in a significant increase of the ON/OFF ratio and the reduction of the idling error. Assuming no decoherence, we calculate such idling error, as well as the errors for the MOVE operation and tunneling measurement, and show that the RezQu architecture can provide high fidelity performance required for medium-scale quantum information processing.

quant-ph↗
arXiv2011

Single-step implementation of the controlled-Z gate in a qubit/bus/qubit device

We propose a simple scheme for generating a high-fidelity controlled-Z (CZ) gate in a three-component qubit/bus/qubit device. The corresponding tune/detune pulse is single-step, with a near-resonant constant undershoot between the 200 and 101 states. During the pulse, the frequency of the first qubit is kept fixed, while the frequency of the second qubit is varied in such a way as to bring the 200 and 101 states close to resonance. As a result, the phase of the 101 state is accumulated via the corresponding second-order anticrossing. For experimentally realistic qubit frequencies and a 75 MHz coupling (150 MHz splitting), a 45 ns gate time can be realized with >99.99% intrinsic fidelity, with errors arising due to the non-adiabaticity of the ramps. The CZ pulse is characterized by two adjustable parameters: the undershoot magnitude and undershoot duration. The pulse does not load an excitation into the bus. This by-passes the previously proposed need for two additional qubit-to-bus and bus-to-qubit MOVE operations. Combined with the recently predicted high-fidelity idling operation in the RezQu architecture [A. Galiautdinov, J. Martinis, A. Korotkov (unpublished)], this controlled-Z scheme may prove useful for implementations on the first generation quantum computers.

quant-ph↗
arXiv2011

Quantum computation with prethreshold superconducting qubits: Single-excitation subspace approach

We describe an alternative approach to quantum computation that is ideally suited for today's sub-threshold-fidelity qubits, and which can be applied to a family of hardware models that includes superconducting qubits with tunable coupling. In this approach, the computation on an n-qubit processor is carried out in the n-dimensional single-excitation subspace (SES) of the full 2^n-dimensional Hilbert space. Because any real Hamiltonian can be directly generated in the SES [E. J. Pritchett et al., arXiv:1008.0701], high-dimensional unitary operations can be carried out in a single step, bypassing the need to decompose into single- and two-qubit gates. Although technically nonscalable and unsuitable for applications (including Shor's) requiring enormous Hilbert spaces, this approach would make practical a first-generation quantum computer capable of achieving significant quantum speedup.

quant-ph↗
arXiv2010

Quantum Simulation of Molecular Collisions with Superconducting Qubits

We introduce a protocol for the fast simulation of $n$-dimensional quantum systems on $n$-qubit quantum computers with tunable couplings. A mapping is given between the control parameters of the quantum computer and the matrix elements of $H_{\rm s}(t)$, an arbitrary, real, time-dependent $n\times n$ dimensional Hamiltonian that is simulated in the $n$-dimensional `single excitation' subspace of the quantum computer. A time-dependent energy/time rescaling minimizes the simulation time on hardware having a fixed coherence time. We demonstrate how three tunably coupled phase qubits simulate a three-channel molecular collision using this protocol, then study the simulation's fidelity as a function of total simulation time.

quant-ph↗
arXiv2009

Greenberger-Horne-Zeilinger state protocols for fully connected qubit networks

We generalize the recently proposed Greenberger-Horne-Zeilinger (GHZ) tripartite protocol [A. Galiautdinov, J. M. Martinis, Phys. Rev. A 78, 010305(R) (2008)] to fully connected networks of weakly coupled qubits interacting by way of anisotropic Heisenberg exchange g(XX+YY)+g1*ZZ. Our model adopted here differs from the more familiar Ising-Heisenberg chain in that here every qubit interacts with every other qubit in the circuit. The assumption of identical couplings on all qubit pairs allows an elegant proof of the protocol for arbitrary N. In order to further make contact with experiment, we study fidelity degradation due to coupling imperfections by numerically simulating the N=3 and N=4 cases. Our simulations indicate that the best fidelity at unequal couplings is achieved when (a) the system is initially prepared in the uniform superposition state (similarly to how it is done in the ideal case), and (b) the entangling time and the final rotations on each of the qubits are appropriately adjusted.

quant-ph↗
arXiv2009

Quantum logic with weakly coupled qubits

There are well-known protocols for performing CNOT quantum logic with qubits coupled by particular high-symmetry (Ising or Heisenberg) interactions. However, many architectures being considered for quantum computation involve qubits or qubits and resonators coupled by more complicated and less symmetric interactions. Here we consider a widely applicable model of weakly but otherwise arbitrarily coupled two-level systems, and use quantum gate design techniques to derive a simple and intuitive CNOT construction. Useful variations and extensions of the solution are given for common special cases.

quant-ph↗
arXiv2009

Quantum theory of elementary processes

In modern physics, one of the greatest divides is that between space-time and quantum fields, as the fiber bundle of the Standard Model indicates. However on the operational grounds the fields and spacetime are not very different. To describe a field in an experimental region we have to assign coordinates to the points of that region in order to speak of the "when" and "where" of the field itself. But to operationally study the topology and to coordinatize the region of spacetime, the use of radars (to send and receive electromagnetic signals) is required. Thus the description of fields (or, rather, processes) and the description of space-time are indistinguishable at the fundamental level. Moreover, classical general relativity already says -- albeit preserving the fiber bundle structure -- that spacetime and matter are intimately related. All this indicates that a new theory of elementary processes (out of which all the usual processes of creation, annihilation and propagation, and consequently the topology of spacetime itself would be constructed) has to be devised. In this thesis I present the foundations of such a finite, discrete, algebraic, quantum theory and apply it to the description of spin-1/2 quanta of the Standard Model.

hep-th↗
arXiv2008

Controlled-NOT logic with nonresonant Josephson phase qubits

We establish theoretical bounds on qubit detuning for high fidelity controlled-NOT logic gate implementations with weakly coupled Josephson phase qubits. It is found that the value of qubit detuning during the entangling pulses must not exceed 2g for two-step, and g for single-step control sequences, where g is the relevant coupling constant.

quant-ph↗
arXiv2008

Maximally entangling tripartite protocols for Josephson phase qubits

We introduce a suit of simple entangling protocols for generating tripartite GHZ and W states in systems with anisotropic exchange interaction g(XX+YY)+g'ZZ. An interesting example is provided by macroscopic entanglement in Josephson phase qubits with capacitive (g'=0) and inductive (0<|g'/g|<0.1) couplings.

quant-ph↗