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Mhs Amin

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Papers by Mhs Amin

Low-temperature behavior of the vortex lattice in unconventional superconductors

Physical Review B

We study the effect of the superconducting gap nodes on the vortex lattice properties of high tem... more We study the effect of the superconducting gap nodes on the vortex lattice properties of high temperature superconductors at very low temperatures. The nonlinear, nonlocal and nonanalytic nature of this effect is shown to have measurable consequences for the vortex lattice geometry and the effective penetration depth in the mixed state as measured by muon-spin-rotation experiments.

Erratum: Consistency of the Adiabatic Theorem [Phys. Rev. Lett.102, 220401 (2009)]

Physical Review Letters

Nonequilibrium quasiclassical theory for Josephson structures

Physical Review B

We present a non-equilibrium quasiclassical formalism suitable for studying linear response ac pr... more We present a non-equilibrium quasiclassical formalism suitable for studying linear response ac properties of Josephson junctions. The non-equilibrium self-consistency equations are satisfied, to very good accuracy, already in zeroth iteration. We use the formalism to study ac Josephson effect in a ballistic superconducting point contact. The real and imaginary parts of the ac linear conductance are calculated both analytically (at low frequencies) and numerically (at arbitrary frequency). They show strong temperature, frequency, and phase dependence. Many anomalous properties appear near φ = π. We ascribe them to the presence of zero energy bound states.

First-order quantum phase transition in adiabatic quantum computation

Physical Review A, 2009

We investigate the connection between local minima in the problem Hamiltonian and first order qua... more We investigate the connection between local minima in the problem Hamiltonian and first order quantum phase transitions during an adiabatic quantum computation. We demonstrate how some properties of the local minima can lead to an extremely small gap that is exponentially sensitive to the Hamiltonian parameters. Using perturbation expansion, we derive an analytical formula that can not only predict the behavior of the gap, but also provide insight on how to controllably vary the gap size by changing the parameters. We show agreement with numerical calculations for a weighted maximum independent set problem instance.

Persistent Currents in Mesoscopic Rings and Boundary Conformal Field Theory

International Journal of Modern Physics B, 1999

A tight-binding model of electron dynamics in mesoscopic normal rings is studied using boundary c... more A tight-binding model of electron dynamics in mesoscopic normal rings is studied using boundary conformal field theory. The partition function is calculated in the low energy limit and the persistent current generated as a function of an external magnetic flux threading the ring is found. We study the cases where there are defects and electron–electron interactions separately. The same temperature scaling for the persistent current is found in each case and the functional form can be fitted, with a high degree of accuracy, to experimental data.

Josephson-phase qubit without tunneling

Physical Review B, 2003

We show that a complete set of one-bit gates can be realized by coupling the two logical states o... more We show that a complete set of one-bit gates can be realized by coupling the two logical states of a phase qubit to a third level (at higher energy) using microwave pulses. Thus, one can achieve coherent control without invoking any tunneling between the qubit levels. We propose two implementations, using rf-SQUIDs and d-wave Josephson junctions.

D + I S Versus D + I D ′ Time Reversal Symmetry Breaking States in Finite Size Systems

Physical Review B, 2002

Mechanisms of spontaneous current generation in an inhomogeneous d -wave superconductor

Physical Review B, 2001

Superconducting quantum storage and processing

2004 IEEE International Solid-State Circuits Conference (IEEE Cat. No.04CH37519), 2004

Superposition and entanglement are the two quantum-mechanical effects required to build a quantum... more

A scalable readout system for a superconducting adiabatic quantum optimization system

Superconductor Science and Technology, 2010

We have designed, fabricated and tested an XY-addressable readout system that is specifically tai... more We have designed, fabricated and tested an XY-addressable readout system that is specifically tailored for the reading of superconducting flux qubits in an integrated circuit that could enable adiabatic quantum optimization. In such a system, the flux qubits only need to be read at the end of an adiabatic evolution when quantum mechanical tunneling has been suppressed, thus simplifying many aspects of the readout process. The readout architecture for an N-qubit adiabatic quantum optimization system comprises N hysteretic dc SQUIDs and N rf SQUID latches controlled by 2 √ N + 2 bias lines. The latching elements are coupled to the qubits and the dc SQUIDs are then coupled to the latching elements. This readout scheme provides two key advantages: First, the latching elements provide exceptional flux sensitivity that significantly exceeds what may be achieved by directly coupling the flux qubits to the dc SQUIDs using a practical mutual inductance. Second, the states of the latching elements are robust against the influence of ac currents generated by the switching of the hysteretic dc SQUIDs, thus allowing one to interrogate the latching elements repeatedly so as to mitigate the effects of stochastic switching of the dc SQUIDs. We demonstrate that it is possible to achieve single qubit errors rates of < 10 −6 with this readout scheme. We have characterized the system-level performance of a 128-qubit readout system and have measured an error probability of 8 × 10 −5 in the presence of optimal latching element bias conditions.

Investigating the performance of an adiabatic quantum optimization processor

Quantum Information Processing, 2012

We calculate median adiabatic times (in seconds) of a specific superconducting adiabatic quantum ... more We calculate median adiabatic times (in seconds) of a specific superconducting adiabatic quantum processor for an NP-hard Ising spin glass instance class with up to N = 128 binary variables. To do so, we ran high performance Quantum Monte Carlo simulations on a large-scale Internet-based computing platform. We compare the median adiabatic times with the median running times of two classical solvers and find that, for problems with up to 128 variables, the adiabatic times for the simulated processor architecture are about 4 and 6 orders of magnitude shorter than the two classical solvers' times. This performance difference shows that, even in the potential absence of a scaling advantage, adiabatic quantum optimization may outperform classical solvers.

Macroscopic Resonant Tunneling in the Presence of Low Frequency Noise

Physical Review Letters, 2008

We develop a theory of macroscopic resonant tunneling of flux in a double-well potential in the p... more We develop a theory of macroscopic resonant tunneling of flux in a double-well potential in the presence of realistic flux noise with significant low-frequency component. The rate of incoherent flux tunneling between the wells exhibits resonant peaks, the shape and position of which reflect qualitative features of the noise, and can thus serve as a diagnostic tool for studying the low-frequency flux noise in SQUID qubits. We show, in particular, that the noise-induced renormalization of the first resonant peak provides direct information on the temperature of the noise source and the strength of its quantum component.

Thermally Assisted Adiabatic Quantum Computation

Physical Review Letters, 2008

We study the effect of a thermal environment on adiabatic quantum computation using the Bloch-Red... more We study the effect of a thermal environment on adiabatic quantum computation using the Bloch-Redfield formalism. We show that in certain cases the environment can enhance the performance in two different ways: (i) by introducing a time scale for thermal mixing near the anticrossing that is smaller than the adiabatic time scale, and (ii) by relaxation after the anticrossing. The former can enhance the scaling of computation when the environment is superohmic, while the latter can only provide a prefactor enhancement. We apply our method to the case of adiabatic Grover search and show that performance better than classical is possible with a superohmic environment, with no a priori knowledge of the energy spectrum.

Continuous Monitoring of Rabi Oscillations in a Josephson Flux Qubit

Physical Review Letters, 2003

Under resonant irradiation, a quantum system can undergo coherent (Rabi) oscillations in time. We... more Under resonant irradiation, a quantum system can undergo coherent (Rabi) oscillations in time. We report evidence for such oscillations in a continuously observed three-Josephson-junction flux qubit, coupled to a high-quality tank circuit tuned to the Rabi frequency. In addition to simplicity, this method of Rabi spectroscopy enabled a long coherence time of about 2.5µs, corresponding to an effective qubit quality factor ∼7000.

Consistency of the Adiabatic Theorem

Physical Review Letters, 2009

The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently... more The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations of the adiabatic theorem all arise from resonant transitions between energy levels. In the absence of fast driven oscillations the traditional adiabatic theorem holds. Implications for adiabatic quantum computation is discussed.

Does Adiabatic Quantum Optimization Fail for NP-Complete Problems?

Physical Review Letters, 2011

It has been recently argued that adiabatic quantum optimization would fail in solving NP-complete... more It has been recently argued that adiabatic quantum optimization would fail in solving NP-complete problems because of the occurrence of exponentially small gaps due to crossing of local minima of the final Hamiltonian with its global minimum near the end of the adiabatic evolution. Using perturbation expansion, we analytically show that for the NP-hard problem of maximum independent set there always exist adiabatic paths along which no such crossings occur. Therefore, in order to prove that adiabatic quantum optimization fails for any NP-complete problem, one must prove that it is impossible to find any such path in polynomial time.

Effect of Local Minima on Adiabatic Quantum Optimization

Physical Review Letters, 2008

We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization,... more We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that, for problems that have an exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. The quantum advantage of adiabatic quantum computation may then be accessed only via the local adiabatic evolution, which requires phase coherence throughout the evolution and knowledge of the spectrum. Such problems, therefore, are not suitable for adiabatic quantum computation.

Quasiparticle Decoherence in d-Wave Superconducting Qubits

Physical Review Letters, 2004

Probing Noise in Flux Qubits via Macroscopic Resonant Tunneling

Physical Review Letters, 2008

Macroscopic resonant tunneling between the two lowest lying states of a bistable RF-SQUID is used... more Macroscopic resonant tunneling between the two lowest lying states of a bistable RF-SQUID is used to characterize noise in a flux qubit. Measurements of the incoherent decay rate as a function of flux bias revealed a Gaussian shaped profile that is not peaked at the resonance point, but is shifted to a bias at which the initial well is higher than the target well. The r.m.s. amplitude of the noise, which is proportional to the decoherence rate 1/T * 2 , was observed to be weakly dependent on temperature below 70 mK. Analysis of these results indicates that the dominant source of low frequency (1/f) flux noise in this device is a quantum mechanical environment in thermal equilibrium.

Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor

Physical Review B, 2010