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S. Ashhab

Publications and source records attributed to S. Ashhab.

At least 37 records · Page 2Linked to original sources
arXiv2012

Selective darkening of degenerate transitions for implementing quantum controlled-NOT gates

We present a theoretical analysis of the selective darkening method for implementing quantum controlled-NOT (CNOT) gates. This method, which we recently proposed and demonstrated, consists of driving two transversely-coupled quantum bits (qubits) with a driving field that is resonant with one of the two qubits. For specific relative amplitudes and phases of the driving field felt by the two qubits, one of the two transitions in the degenerate pair is darkened, or in other words, becomes forbidden by effective selection rules. At these driving conditions, the evolution of the two-qubit state realizes a CNOT gate. The gate speed is found to be limited only by the coupling energy J, which is the fundamental speed limit for any entangling gate. Numerical simulations show that at gate speeds corresponding to 0.48J and 0.07J, the gate fidelity is 99% and 99.99%, respectively, and increases further for lower gate speeds. In addition, the effect of higher-lying energy levels and weak anharmonicity is studied, as well as the scalability of the method to systems of multiple qubits. We conclude that in all these respects this method is competitive with existing schemes for creating entanglement, with the added advantages of being applicable for qubits operating at fixed frequencies (either by design or for exploitation of coherence sweet-spots) and having the simplicity of microwave-only operation.

quant-ph↗
arXiv2012

Quantum algorithm for obtaining the energy spectrum of a physical system

We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e. the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a polynomially increasing number of energy levels. A probe qubit is coupled to a quantum register that represents the system of interest such that the probe exhibits a dynamical response only when it is resonant with a transition in the system. By varying the probe's frequency and the system-probe coupling operator, any desired part of the energy spectrum can be obtained. The algorithm can also be used to deterministically prepare any energy eigenstate. As an example, we have simulated running the algorithm and obtained the energy spectrum of the water molecule.

quant-ph↗
arXiv2012

Speed limits for quantum gates in multi-qubit systems

We use analytical and numerical calculations to obtain speed limits for various unitary quantum operations in multiqubit systems under typical experimental conditions. The operations that we consider include single-, two-, and three-qubit gates, as well as quantum-state transfer in a chain of qubits. We find in particular that simple methods for implementing two-qubit gates generally provide the fastest possible implementations of these gates. We also find that the three-qubit Toffoli gate time varies greatly depending on the type of interactions and the system's geometry, taking only slightly longer than a two-qubit controlled-NOT (CNOT) gate for a triangle geometry. The speed limit for quantum-state transfer across a qubit chain is set by the maximum spin-wave speed in the chain.

quant-ph↗
arXiv2012

Inverse Landau-Zener-Stuckelberg problem for qubit-resonator systems

We consider theoretically a superconducting qubit - nanomechanical resonator (NR) system, which was realized by LaHaye et al. [Nature 459, 960 (2009)]. First, we study the problem where the state of the strongly driven qubit is probed through the frequency shift of the low-frequency NR. In the case where the coupling is capacitive, the measured quantity can be related to the so-called quantum capacitance. Our theoretical results agree with the experimentally observed result that, under resonant driving, the frequency shift repeatedly changes sign. We then formulate and solve the inverse Landau-Zener-Stuckelberg problem, where we assume the driven qubit's state to be known (i.e. measured by some other device) and aim to find the parameters of the qubit's Hamiltonian. In particular, for our system the qubit's bias is defined by the NR's displacement. This may provide a tool for monitoring of the NR's position.

cond-mat.mes-hall↗
arXiv2011

Quantum algorithm for simulating the dynamics of an open quantum system

In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment and their interaction: one basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the dynamics of an open quantum system. On a quantum computer, the environment can be simulated using ancilla qubits with properly chosen single-qubit frequencies and with properly designed coupling to the system qubits. The parameters used in the simulation are easily derived from the parameters of the system+environment Hamiltonian. The algorithm is designed to simulate Markovian dynamics, but it can also be used to simulate non-Markovian dynamics provided that this dynamics can be obtained by embedding the system of interest into a larger system that obeys Markovian dynamics. We estimate the resource requirements for the algorithm. In particular, we show that for sufficiently slow decoherence a single ancilla qubit could be sufficient to represent the entire environment, in principle.

quant-ph↗
arXiv2010

Control-free control: manipulating a quantum system using only a limited set of measurements

We present and discuss different protocols for preparing an arbitrary quantum state of a qubit using only a restricted set of measurements, with no unitary operations at all. We show that an arbitrary state can indeed be prepared, provided that the available measurements satisfy certain requirements. Our results shed light on the role that measurement-induced back-action plays in quantum feedback control and the extent to which this back-action can be exploited in quantum-control protocols.

quant-ph↗
arXiv2010

Selective darkening of degenerate transitions demonstrated with two superconducting quantum bits

Controlled manipulation of quantum states is central to studying natural and artificial quantum systems. If a quantum system consists of interacting sub-units, the nature of the coupling may lead to quantum levels with degenerate energy differences. This degeneracy makes frequency-selective quantum operations impossible. For the prominent group of transversely coupled two-level systems, i.e. qubits, we introduce a method to selectively suppress one transition of a degenerate pair while coherently exciting the other, effectively creating artificial selection rules. It requires driving two qubits simultaneously with the same frequency and specified relative amplitude and phase. We demonstrate our method on a pair of superconducting flux qubits. It can directly be applied to the other superconducting qubits, and to any other qubit type that allows for individual driving. Our results provide a single-pulse controlled-NOT gate for the class of transversely coupled qubits.

cond-mat.supr-con↗
arXiv2010

Landau-Zener-Stuckelberg interferometry

A transition between energy levels at an avoided crossing is known as a Landau-Zener transition. When a two-level system (TLS) is subject to periodic driving with sufficiently large amplitude, a sequence of transitions occurs. The phase accumulated between transitions (commonly known as the Stuckelberg phase) may result in constructive or destructive interference. Accordingly, the physical observables of the system exhibit periodic dependence on the various system parameters. This phenomenon is often referred to as Landau-Zener-Stuckelberg (LZS) interferometry. Phenomena related to LZS interferometry occur in a variety of physical systems. In particular, recent experiments on LZS interferometry in superconducting TLSs (qubits) have demonstrated the potential for using this kind of interferometry as an effective tool for obtaining the parameters characterizing the TLS as well as its interaction with the control fields and with the environment. Furthermore, strong driving could allow for fast and reliable control of the quantum system. Here we review recent experimental results on LZS interferometry, and we present related theory.

cond-mat.supr-con↗
arXiv2010

Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states

We consider a system composed of a two-level system (i.e. a qubit) and a harmonic oscillator in the ultrastrong-coupling regime, where the coupling strength is comparable to the qubit and oscillator energy scales. Special emphasis is placed on the possibility of preparing nonclassical states in this system. These nonclassical states include squeezed states, Schrodinger-cat states and entangled states. We start by comparing the predictions of a number of analytical methods that can be used to describe the system under different assumptions, thus analyzing the properties of the system in various parameter regimes. We then examine the ground state of the system and analyze its nonclassical properties. We finally discuss some questions related to the possible experimental observation of the nonclassical states and the effect of decoherence.

quant-ph↗
arXiv2009

The information about the state of a charge qubit gained by a weakly coupled quantum point contact

We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. We consider the general case where the qubit Hamiltonian and the qubit's operator probed by the detector do not commute. Because the qubit's state keeps evolving while being probed and the measurement data is mixed with a detector-related background noise, one might expect the detector to fail in this case. We show, however, that under suitable conditions and by proper analysis of the measurement data useful information about the initial state of the qubit can be extracted. Our approach complements the usual master-equation and quantum-trajectory approaches, which describe the evolution of the qubit's quantum state during the measurement process but do not keep track of the acquired measurement information.

quant-ph↗
arXiv2009

Bell's experiment with intra- and inter-pair entanglement: Single-particle mode entanglement as a case study

Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large many-body system where all the pairs are generally entangled with each other. Using an explicit example based on single mode entanglement and an ancillary Bose-Einstein condensate, we show that the Bell-inequality violation in such systems can display statistical properties that are remarkably different from those obtained using identically prepared, independent pairs. In particular, one can have probabilistic violation of Bell's inequalities in which a finite fraction of all the runs result in violation, even though there could be no violation when averaging over all the runs. Whether or not a particular run of results will end up being local realistically explainable is "decided" by a sequence of quantum (random) outcomes.

quant-ph↗
arXiv2009

The information about the state of a qubit gained by a weakly coupled detector

We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. In particular, we focus on the case when the qubit Hamiltonian and the qubit's operator being probed by the detector do not commute. Because the qubit's state keeps evolving while being probed and because the measurement data is mixed with a detector-related background noise, one might expect the detector to fail in this case. We show, however, that under suitable conditions and by proper analysis of the measurement data useful information about the state of the qubit can be extracted. It turns out that the measurement basis is stochastically determined every time the experiment is repeated. We analyze in detail the probability distributions that govern the choice of measurement bases. We also analyze the information acquisition rate and show that it is largely unaffected by the apparent conflict between the measurement and intrinsic qubit dynamics. We discuss the relation between our analysis and the stochastic master equation that describes the evolution of the qubit's state under the influence of measurement and decoherence. In particular, we write down a stochastic equation that encompasses the usual stochastic master equation for the evolution of the qubit's density matrix and additionally contains the measurement information that can be extracted from the observed signal.

quant-ph↗
arXiv2009

How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100 without using weak measurements

We discuss two questions related to the concept of weak values as seen from the standard quantum-mechanics point of view. In the first part of the paper, we describe a scenario where unphysical results similar to those encountered in the study of weak values are obtained using a simple experimental setup that does not involve weak measurements. In the second part of the paper, we discuss the correct physical description, according to quantum mechanics, of what is being measured in a weak-value-type experiment.

quant-ph↗
arXiv2009

Two-level systems driven by large-amplitude fields

We analyze the dynamics of a two-level system subject to driving by large-amplitude external fields, focusing on the resonance properties in the case of driving around the region of avoided level crossing. In particular, we consider three main questions that characterize resonance dynamics: (1) the resonance condition, (2) the frequency of the resulting oscillations on resonance and (3) the width of the resonance. We identify the regions of validity of different approximations. In a large region of the parameter space, we use a geometric picture in order to obtain both a simple understanding of the dynamics and quantitative results. The geometric approach is obtained by dividing the evolution into discrete time steps, with each time step described by either a phase shift on the basis states or a coherent mixing process corresponding to a Landau-Zener crossing. We compare the results of the geometric picture with those of a rotating-wave approximation. We also comment briefly on the prospects of employing strong driving as a useful tool to manipulate two-level systems.

quant-ph↗
arXiv2009

Weak and strong measurement of a qubit using a switching-based detector

We analyze the operation of a switching-based detector that probes a qubit's observable that does not commute with the qubit's Hamiltonian, leading to a nontrivial interplay between the measurement and free-qubit dynamics. In order to obtain analytic results and develop intuitive understanding of the different possible regimes of operation, we use a theoretical model where the detector is a quantum two-level system that is constantly monitored by a macroscopic system. We analyze how to interpret the outcome of the measurement and how the state of the qubit evolves while it is being measured. We find that the answers to the above questions depend on the relation between the different parameters in the problem. In addition to the traditional strong-measurement regime, we identify a number of regimes associated with weak qubit-detector coupling. An incoherent detector whose switching time is measurable with high accuracy can provide high-fidelity information, but the measurement basis is determined only upon switching of the detector. An incoherent detector whose switching time can be known only with low accuracy provides a measurement in the qubit's energy eigenbasis with reduced measurement fidelity. A coherent detector measures the qubit in its energy eigenbasis and, under certain conditions, can provide high-fidelity information.

quant-ph↗
arXiv2009

Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer

We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number $m$ of electrons occupying a given number $n$ of spin orbitals. Each spin orbital is mapped to a qubit: the states $| 1 >$ and $| 0>$ of the qubit represent, respectively, whether the spin orbital is occupied by an electron or not. To prepare a general state in the full Hilbert space of $n$ qubits, which is of dimension $2^{n}$%, $O(2^{n})$ controlled-NOT gates are needed, i.e., the number of gates scales \emph{exponentially} with the number of qubits. We make use of the fact that the state to be prepared lies in a smaller Hilbert space, and we find an algorithm that requires at most $O(2^{m+1} n^{m}/{m!})$ gates, i.e., scales \emph{polynomially} with the number of qubits $n$, provided $n\gg m$. The algorithm is simulated numerically for the cases of the hydrogen molecule and the water molecule. The numerical simulations show that when additional symmetries of the system are considered, the number of gates to prepare the state can be drastically reduced, in the examples considered in this paper, by several orders of magnitude, from the above estimate.

quant-ph↗
arXiv2009

Single-artificial-atom lasing using a voltage-biased superconducting charge qubit

We consider a system composed of a single artificial atom coupled to a cavity mode. The artificial atom is biased such that the most dominant relaxation process in the system takes the atom from its ground state to its excited state, thus ensuring population inversion. A recent experimental manifestation of this situation was achieved using a voltage-biased superconducting charge qubit. Even under the condition of `inverted relaxation', lasing action can be suppressed if the `relaxation' rate is larger than a certain threshold value. Using simple transition-rate arguments and a semiclassical calculation, we derive analytic expressions for the lasing suppression condition and the state of the cavity in both the lasing and suppressed-lasing regimes. The results of numerical calculations agree very well with the analytically derived results. We start by analyzing a simplified two-level-atom model, and we then analyze a three-level-atom model that should describe accurately the recently realized superconducting artificial-atom laser.

cond-mat.supr-con↗