Qubit Measurement Research Articles

Dressed relaxation and dephasing in a strongly driven two-level system

We study relaxation and dephasing in a strongly driven two-level system interacting with its environment. We develop a theory which gives a straightforward physical picture of the complex dynamics of the system in terms of dressed states. In addition to the dressing of the energy diagram, we describe the dressing of relaxation and dephasing. We find a good quantitative agreement between the theoretical calculations and measurements of a superconducting qubit driven by an intense microwave field. The competition of various processes leads to a rich structure in the observed behavior, including signatures of population inversion.

Noise-induced looping on the Bloch sphere: Oscillatory effects in dephasing of qubits subject to broad-spectrum noise

For many implementations of quantum computing, 1/f and other types of broad-spectrum noise are an important source of decoherence. An important step forward would be the ability to back out the characteristics of this noise from qubit measurements and to see if it leads to new physical effects. For certain types of qubits, the working point of the qubit can be varied. Using a new mathematical method that is suited to treat all working points, we present theoretical results that show how this degree of freedom can be used to extract noise parameters and to predict a new effect: noise-induced looping on the Bloch sphere. We analyze data on superconducting qubits to show that they are very near the parameter regime where this looping should be observed.

Scheme for Bell state measurement in a g-factor engineered double dot

We proposed a possible protocol for Bell state measurements of spin qubits in a double quantum dot (QD). Our scheme consists of Pauli spin blockade measurements and biaxial electron spin resonance. It is assumed that the two QDs here are designed so that the Landé g-factors satisfy g1 = −g2 with the use of g-factor engineering. The opposite sign of the g-factors cancel the average of the Zeeman fields on the two QDs, and enable us to swap three spin-triplet states for a spin-singlet state sequentially. We showed that it is possible to implement the full Bell state measurement by the sequential spin-to-charge conversions in the QD-based spin qubits.

Quantum theory of unambiguous measurements

Quantum theory of unambiguous measurementsIn the present paper I formulate a framework that accommodates many unambiguous discrimination problems. I show that the prior information about any type of constituent (state, channel, or observable) allows us to reformulate the discrimination among finite number of alternatives as the discrimination among finite number of average constituents. Using this framework I solve several unambiguous tasks. I present a solution to optimal unambiguous comparison of two ensembles of unknown quantum states. I consider two cases: 1) The two unknown states are arbitrary pure states of qudits. 2) Alternatively, they are coherent states of single-mode optical fields. For this case I propose simple and optimal experimental setup composed of beam-splitters and a photodetector. As a second tasks I consider an unambiguous identification (UI) of coherent states. In this task identical quantum systems are prepared in coherent states and labeled as unknown and reference states, respectively. The promise is that one reference state is the same as the unknown state and the task is to find out unambiguously which one it is. The particular choice of the reference states is unknown to us, and only the probability distribution describing this choice is known. In a general case when multiple copies of unknown and reference states are available I propose a scheme consisting of beamsplitters and photodetectors that is optimal within linear optics. UI can be considered as a search in a quantum database, whose elements are the reference states and the query is represented by the unknown state. This perspective motivated me to show that reference states can be recovered after the measurement and might be used (with reduced success rate) in subsequent UI. Moreover, I analyze the influence of noise in preparation of coherent states on the performance of the proposed setup. Another problem I address is the unambiguous comparison of a pair of unknown qudit unitary channels. I characterize all solutions and identify the optimal ones. I prove that in optimal experiments for comparison of unitary channels the entanglement is necessary. The last task I studied is the unambiguous comparison of unknown non-degenerate projective measurements. I distinguish between measurement devices with apriori labeled and unlabeled outcomes. In both cases only the difference of the measurements can be concluded unambiguously. For the labeled case I derive the optimal strategy if each unknown measurement is used only once. However, if the apparatuses are not labeled, then each measurement device must be used (at least) twice. In particular, for qubit measurement apparatuses with unlabeled outcomes I derive the optimal test state in the two-shots scenario.

Quantum nondemolition measurements of a qubit coupled to a harmonic oscillator

We theoretically describe the weak measurement of a two-level system (qubit) and quantify the degree to which such a qubit measurement has a quantum nondemolition (QND) character. The qubit is coupled to a harmonic oscillator, which undergoes a projective measurement. Information on the qubit state is extracted from the oscillator measurement outcomes, and the QND character of the measurement is inferred from the result of subsequent measurements of the oscillator. We use the positive operator valued measure (POVM) formalism to describe the qubit measurement. Two mechanisms lead to deviations from a perfect QND measurement: (i) the quantum fluctuations of the oscillator, and (ii) quantum tunneling between the qubit states $|0⟩$ and $|1⟩$ during measurements. Our theory can be applied to QND measurements performed on superconducting qubits coupled to a circuit oscillator.

Scanning quantum decoherence microscopy

The use of qubits as sensitive nanoscale magnetometers has been studied theoretically andrecently demonstrated experimentally. In this paper we propose a new concept, in which ascanning two-state quantum system is used to probe a sample through the subtle effects ofdecoherence. Mapping both the Hamiltonian and decoherence properties of a qubitsimultaneously provides a unique image of the magnetic (or electric) field properties at thenanoscale. The resulting images are sensitive to the temporal as well as spatial variation inthe fields created by the sample. As examples we theoretically study two applications; onefrom condensed matter physics, the other biophysics. The individual components requiredto realize the simplest version of this device (characterization and measurement ofqubits, nanoscale positioning) have already been demonstrated experimentally.

Product measurements and fully symmetric measurements in qubit-pair tomography: A numerical study

State tomography on qubit pairs is routinely carried out by measuring the two qubits separately, while one expects a higher efficiency from tomography with highly symmetric joint measurements of both qubits. Our numerical study of simulated experiments does not support such expectations.

Quantum computation via measurements on the low-temperature state of a many-body system

We consider measurement-based quantum computation using the state of a spin-lattice system in equilibrium with a thermal bath and free to evolve under its own Hamiltonian. Any single qubit measurements disturb the system from equilibrium and, with adaptive measurements performed at a finite rate, the resulting dynamics reduces the fidelity of the computation. We show that it is possible to describe the loss in fidelity by a single quantum operation on the encoded quantum state that is independent of the measurement history. To achieve this simple description, we choose a particular form of spin-boson coupling to describe the interaction with the environment, and perform measurements periodically at a natural rate determined by the energy gap of the system. We found that an optimal cooling exists, which is a trade-off between keeping the system cool enough that the resource state remains close to the ground state, but also isolated enough that the cooling does not strongly interfere with the dynamics of the computation. For a sufficiently low temperature we obtain a fault-tolerant threshold for the couplings to the environment.

Reduced dynamics with renormalization in solid-state charge qubit measurement

Quantum measurement will inevitably cause backaction on the measured system, resultingin the well-known dephasing and relaxation. In this paper, in the context of solid-statequbit measurement by a mesoscopic detector, we show that an alternative backactionknown as renormalization is important under some circumstances. This effect is largelyoverlooked in the theory of quantum measurement.

Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields

We consider a one-dimensional spin chain for which the ground state is the cluster state, capable of functioning as a quantum computational wire when subjected to local adaptive measurements of individual qubits, and investigate the robustness of this property to local and coupled (Ising-type) perturbations. We investigate the ground state both by identifying suitable correlation functions as order parameters, as well as numerically using a variational method based on matrix product states. We find that the model retains an infinite localizable entanglement length for Ising and local fields up to a quantum phase transition, but that the resulting entangled state is not simply characterized by a Pauli correction based on the measurement results.

Nanomechanical measurements of a superconducting qubit

The observation of the quantum states of motion of a macroscopic mechanical structure remains an open challenge in quantum-state preparation and measurement. One approach that has received extensive theoretical attention is the integration of superconducting qubits as control and detection elements in nanoelectromechanical systems (NEMS). Here we report measurements of a NEMS resonator coupled to a superconducting qubit, a Cooper-pair box. We demonstrate that the coupling results in a dispersive shift of the nanomechanical frequency that is the mechanical analogue of the 'single-atom index effect' experienced by electromagnetic resonators in cavity quantum electrodynamics. The large magnitude of the dispersive interaction allows us to perform NEMS-based spectroscopy of the superconducting qubit, and enables observation of Landau-Zener interference effects-a demonstration of nanomechanical read-out of quantum interference.

Algorithms on ensemble quantum computers.

In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor’s factorization algorithm, Grover’s search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and sigma_{z}^{1/4}, as these operations cannot be implemented “bitwise”, and their standard fault-tolerant implementations require measurement.

Coherent Rabi response of a charge-phase qubit under microwave irradiation

We report on radio-frequency (rf) measurements of the charge-phase qubit being under continuous microwave irradiation in the state of weak coupling to a radio-frequency tank circuit. We studied the rf impedance dependence on the two important parameters such as the power of microwave irradiation, whose frequency is close to the gap between the two lowest qubit energy levels, and the temperature of the internal heat bath. We have found that backaction effects of the qubit on the rf tank and vice versa, tank on the qubit, lead to a negative as well as a positive real part of the qubit impedance $\text{Re}\text{ }Z(\ensuremath{\omega})$ seen by the tank. We have implemented noise spectroscopy measurements for direct impedance readout at the extreme points corresponding to maximum voltage response and obtained absolute values of about $0.017\text{ }\ensuremath{\Omega}$ for the negative and positive $\text{Re}\text{ }Z(\ensuremath{\omega})$. Our results demonstrate the existence and persistence of the coherent single- and multiphoton Rabi dynamics of the qubit with both negative and positive dynamic resistances inserted into the tank in the temperature range of 10--200 mK.

Scalable, High-Speed Measurement-Based Quantum Computer Using Trapped Ions

We describe a scalable, high-speed, and robust architecture for measurement-based quantum computing with trapped ions. Measurement-based architectures offer a way to speed up operation of a quantum computer significantly by parallelizing the slow entangling operations and transferring the speed requirement to fast measurement of qubits. We show that a 3D cluster state suitable for fault-tolerant measurement-based quantum computing can be implemented on a 2D array of ion traps. We propose the projective measurement of ions via multiphoton photoionization for nanosecond operation and discuss the viability of such a scheme for Ca ions.

Experimental Quantum Process Discrimination

Discrimination between unknown processes chosen from a finite set is experimentally shown to be possible even in the case of nonorthogonal processes. We demonstrate unambiguous deterministic quantum process discrimination of nonorthogonal processes using properties of entanglement, additional known unitaries, or classical communication. Single qubit measurement and unitary processes and multipartite unitaries (where the unitary acts nonseparably across two distant locations) acting on photons are discriminated with a confidence of >or=97% in all cases.

Unusual decoherence in qubit measurements with a Bose-Einstein condensate

We consider an electrostatic qubit located near a Bose-Einstein condensate (BEC) of noninteracting bosons in a double-well potential, which is used for qubit measurements. Tracing out the BEC variables we obtain a simple analytical expression for the qubit's density matrix. The qubit's evolution exhibits a slow $(\ensuremath{\propto}1/\sqrt{t})$ damping of the qubit's coherence term, which however turns to be a Gaussian one in the case of static qubit. This is in contrast to the exponential damping produced by most classical detectors. The decoherence is, in general, incomplete and strongly depends on the initial state of the qubit.

Weak measurement of qubit oscillations with strong response detectors: Violation of the fundamental bound imposed on linear detectors

Qubit measurement by mesoscopic charge detectors has received great interest in the community of mesoscopic transport and solid-state quantum computation, and some controversial issues still remain unresolved. In this work, we revisit the continuous weak measurement of a solid-state qubit by single electron transistors (SETs) in nonlinear-response regime. For two SET models typically used in the literature, we find that the signal-to-noise ratio can violate the universal upper bound ``4,'' which is imposed quantum mechanically on linear-response detectors. This different result can be understood by means of the cross correlation of the detector currents by viewing the two junctions of the single SET as two detectors. Possible limitation of the potential-scattering approach to this result is also discussed.

Adaptive Measurements in the Optical Quantum Information Laboratory

Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example, they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom bound, measurement of the phase of a quantum oscillator with accuracy approaching (or in some cases attaining) the Heisenberg limit (HL), and estimation of phase in interferometry with a variance scaling at the HL, using only single qubit measurement and control. Each of these examples has close links with quantum information, in particular, experimental optical quantum information: the first is a basic quantum communication protocol; the second has potential application in linear optical quantum computing; the third uses an adaptive protocol inspired by the quantum phase estimation algorithm. We discuss each of these examples and their implementation in the laboratory, but concentrate upon the last, which was published most recently [Higgins <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nature</i> , vol. 450, p. 393, 2007].

Computation with coherent states via teleportations to and from a quantum bus

In this paper we present results illustrating the power and flexibility of one-bit teleportations in quantum bus computation. We first show a scheme to perform a universal set of gates on continuous variable modes, which we call a quantum bus or qubus, using controlled phase-space rotations, homodyne detection, ancilla qubits and single qubit measurement. The resource usage for this scheme is lower than any previous scheme to date. We then illustrate how one-bit teleportations into a qubus can be used to encode qubit states into a quantum repetition code, which in turn can be used as an efficient method for producing GHZ states that can be used to create large cluster states. Each of these schemes can be modified so that teleportation measurements are post-selected to yield outputs with higher fidelity, without changing the physical parameters of the system.

Coexistence of qubit effects

We characterize all coexistent pairs of qubit effects. This gives an exhaustive description of all pairs of events allowed, in principle, to occur in a single qubit measurement. The char- acterization consists of three disjoint conditions which are easy to check for a given pair of effects. Known special cases are shown to follow from our general characterization theorem.