Qubit Register Research Articles

Quantum abacus for counting and factorizing numbers

We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. A 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base 2, base 3, or base d representation. In operating the algorithm, the number n < N = d^K is read into a K-qudit register through its interaction with a stream of n particles passing in a nearby wire; this step corresponds to a quantum Fourier transformation from the Hilbert space of particles to the Hilbert space of qudit states. An inverse quantum Fourier transformation provides the number n in the base d representation; the inverse transformation is fully quantum at the level of individual qudits, while a simpler semi-classical version can be used on the level of qudit registers. Combining registers of qubits, qutrits, and qudits, where d is a prime number, with a simpler single-shot measurement allows to find the powers of 2, 3, and other primes d in the number n. We show, that the counting task naturally leads to the shift operation and an algorithm based on the quantum Fourier transformation. We discuss possible implementations of the algorithm using quantum spin-d systems, d-well systems, and their emulation with spin-1/2 or double-well systems. We establish the analogy between our counting algorithm and the phase estimation algorithm and make use of the latter's performance analysis in stabilizing our scheme. Applications embrace a quantum metrological scheme to measure a voltage (analog to digital converter) and a simple procedure to entangle multi-particle states.

Electrons spin in the field

Nanowires are candidates for enabling the exchange of quantum information between light and matter. The rapid control of a single electron spin by solely electrical means brings this possibility closer. See Letter p.1084 A promising new form of quantum bit (qubit), the spin–orbit qubit, may be an improvement over both charge and spin qubits. In quantum physics, the motion of electrons can influence their spins through a fundamental effect called the spin–orbit interaction. Nadj-Perge et al. implement a spin–orbit quantum bit in an indium arsenide nanowire. The spin–orbit qubit is electrically controllable, and information can be stored in the spin. Nanowires are particularly suited to quantum computing as they can serve as one-dimensional templates for scalable qubit registers and can function in both electronic and optical devices.

Spin–orbit qubit in a semiconductor nanowire

Motion of electrons can influence their spins through a fundamental effect called spin-orbit interaction. This interaction provides a way to control spins electrically and thus lies at the foundation of spintronics. Even at the level of single electrons, the spin-orbit interaction has proven promising for coherent spin rotations. Here we implement a spin-orbit quantum bit (qubit) in an indium arsenide nanowire, where the spin-orbit interaction is so strong that spin and motion can no longer be separated. In this regime, we realize fast qubit rotations and universal single-qubit control using only electric fields; the qubits are hosted in single-electron quantum dots that are individually addressable. We enhance coherence by dynamically decoupling the qubits from the environment. Nanowires offer various advantages for quantum computing: they can serve as one-dimensional templates for scalable qubit registers, and it is possible to vary the material even during wire growth. Such flexibility can be used to design wires with suppressed decoherence and to push semiconductor qubit fidelities towards error correction levels. Furthermore, electrical dots can be integrated with optical dots in p-n junction nanowires. The coherence times achieved here are sufficient for the conversion of an electronic qubit into a photon, which can serve as a flying qubit for long-distance quantum communication.

Ancilla-driven universal quantum computation

We introduce a model of quantum computation intermediate between the gate-based and measurement-based models. A quantum register is manipulated remotely with the help of a single ancilla that ``drives'' the evolution of the register. The fully controlled ancilla qubit is coupled to the computational register only via a fixed unitary two-qubit interaction and then measured in suitable bases, driving both single- and two-qubit operations on the register. Arbitrary single-qubit operations directly on register qubits are not needed. We characterize all interactions $E$ that induce a unitary, stepwise deterministic measurement back-action on the register sufficient to implement any quantum channel. Our scheme offers experimental advantages for computation, state preparation, and generalized measurements, since no tunable control of the register is required.

Strong entanglement causes low gate fidelity in inaccurate one-way quantum computation

We study how entanglement among the register qubits affects the gate fidelity in the one-way quantum computation if a measurement is inaccurate. We derive an inequality which shows that the mean gate fidelity is upper bounded by a decreasing function of the magnitude of the error of the measurement and the amount of the entanglement between the measured qubit and other register qubits. The consequence of this inequality is that, for a given amount of entanglement, which is theoretically calculated once the algorithm is fixed, we can estimate from this inequality how small the magnitude of the error should be in order not to make the gate fidelity below a threshold, which is specified by a technical requirement in a particular experimental setup or by the threshold theorem of the fault-tolerant quantum computation.

Continuous quantum error correction as classical hybrid control

The standard formulation of quantum error correction (QEC) comprises repeated cycles of error estimation and corrective intervention in the free dynamics of a qubit register. QEC can thus be seen as a form of feedback control, and it is of interest to seek a deeper understanding of the connection between the associated theories. Here we present a focused case study within this broad program, connecting continuous QEC with elements of hybrid control theory. We show that canonical methods of the latter engineering discipline, such as recursive filtering and dynamic programming approaches to solving the optimal control problem, can be applied fruitfully in the design of separated controller structures for quantum memories based on coding and continuous syndrome measurement.

Characterizing multipartite symmetric Dicke states under the effects of noise

We study genuine multipartite entanglement (GME) in a system of n qubits prepared in symmetric Dicke states and subjected to the influences of noise. We provide general, setup-independent expressions for experimentally favorable tools such as fidelity- and collective spin-based entanglement witnesses, as well as entangled-class discriminators and multi-point correlation functions. Besides highlighting the effects of the environment on large qubit registers, we also discuss strategies for the robust detection of GME. Our work provides techniques and results for the experimental communities interested in investigating and characterizing multipartite entangled states by introducing realistic milestones for setup design and associated predictions.

Demonstration of two-qubit algorithms with a superconducting quantum processor

Quantum computers, which harness the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact-such as factoring large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized register of qubits, which coherently evolves into a final state containing the result of the computation. Building a quantum processor is challenging because of the need to meet simultaneously requirements that are in conflict: state preparation, long coherence times, universal gate operations and qubit readout. Processors based on a few qubits have been demonstrated using nuclear magnetic resonance, cold ion trap and optical systems, but a solid-state realization has remained an outstanding challenge. Here we demonstrate a two-qubit superconducting processor and the implementation of the Grover search and Deutsch-Jozsa quantum algorithms. We use a two-qubit interaction, tunable in strength by two orders of magnitude on nanosecond timescales, which is mediated by a cavity bus in a circuit quantum electrodynamics architecture. This interaction allows the generation of highly entangled states with concurrence up to 94 per cent. Although this processor constitutes an important step in quantum computing with integrated circuits, continuing efforts to increase qubit coherence times, gate performance and register size will be required to fulfil the promise of a scalable technology.

Scaling the neutral-atom Rydberg gate quantum computer by collective encoding in holmium atoms

We discuss a method for scaling a neutral atom Rydberg gate quantum processor to a large number of qubits. Limits are derived showing that the number of qubits that can be directly connected by entangling gates with errors at the $10^{-3}$ level using long range Rydberg interactions between sites in an optical lattice, without mechanical motion or swap chains, is about 500 in two dimensions and 7500 in three dimensions. A scaling factor of 60 at a smaller number of sites can be obtained using collective register encoding in the hyperfine ground states of the rare earth atom Holmium. We present a detailed analysis of operation of the 60 qubit register in Holmium. Combining a lattice of multi-qubit ensembles with collective encoding results in a feasible design for a 1000 qubit fully connected quantum processor.

Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods

In building a quantum-information processor (QIP), the challenge is to coherently control a large quantum system well enough to perform an arbitrary quantum algorithm and to be able to correct errors induced by decoherence. Nuclear magnetic resonance (NMR) QIPs offer an excellent testbed on which to develop and benchmark tools and techniques to control quantum systems. Two main issues to consider when designing control methods are accuracy and efficiency, for which two complementary approaches have been developed so far to control qubit registers with liquid-state NMR methods. The first applies optimal control theory to numerically optimize the control fields to implement unitary operations on low-dimensional systems with high fidelity. The second technique is based on the efficient optimization of a sequence of imperfect control elements so that implementation of a full quantum algorithm is possible while minimizing error accumulation. This paper summarizes our work in implementing both of these methods. Furthermore, we show that taken together, they form a basis to design quantum control methods for a block-architecture QIP so that large system size is not a barrier to implementing optimal control techniques.

Control-limited perfect state transfer, quantum stochastic resonance, and many-body entangling gate in imperfect qubit registers

We propose a protocol for perfect quantum state transfer that is resilient to a broad class of realistic experimental imperfections, including noise sources that could be modeled either as independent Markovian baths or as certain forms of spatially correlated environments. We highlight interesting connections between the fidelity of state transfer and quantum stochastic resonance effects. The scheme is flexible enough to act as an effective entangling gate for the generation of genuine multipartite entanglement in a control-limited setting. Possible experimental implementations using superconducting qubits are also briefly discussed.

Fast initialization of a high-fidelity quantum register using optical superlattices

We propose a method for the fast generation of a quantum register of addressable qubits consisting of ultracold atoms stored in an optical lattice. Starting with a half filled lattice we remove every second lattice barrier by adiabatically switching on a superlattice potential which leads to a long wavelength lattice in the Mott insulator state with unit filling. The larger periodicity of the resulting lattice could make individual addressing of the atoms via an external laser feasible. We develop a Bose-Hubbard-like model for describing the dynamics of cold atoms in a lattice when doubling the lattice periodicity via the addition of a superlattice potential. The dynamics of the transition from a half filled to a commensurately filled lattice is analysed numerically with the help of the time evolving block decimation algorithm and analytically using the Kibble–Zurek theory. We show that the timescale for the whole process, i.e. creating the half filled lattice and subsequent doubling of the lattice periodicity, is significantly faster than adiabatic direct quantum-freezing of a superfluid into a Mott insulator for large lattice periods. Our method therefore provides a high-fidelity quantum register of addressable qubits on a fast timescale.

Quantum-state reconstruction with imperfect rotations on an inhomogeneously broadened ensemble of qubits

We present a method for performing quantum-state reconstruction on qubits and qubit registers in the presence of decoherence and inhomogeneous broadening. The method assumes only rudimentary single-qubit rotations as well as knowledge of decoherence and loss mechanisms. We show that full state reconstruction is possible even in the case where single-qubit rotations may only be performed imperfectly. Furthermore, we show that for ensemble quantum-computing proposals, quantum-state reconstruction is possible even if the ensemble experiences inhomogeneous broadening and if only imperfect qubit manipulations are available during state preparation and reconstruction.

Scalable designs for quantum computing with rare-earth-ion-doped crystals

Due to inhomogeneous broadening, the absorption lines of rare-earth-ion dopants in crystals are many order of magnitudes wider than the homogeneous linewidths. Several ways have been proposed to use ions with different inhomogeneous shifts as qubit registers, and to perform gate operations between such registers by means of the static dipole coupling between the ions. In this paper we show that in order to implement high-fidelity quantum gate operations by means of the static dipole interaction, we require the participating ions to be strongly coupled, and that the density of such strongly coupled registers in general scales poorly with register size. Although this is critical to previous proposals which rely on a high density of functional registers, we describe architectures and preparation strategies that will allow scalable quantum computers based on rare-earth-ion-doped crystals.

Coherent manipulation of atomic qubits in optical micropotentials

We experimentally demonstrate the coherent manipulation of atomic states in far-detuned dipole traps and registers of dipole traps based on two-dimensional arrays of microlenses. By applying Rabi, Ramsey, and spin-echo techniques, we systematically investigate the dephasing mechanisms and determine the coherence time. Simultaneous Ramsey measurements in up to 16 dipole traps are performed and proves the scalability of our approach. This represents an important step in the application of scalable registers of atomic qubits for quantum information processing. In addition, this system can serve as the basis for novel atomic clocks making use of the parallel operation of a large number of individual clocks each remaining separately addressable.

Entanglement and its role in Shor's algorithm

Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their classical counterparts. The nature of this resource is still not fully understood: here we use numerical simulation to investigate how entanglement between register qubits varies as Shor's algorithm is run on a quantum computer. The shifting patterns in the entanglement are found to relate to the choice of basis for the quantum Fourier transform.

Near-perfect simultaneous measurement of a qubit register

Simultaneous measurement of multiple qubits stored in hyperfine levels of trapped 111Cd+ ions is realized with an intensified charge-coupled device (CCD) imager. A general theory of fluorescence detection for hyperfine qubits is presented and applied to experimental data. The use of an imager for photon detection allows for multiple qubit state measurement with detection fidelities of greater than 98%. Improvements in readout speed and fidelity are discussed in the context of scalable quantum computation architectures.

Near-perfect simultaneous measurement of a qubit register

Simultaneous measurement of multiple qubits stored in hyperfine levels of trapped ^{111}Cd^+ ions is realized with an intensified charge-coupled device (CCD) imager. A general theory of fluorescence detection for hyperfine qubits is presented and applied to experimental data. The use of an imager for photon detection allows for multiple qubit state measurement with detection fidelities of greater than $98\%$. Improvements in readout speed and fidelity are discussed in the context of scalable quantum computation architectures.

Quantum information processing in optical lattices and magnetic microtraps

AbstractWe review our experiments on quantum information processing with neutral atoms in optical lattices and magnetic microtraps. Atoms in an optical lattice in the Mott insulator regime serve as a large qubit register. A spin‐dependent lattice is used to split and delocalize the atomic wave functions in a controlled and coherent way over a defined number of lattice sites. This is used to experimentally demonstrate a massively parallel quantum gate array, which allows the creation of a highly entangled many‐body cluster state through coherent collisions between atoms on neighbouring lattice sites. In magnetic microtraps on an atom chip, we demonstrate coherent manipulation of atomic qubit states and measure coherence lifetimes exceeding one second at micron‐distance from the chip surface. We show that microwave near‐fields on the chip can be used to create state‐dependent potentials for the implementation of a quantum controlled phase gate with these robust qubit states. For single atom detection and preparation, we have developed high finesse fiber Fabry‐Perot cavities and integrated them on the ato m chip. We present an experiment in which we detected a very small number of cold atoms magnetically trapped in the cavity using the atom chip.

Spin-bus concept of spin quantum computing

We present a spin-bus concept of quantum computing where an electron spin $S=1∕2$ acts as a bus qubit connected to a finite number $N$ of nuclear spins $I=1∕2$ serving as client qubits. Spin-bus clusters are considered as local processing units and may be interconnected with other spin-bus clusters via electron-electron coupling in a scaled up version. Here we lay the ground for the basic functional unit with long qubit registers, provide the theory and experimental verification of correlated qubit states, and demonstrate the Deutsch algorithm. Experiments were performed on a qubyte plus one nuclear spin in a solid state system.