Robust Quantum Computation Research Articles

Robust quantum gates for singlet-triplet spin qubits using composite pulses

We present a comprehensive theoretical treatment of SUPCODE, a method for generating dynamically corrected quantum gate operations, which are immune to random noise in the environment, by using carefully designed sequences of soft pulses. SUPCODE enables dynamical error suppression even when the control field is constrained to be positive and uniaxial, making it particularly suited to counteracting the effects of noise in systems subject to these constraints such as singlet-triplet qubits. We describe and explain in detail how to generate SUPCODE pulse sequences for arbitrary single-qubit gates and provide several explicit examples of sequences that implement commonly used gates, including the single-qubit Clifford gates. We develop sequences for noise-resistant two-qubit gates for two exchanged-coupled singlet-triplet qubits by cascading robust single-qubit gates, leading to a 35% reduction in gate time compared to previous works. This cascade approach can be scaled up to produce gates for an arbitrary-length spin qubit array, and is thus relevant to scalable quantum computing architectures. To more accurately describe real spin qubit experiments, we show how to design sequences that incorporate additional features and practical constraints such as sample-specific charge noise models and finite pulse rise times. We provide a detailed analysis based on randomized benchmarking to show how SUPCODE gates perform under realistic $1/f^\alpha$ noise and find a strong dependence of gate fidelity on the exponent $\alpha$, with best performance for $\alpha>1$. Our SUPCODE sequences can therefore be used to implement robust universal quantum computation while accommodating the fundamental constraints and experimental realities of singlet-triplet qubits.

Experimental realization of non-Abelian non-adiabatic geometric gates

The geometric aspects of quantum mechanics are emphasized most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a path in Hilbert space, that is, the space of quantum states of the system. The geometric phase is determined only by the shape of this path and is, in its simplest form, a real number. However, if the system has degenerate energy levels, then matrix-valued geometric state transformations, known as non-Abelian holonomies--the effect of which depends on the order of two consecutive paths--can be obtained. They are important, for example, for the creation of synthetic gauge fields in cold atomic gases or the description of non-Abelian anyon statistics. Moreover, there are proposals to exploit non-Abelian holonomic gates for the purposes of noise-resilient quantum computation. In contrast to Abelian geometric operations, non-Abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins, and without full characterization of the geometric process and its non-commutative nature. Here we realize non-Abelian non-adiabatic holonomic quantum operations on a single, superconducting, artificial three-level atom by applying a well-controlled, two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates that exceed 95 per cent. We show that two different quantum gates, originating from two distinct paths in Hilbert space, yield non-equivalent transformations when applied in different orders. This provides evidence for the non-Abelian character of the implemented holonomic quantum operations. In combination with a non-trivial two-quantum-bit gate, our method suggests a way to universal holonomic quantum computing.

Quantum computing: a gentle introduction

The combination of two of the twentieth centurys most influential and revolutionary scientific theories, information theory and quantum mechanics, gave rise to a radically new view of computing and information. Quantum information processing explores the implications of using quantum mechanics instead of classical mechanics to model information and its processing. Quantum computing is not about changing the physical substrate on which computation is done from classical to quantum but about changing the notion of computation itself, at the most basic level. The fundamental unit of computation is no longer the bit but the quantum bit or qubit. This comprehensive introduction to the field offers a thorough exposition of quantum computing and the underlying concepts of quantum physics, explaining all the relevant mathematics and offering numerous examples. With its careful development of concepts and thorough explanations, the book makes quantum computing accessible to students and professionals in mathematics, computer science, and engineering. A reader with no prior knowledge of quantum physics (but with sufficient knowledge of linear algebra) will be able to gain a fluent understanding by working through the book. The text covers the basic building blocks of quantum information processing, quantum bits and quantum gates, showing their relationship to the key quantum concepts of quantum measurement, quantum state transformation, and entanglement between quantum subsystems; it treats quantum algorithms, discussing notions of complexity and describing a number of simple algorithms as well as the most significant algorithms to date; and it explores entanglement and robust quantum computation, investigating such topics as quantifying entanglement, decoherence, quantum error correction, and fault tolerance.

Improved phase-gate reliability in systems with neutral Ising anyons

Recent proposals using heterostructures of superconducting and either topologically insulating or semiconducting layers have been put forth as possible platforms for topological quantum computation. These systems are predicted to contain Ising anyons and share the feature of having only neutral edge excitations. In this note, we show that these proposals can be combined with the recently proposed "sack geometry" for implementation of a phase gate in order to conduct robust universal quantum computation. In addition, we propose a general method for adjusting edge tunneling rates in such systems, which is necessary for the control of interferometric devices. The error rate for the phase gate in neutral Ising systems is parametrically smaller than for a similar geometry in which the edge modes carry charge: it goes as $T^3$ rather than $T$ at low temperatures. At zero temperature, the phase variance becomes constant at long times rather than carrying a logarithmic divergence.

Simulation of anyons with tensor network algorithms

Interacting systems of anyons pose a unique challenge to condensed matter simulations due to their non-trivial exchange statistics. These systems are of great interest as they have the potential for robust universal quantum computation, but numerical tools for studying them are as yet limited. We show how existing tensor network algorithms may be adapted for use with systems of anyons, and demonstrate this process for the 1-D Multi-scale Entanglement Renormalisation Ansatz (MERA). We apply the MERA to infinite chains of interacting Fibonacci anyons, computing their scaling dimensions and local scaling operators. The scaling dimensions obtained are seen to be in agreement with conformal field theory. The techniques developed are applicable to any tensor network algorithm, and the ability to adapt these ansaetze for use on anyonic systems opens the door for numerical simulation of large systems of free and interacting anyons in one and two dimensions.

Robust and scalable optical one-way quantum computation

We propose an efficient approach for deterministically generating scalable cluster states with photons. This approach involves unitary transformations performed on atoms coupled to optical cavities. Its operation cost scales linearly with the number of qubits in the cluster state, and photon qubits are encoded such that single-qubit operations can be easily implemented by using linear optics. Robust optical one-way quantum computation can be performed since cluster states can be stored in atoms and then transferred to photons that can be easily operated and measured. Therefore, this proposal could help performing robust large-scale optical one-way quantum computation.

Robust Quantum Computation with Superconducting Charge Qubits via Coherent Pulses

To achieve robust gate operations on superconducting charge qubits, we theoretically propose a feasible scheme to realize geometric quantum computation via coherent pulses. Only by adiabatically tuning the microwave pulses applied to the gate capacitance can the Berry phases associated with the system be acquired, from which we construct a universal set of geometric gates. Combining the geometric approach with the coherent pulse technique, robust quantum operations aimed at combating noise errors may be implemented experimentally.

Robust and fast geometric quantum computation with multiqubit gates in cavity QED

A scheme is proposed for realizing geometric quantum computation with one-qubit unitary gates and $N$-qubit $(N\ensuremath{\ge}2)$ phase gates in cavity QED. In the scheme, the cavity field and excited states are virtually excited by controlling appropriately atom-field couplings and engineering adiabatic passage; thus the gate operations are insensitive to the cavity decay and the atomic spontaneous emission. Furthermore, the $N$-qubit $(N\ensuremath{\ge}2)$ geometric phase gates can be realized just by one step and the required time does not increase with the number of qubits, which can significantly reduce complexity of physical realization of practical quantum computation and quantum algorithms.

A new phase in quantum computation

Large-scale quantum computers are hard to construct because quantum systems easily lose their coherence through interaction with the environment. Researchers have tried to avoid this problem by using geometric phase shifts in the design of quantum gates to perform information processing. Experiments and simulations have shown that these gates may be tolerant to certain types of faults, and may therefore be useful for robust quantum computation.

Anyonic interferometry and protected memories in atomic spin lattices

Strongly correlated quantum systems can exhibit exotic behaviour called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasiparticles with anyonic statistics and have been proposed as candidates for naturally error-free quantum computation. However, anyons have never been observed in nature directly. Here, we describe how to unambiguously detect and characterize such states in recently proposed spin–lattice realizations using ultracold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by carrying out global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations. A proposal describes how to detect topologically ordered states of ultracold matter in an optical lattice, and shows how these exotic states, which strongly correlated quantum systems can exhibit, could be harnessed for practical applications, such as robust quantum computation.

Robust quantum computation of the quantum kicked Harper model and dissipative decoherence

The effects of the dissipative decoherence on the quantum computation of the quantum kicked Harper (QKH) model are investigated using the quantum trajectory approach and the quantum Monte Carlo method. The simulation shows that the dynamical localization for the QKH model and the stochastic web in phase space are destroyed by moderate levels of dissipation. Taking the phase damping channel as the noise model, the universal law for fidelity decay and the timescales of reliable computation are analyzed. Compared with the static imperfections, the timescales for reliable computation of the dissipative system drop more quickly with the increase of the number of qubits when the decay rate is under a certain threshold. While above the threshold, the timescales drop more quickly in the presence of static imperfections.

Does Our Universe Allow for Robust Quantum Computation?

An approach for analyzing quantum decoherence may help push the boundaries of quantum computing.

Robust quantum computation of the kicked Harper model and quantum chaos

The stability of quantum computating of the kicked Harper model with various perturbations is investigated. Above a certain threshold of the imperfections, quantum chaos sets in. The effects of the noise errors and the static imperfections on the quantum computation are analyzed by comparing the statistical ergodic properties and the Husimi functions of the perturbed eigenstates with the ideal eigenstates of the Floquet operator. It is shown that the fidelity decay with static imperfections is exponential while it is Gaussian with noise errors. The time scales of reliable computation with these perturbations are obtained through numerical simulations. Due to the errors in classical computation the distance of two initial states increases exponentially, while the stability of quantum computation is independent of the integrable or chaotic nature of the underlying dynamics.

Schemes for robust quantum computation with polar molecules

We propose to use a new platform - ultracold polar molecules - for quantum computing with switchable interactions. The on/off switch is accomplished by selective excitation of one of the "0" or "1" qubits - long-lived molecular states - to an "excited" molecular state with a considerably different dipole moment. We describe various schemes based on this switching of dipolar interactions where the selective excitation between ground and excited states is accomplished via optical, micro-wave, or electric fields. We also generalize the schemes to take advantage of the dipole blockade mechanism when dipolar interactions are very strong. These schemes can be realized in several recently proposed architectures.

Parallelism for quantum computation with qudits

Robust quantum computation with $d$-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high-fidelity two-qudit gates. We first describe how to implement parallel single-qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth (time) of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the alkali-metal atoms $^{87}\mathrm{Rb}$ and $^{133}\mathrm{Cs}$. Second, we provide a protocol for implementing parallelized nonlocal two-qudit gates using the assistance of entangled qubit pairs. Using known protocols for qubit entanglement purification, this offers the possibility of high-fidelity two-qudit gates.

Repeat-until-success quantum computing using stationary and flying qubits

We introduce an architecture for robust and scalable quantum computation using both stationary qubits (e.g., single photon sources made out of trapped atoms, molecules, ions, quantum dots, or defect centers in solids) and flying qubits (e.g., photons). Our scheme solves some of the most pressing problems in existing nonhybrid proposals, which include the difficulty of scaling conventional stationary qubit approaches, and the lack of practical means for storing single photons in linear optics setups. We combine elements of two previous proposals for distributed quantum computing, namely the efficient photon-loss tolerant build up of cluster states by Barrett and Kok [Phys. Rev. A 71, 060310(R) (2005)] with the idea of repeat-until-success (RUS) quantum computing by Lim et al. [Phys. Rev. Lett. 95, 030505 (2005)]. This idea can be used to perform eventually deterministic two qubit logic gates on spatially separated stationary qubits via photon pair measurements. Under nonideal conditions, where photon loss is a possibility, the resulting gates can still be used to build graph states for one-way quantum computing. In this paper, we describe the RUS method, present possible experimental realizations, and analyze the generation of graph states.

Pseudospin quantum computation in semiconductor nanostructures.

We theoretically show that spontaneously interlayer-coherent bilayer quantum Hall droplets should allow robust and fault-tolerant pseudospin quantum computation in semiconductor nanostructures with voltage-tuned external gates providing qubit control and a quantum Ising Hamiltonian providing qubit entanglement. Using a spin-boson model, we estimate decoherence to be small (approximately 10(-5)).

Geometric manipulation of trapped ions for quantum computation.

We propose an experimentally feasible scheme to achieve quantum computation based solely on geometric manipulations of a quantum system. The desired geometric operations are obtained by driving the quantum system to undergo appropriate adiabatic cyclic evolutions. Our implementation of the all-geometric quantum computation is based on laser manipulation of a set of trapped ions. An all-geometric approach, apart from its fundamental interest, offers a possible method for robust quantum computation.

Robustness of decoherence-free subspaces for quantum computation

It was shown recently [D.A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998)] that within the framework of the semigroup Markovian master equation, decoherence-free (DF) subspaces exist which are stable to first order in time to a perturbation. Here this result is extended to the non-Markovian regime and generalized. In particular, it is shown that within both the semigroup and the non-Markovian operator sum representation, DF subspaces are stable to all orders in time to a symmetry-breaking perturbation. DF subspaces are thus ideal for quantum memory applications. For quantum computation, however, the stability result does not extend beyond the first order. Thus, to perform robust quantum computation in DF subspaces, they must be supplemented with quantum error correcting codes.

Efficient fault-tolerant quantum computing

Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible quantum codes are obtained, and good candidates exhibited. This permits a new analysis of the permissible error rates and minimum overheads for robust quantum computing. It is found that, under the standard noise model of ubiquitous stochastic, uncorrelated errors, a quantum computer need be only an order of magnitude larger than the logical machine contained within it in order to be reliable. For example, a scale-up by a factor of 22, with gate error rate of order $10^{-5}$, is sufficient to permit large quantum algorithms such as factorization of thousand-digit numbers.