Progress in Compensating Pulse Sequences for Quantum Computation

Merrill, J. True; Brown, Kenneth R.

doi:10.1002/9781118742631.ch10

Advances in Chemical Physics

2014

DOI: 10.1002/9781118742631.ch10

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Progress in Compensating Pulse Sequences for Quantum Computation

J. True Merrill

Kenneth R. Brown

Abstract: The control of qubit states is often impeded by systematic control errors. Compensating pulse sequences have emerged as a resource efficient method for quantum error reduction. In this review, we discuss compensating composite pulse methods, and introduce a unifying control-theoretic framework using a dynamic interaction picture. This admits a novel geometric picture where sequences are interpreted as vector paths on the dynamical Lie algebra. Sequences for single-qubit and multi-qubit operations are described… Show more

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Cited by 67 publications

(88 citation statements)

References 97 publications

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“…The FFs for much more complex control, such as compensating composite pulses 17,18 , can be calculated and experimentally validated as well (Fig. 1e).…”

mentioning

confidence: 86%

“…d, Schematic representation of the quasi-white noise power spectrum with cuto ω c employed in c and single-tone power spectrum with frequency ω t employed in f and g. Noise strength parameterized by α. e, Calculated F (ω), for primitive and compensating π pulses (ref. 18). Vertical lines indicate frequencies where F (ω) for SK1 (red) and BB1 (black) cross primitive (blue), indicating an expected inversion of performance.…”

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confidence: 99%

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Experimental noise filtering by quantum control

et al. 2014

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Extrinsic interference is routinely faced in systems engineering, and a common solution is to rely on a broad class of filtering techniques to a ord stability to intrinsically unstable systems or isolate particular signals from a noisy background. Experimentalists leading the development of a new generation of quantum-enabled technologies similarly encounter time-varying noise in realistic laboratory settings. They face substantial challenges in either suppressing such noise for high-fidelity quantum operations 1 or controllably exploiting it in quantum-enhanced sensing [2][3][4] or system identification tasks 5,6 , due to a lack of e cient, validated approaches to understanding and predicting quantum dynamics in the presence of realistic time-varying noise. In this work we use the theory of quantum control engineering . We demonstrate the utility of these constructs for directly predicting the evolution of a quantum state in a realistic noisy environment as well as for developing novel robust control and sensing protocols. These experiments provide a significant advance in our understanding of the physics underlying controlled quantum dynamics, and unlock new capabilities for the emerging field of quantum systems engineering.Time-varying noise coupled to quantum systems-typically qubits-generically results in decoherence, or a loss of 'quantumness' of the system. Broadly, one may think of the state of the quantum system becoming randomized through uncontrolled (and often uncontrollable) interactions with the environment during both idle periods and active control operations (Fig. 1a). Despite the ubiquity of this phenomenon, it is a challenging problem to predict the average evolution of a qubit state undergoing a specific, but arbitrary operation in the presence of realistic time-dependent noise-how much randomization does one expect and how well can one perform the target operation? Making such predictions accurately is precisely the capability that experimentalists require in realistic laboratory settings. Moreover, this capability is fundamental to the development of novel control techniques designed to modify or suppress decoherence as researchers attempt to build quantum-enabled technologies for applications such as quantum information and quantum sensing.These considerations motivate the development of novel engineering-inspired analytic tools enabling a user to accurately predict the behaviour of a controlled quantum system in realistic laboratory environments. Recent work has demonstrated that the average dynamics of a controlled qubit state evolution may be captured using filter-transfer functions (FFs) characterizing the control. The fidelity of an arbitrary operation over duration τ ,, is degraded owing to frequency-domain spectral overlap between noise in the environment given by a power spectrum S(ω), and the filter-transfer functions denoted F(ω) (Methods) [11][12][13][14] . The FF description of ensemble-average quantum dynamics tremendously simplifies the task of analysing the expected performa...

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“…The FFs for much more complex control, such as compensating composite pulses 17,18 , can be calculated and experimentally validated as well (Fig. 1e).…”

mentioning

confidence: 86%

mentioning

confidence: 99%

Experimental noise filtering by quantum control

et al. 2014

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“…A composite pulse sequence can be used in place of a single Raman pulse to make it robust against systematic errors such as amplitude, timing, crosstalk, or detuning errors [5,19,20,[25][26][27] and time-dependent control errors [28]. In our experiment, the impact of residual systematic amplitude errors in the Raman beams is suppressed through the use of compensating pulse sequences.…”

mentioning

confidence: 99%

“…In the absence of noise, the target rotation R(θ,φ) rotates the Bloch vector by an angle θ around the axis σ φ ≡ X cos φ + Y sin φ, represented by a unitary propagator R(θ,φ) = exp(− i 2 θσ φ ). The B2 compensation sequence (also known as BB1), introduced by Wimperis [19], is designed to correct the errors in the pulse area (due to amplitude or timing errors) to O( 2 ), where is the fractional error in the control signal [25]. B2 compensation translates each single rotation into a sequence of four rotations.…”

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confidence: 99%

Error compensation of single-qubit gates in a surface-electrode ion trap using composite pulses

et al. 2015

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The fidelity of laser-driven quantum logic operations on trapped ion qubits tend to be lower than microwavedriven logic operations due to the difficulty of stabilizing the driving fields at the ion location. Through stabilization of the driving optical fields and use of composite pulse sequences, we demonstrate high-fidelity single-qubit gates for the hyperfine qubit of a 171 Yb + ion trapped in a microfabricated surface-electrode ion trap. Gate error is characterized using a randomized benchmarking protocol and an average error per randomized Clifford group gate of 3.6(3) × 10 −4 is measured. We also report experimental realization of palindromic pulse sequences that scale efficiently in sequence length. The trapped atomic ion qubits feature desirable properties for use in a quantum computer such as long coherence times [1], high-fidelity qubit measurement [2], and universal logic gates [3]. The quality of quantum logic gate operations on trapped ion qubits has been limited by the stability of the control fields at the ion location used to implement the gate operations. For this reason, the logic gates utilizing microwave fields [4][5][6][7] have shown gate fidelities several orders of magnitude better than those using laser fields [8][9][10]. The laser beams used to drive either Raman gates for a hyperfine ion qubit or optical gates between metastable qubit states are subject to severe wave-front distortion in air due to turbulence, leading to amplitude and phase fluctuations of the optical field at the ion location that limited the gate fidelity in the 0.5% range [8,11].Microfabricated surface-electrode ion traps, where atomic ions are trapped above a two-dimensional surface of electrodes, can provide a scalable platform on which to build an ion-based quantum computer [12,13]. Experiments using surface traps have demonstrated coherence times of more than 1 s [14], state detection with fidelities greater than 99.9% [2], and low-error single-qubit gates [ 2.0(2) × 10 −5 ] using integrated microwave waveguides [4,7]. Use of high-power UV lasers close to the trap surface can lead to substantial charging due to unwanted exposure [15]. The recent development of single-mode fibers capable of delivering high-power UV laser beams [16] opens the possibility of significantly reducing the free-space UV beam path length and delivering a clean spatial mode to the ions, eliminating unwanted scattering off nearby trap structures.Here we demonstrate low-error single-qubit gates performed using stimulated Raman transitions on an ion qubit trapped in a microfabricated chip trap. Gate errors are measured using a randomized benchmarking protocol [8,17,18], where amplitude error in the control beam is compensated using various pulse sequence techniques [19,20]. Using B2 compensation [19], we demonstrate single-qubit gates with an average error per randomized Clifford group gate of 3.6(3) × 10 −4 . We also show that compact palindromic pulse compensation sequences (PDn) [20] compensate for amplitude errors as designed. Two hyperfin...

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“…The pulse-area error model puts a distribution on this angle. The mean is zero, since systematic errors can be removed with calibration [37].…”

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confidence: 99%

Quantum error-correction failure distributions: Comparison of coherent and stochastic error models

et al. 2017

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We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault tolerant quantum error correcting circuit for a d = 3 Steane and surface code. We find that the output distributions are markedly different for the two error models, showing that no simple mapping between the two error models exists. Coherent errors create very broad and heavy-tailed failure distributions. This suggests that they are susceptible to outlier events and that mean statistics, such as pseudo-threshold estimates, may not provide the key figure of merit. This provides further statistical insight into why coherent errors can be so harmful for quantum error correction. These output probability distributions may also provide a useful metric that can be utilized when optimizing quantum error correcting codes and decoding procedures for purely coherent errors.

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Progress in Compensating Pulse Sequences for Quantum Computation

Cited by 67 publications

References 97 publications

Experimental noise filtering by quantum control

Experimental noise filtering by quantum control

Error compensation of single-qubit gates in a surface-electrode ion trap using composite pulses

Quantum error-correction failure distributions: Comparison of coherent and stochastic error models

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