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Walsh-synthesized noise-filtering quantum logic
Quantum Physics · Submitted 7 Oct 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We study a novel class of open-loop control protocols constructed to perform arbitrary nontrivial single-qubit logic operations robust against time-dependent non-Markovian noise.
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The abstract, sentence by sentence
We study a novel class of open-loop control protocols constructed to perform arbitrary nontrivial single-qubit logic operations robust against time-dependent non-Markovian noise. Amplitude and phase modulation protocols are crafted leveraging insights from functional synthesis and the basis set of Walsh functions. We employ the experimentally validated generalized filter-transfer function formalism in order to find optimized control protocols for target operations in SU(2) by defining a cost function for the filter-transfer function to be minimized through the applied modulation. Our work details the various techniques by which we define and then optimize the filter-synthesis process in the Walsh basis, including the definition of specific analytic design rules which serve to efficiently constrain the available synthesis space. This approach yields modulated-gate constructions consisting of chains of discrete pulse-segments of arbitrary form, whose modulation envelopes possess intrinsic compatibility with digital logic and clocking. We derive novel families of Walsh-modulated noise filters designed to suppress dephasing and coherent amplitude-damping noise, and describe how well-known sequences derived in NMR also fall within the Walsh-synthesis framework. Finally, our work considers the effects of realistic experimental constraints such as limited modulation bandwidth on achievable filter performance.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study a novel class of open-loop control protocols constructed to perform arbitrary nontrivial single-qubit logic operations robust against time-dependent non-Markovian noise. | contribution 1.00 | 0.87 | 0.33 | asserted 0.98 |
| s1 | Amplitude and phase modulation protocols are crafted leveraging insights from functional synthesis and the basis set of Walsh functions. | method 0.92 | 0.89 | 0.05 | asserted 1.00 |
| s2 | We employ the experimentally validated generalized filter-transfer function formalism in order to find optimized control protocols for target operations in SU(2) by defining a cost function for the filter-transfer function to be minimized through the applied modulation. | method 0.99 | 0.92 | 0.09 | asserted 1.00 |
| s3 | Our work details the various techniques by which we define and then optimize the filter-synthesis process in the Walsh basis, including the definition of specific analytic design rules which serve to efficiently constrain the available synthesis space. | method 0.79 | 0.94 | 0.08 | asserted 1.00 |
| s4 | This approach yields modulated-gate constructions consisting of chains of discrete pulse-segments of arbitrary form, whose modulation envelopes possess intrinsic compatibility with digital logic and clocking. | result 0.50 | 0.89 | 0.18 | asserted 1.00 |
| s5 | We derive novel families of Walsh-modulated noise filters designed to suppress dephasing and coherent amplitude-damping noise, and describe how well-known sequences derived in NMR also fall within the Walsh-synthesis framework. | contribution 0.91 | 0.93 | 0.18 | asserted 1.00 |
| s6 | Finally, our work considers the effects of realistic experimental constraints such as limited modulation bandwidth on achievable filter performance. | limitation 0.56 | 0.86 | 0.06 | asserted 0.75 |
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Original abstract
We study a novel class of open-loop control protocols constructed to perform arbitrary nontrivial single-qubit logic operations robust against time-dependent non-Markovian noise. Amplitude and phase modulation protocols are crafted leveraging insights from functional synthesis and the basis set of Walsh functions. We employ the experimentally validated generalized filter-transfer function formalism in order to find optimized control protocols for target operations in SU(2) by defining a cost function for the filter-transfer function to be minimized through the applied modulation. Our work details the various techniques by which we define and then optimize the filter-synthesis process in the Walsh basis, including the definition of specific analytic design rules which serve to efficiently constrain the available synthesis space. This approach yields modulated-gate constructions consisting of chains of discrete pulse-segments of arbitrary form, whose modulation envelopes possess intrinsic compatibility with digital logic and clocking. We derive novel families of Walsh-modulated noise filters designed to suppress dephasing and coherent amplitude-damping noise, and describe how well-known sequences derived in NMR also fall within the Walsh-synthesis framework. Finally, our work considers the effects of realistic experimental constraints such as limited modulation bandwidth on achievable filter performance.
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What it cites · 3 sentences without a confident label
Compares with 1 paper
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This contrasts with similar composite pulse methods in NMR and quantum information [ref] which generally rely on structures defined in continuous time[Pulse periods taking non-integer multiples values of $τ_min$ then have intrinsic conflict with implementation in discretized time via digital control, giving rise to residual errors.].
Progress in compensating pulse sequences for quantum computation · Walsh-Synthesized Filters · 0.98
Cites as support 1 paper
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This has been validated using experiments on trapped ions [ref] , and formalized rigorously in Ref. [ref] , where it has been shown that $p≤μ$, but $p^*$ over a user-defined band is unrelated to $μ$.
A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control · Time-domain filter order vs. Magnus order · 1.00
Cites as background 1 paper
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In particular, open-loop dynamical error suppression strategies (without the need for measurement or feedback) such as dynamic decoupling (DD) [ref] , dynamically corrected gates (DCGs) [ref] , and composite pulsing [ref] , have emerged as resource-efficient approaches for physical-layer decoherence control.
Progress in compensating pulse sequences for quantum computation · Introduction · 0.82
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