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Quantum Computing: Lecture Notes
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This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in subsequent years. The first 10 chapters cover the circuit model and the main quantum algorithms (Deutsch-Jozsa, Simon, Shor, Hidden Subgroup Problem, Grover, quantum walks, Hamiltonian simulation and HHL). They are followed by 4 chapters about complexity, 4 chapters about distributed ("Alice and Bob") settings, a chapter about quantum machine learning, and a final chapter about quantum error correction. Appendices A and B give a brief introduction to the required linear algebra and some other mathematical and computer science background. All chapters come with exercises, with some hints provided in Appendix C.
Forward citations
Cited by 10 Pith papers
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Multi-Prover Interactive Proof Systems with Leakage
Two-prover one-round MIP protocols for NEXP and MIP* protocols for RE remain sound against any polynomial bits of leakage between provers.
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The power of unentanglement without destructive interference
StoqMA(2) contains NP with Õ(√n)-qubit proofs and completeness error 2^{-polylog(n)}, is contained in EXP, and satisfies StoqMA(k)=StoqMA(2) for k≥2 when completeness error is negligible.
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Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise
New quantum mean estimators and SGD variants achieve query complexity Õ(√d ε^{-(5p-4)/(2p-2)}) for nonconvex and Õ(√d ε^{-(3p-2)/(2p-2)} + ε^{-2}) for convex heavy-tailed stochastic optimization, improving on classica...
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An Initialization-free Quantum Algorithm for General Abelian Hidden Subgroup Problem
An initialization-free quantum algorithm solves the hidden subgroup problem over all finite abelian groups, reusing an arbitrary mixed auxiliary state and restoring it, with O(log|G|) queries and O(log^3|G|) operations.
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Efficient Measurement of Bosonic Non-Gaussianity
A new measure, non-Gaussian entropy, and a beam-splitter protocol estimate bosonic non-Gaussianity using only a constant number of state copies, avoiding full tomography.
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A slightly improved upper bound for quantum statistical zero-knowledge
QSZK and its non-interactive variant NIQSZK stay inside QIP(2)∩co-QIP(2), now with an honest prover that runs in quantum linear space and single-exponential time.
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Position: Quantum Kernel Machines Should Move Beyond Scalar-Valued Kernels to Realize Their Potential
The paper proposes a roadmap for quantum operator-valued kernels and shows on simulated quantum channel estimation that they can outperform scalar-valued quantum kernels.
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Estimation of trace distance between two arbitrary quantum states
The paper's quantum trace-distance algorithm is undermined by an invalid phase-to-eigenvalue mapping and internal algebraic inconsistencies.
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A Quantum Path to Partial Differential Equations
Lecture notes that organize quantum PDE algorithms around block encodings of finite-difference and finite-element operators, tracking discretization, preparation, normalization, postselection, and measurement costs.
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Hybrid Quantum Neural Networks: Theory, Implementations, and Applications
A balanced review of hybrid quantum neural networks, concluding that quantum layers help on structured, small-scale and quantum-native problems but do not yet beat classical models on generic benchmarks.
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