Search Results - "Schaeffer, Luke"

The Classification of Clifford Gates over Qubits by Grier, Daniel, Schaeffer, Luke

“…We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates…”
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Sample-optimal classical shadows for pure states by Daniel Grier, Hakop Pashayan, Luke Schaeffer

“…We consider the classical shadows task for pure states in the setting of both joint and independent measurements. The task is to measure few copies of an…”
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Trading T gates for dirty qubits in state preparation and unitary synthesis by Guang Hao Low, Vadym Kliuchnikov, Luke Schaeffer

“…Efficient synthesis of arbitrary quantum states and unitaries from a universal fault-tolerant gate-set e.g. Clifford+T is a key subroutine in quantum…”
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Fast simulation of planar Clifford circuits by Gosset, David, Grier, Daniel, Kerzner, Alex, Schaeffer, Luke

“…A general quantum circuit can be simulated classically in exponential time. If it has a planar layout, then a tensor-network contraction algorithm due to…”
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Decidability for Sturmian words by Hieronymi, Philipp, Ma, Dun, Oei, Reed, Schaeffer, Luke, Schulz, Christian, Shallit, Jeffrey

“…We show that the first-order theory of Sturmian words over Presburger arithmetic is decidable. Using a general adder recognizing addition in Ostrowski…”
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Ostrowski-automatic sequences: Theory and applications by Baranwal, Aseem, Schaeffer, Luke, Shallit, Jeffrey

“…We extend the notion of k-automatic sequences to Ostrowski-automatic sequences, and develop a procedure to computationally decide certain combinatorial and…”
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Closed, Palindromic, Rich, Privileged, Trapezoidal, and Balanced Words in Automatic Sequences by Schaeffer, Luke, Shallit, Jeffrey

“…We prove that the property of being closed (resp., palindromic, rich, privileged trapezoidal, balanced) is expressible in first-order logic for automatic (and…”
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A Quantum Query Complexity Trichotomy for Regular Languages by Aaronson, Scott, Grier, Daniel, Schaeffer, Luke

“…We present a trichotomy theorem for the quantum query complexity of regular languages. Every regular language has quantum query complexity Θ(1), Θ̃(√ n), or…”
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Decision algorithms for Fibonacci-automatic words, II: Related sequences and avoidability by Du, Chen Fei, Mousavi, Hamoon, Rowland, Eric, Schaeffer, Luke, Shallit, Jeffrey

“…We use a decision procedure for the “Fibonacci-automatic” words to solve problems about a number of different sequences. In particular, we prove that there…”
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Succinct Fermion Data Structures by Carolan, Joseph, Schaeffer, Luke

“…Simulating fermionic systems on a quantum computer requires representing fermionic states using qubits. The complexity of many simulation algorithms depends on…”
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The Classification of Clifford Gates over Qubits by Grier, Daniel, Schaeffer, Luke

“…Quantum 6, 734 (2022) We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of…”
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Principal eigenstate classical shadows by Grier, Daniel, Pashayan, Hakop, Schaeffer, Luke

“…Proceedings of Thirty Seventh Conference on Learning Theory (COLT 2024), PMLR 247:2122-2165 Given many copies of an unknown quantum state $\rho$, we consider…”
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Sample-optimal classical shadows for pure states by Grier, Daniel, Pashayan, Hakop, Schaeffer, Luke

“…Quantum 8, 1373 (2024) We consider the classical shadows task for pure states in the setting of both joint and independent measurements. The task is to measure…”
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Beatty Sequences for a Quadratic Irrational: Decidability and Applications by Schaeffer, Luke, Shallit, Jeffrey, Zorcic, Stefan

“…Let $\alpha$ and $\beta$ belong to the same quadratic field. We show that the inhomogeneous Beatty sequence $(\lfloor n \alpha + \beta \rfloor)_{n \geq 1}$ is…”
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String Attractors for Automatic Sequences by Schaeffer, Luke, Shallit, Jeffrey

“…We show that it is decidable, given an automatic sequence $\bf s$ and a constant $c$, whether all prefixes of $\bf s$ have a string attractor of size $\leq c$…”
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Interactive shallow Clifford circuits: quantum advantage against NC$^1$ and beyond by Grier, Daniel, Schaeffer, Luke

“…Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can…”
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Trading T gates for dirty qubits in state preparation and unitary synthesis by Low, Guang Hao, Kliuchnikov, Vadym, Schaeffer, Luke

“…Quantum 8, 1375 (2024) Efficient synthesis of arbitrary quantum states and unitaries from a universal fault-tolerant gate-set e.g. Clifford+T is a key…”
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Fast simulation of planar Clifford circuits by Gosset, David, Grier, Daniel, Kerzner, Alex, Schaeffer, Luke

“…Quantum 8, 1251 (2024) A general quantum circuit can be simulated classically in exponential time. If it has a planar layout, then a tensor-network contraction…”
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Decidability for Sturmian words by Hieronymi, Philipp, Ma, Dun, Oei, Reed, Schaeffer, Luke, Schulz, Christian, Shallit, Jeffrey

“…Logical Methods in Computer Science, Volume 20, Issue 3 (August 5, 2024) lmcs:9980 We show that the first-order theory of Sturmian words over Presburger…”
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Interactive quantum advantage with noisy, shallow Clifford circuits by Grier, Daniel, Ju, Nathan, Schaeffer, Luke

“…Recent work by Bravyi et al. constructs a relation problem that a noisy constant-depth quantum circuit (QNC$^0$) can solve with near certainty (probability $1…”
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