Richard Cleve
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View article: Improved Clifford operations in constant commutative depth
Improved Clifford operations in constant commutative depth Open
The commutative depth model allows gates that commute with each other to be performed in parallel. We show how to compute Clifford operations in constant commutative depth more efficiently than was previously known. Bravyi, Maslov, and Nam…
View article: Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement
Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement Open
We consider a bipartite transformation that we call self-embezzlement and use it to prove a constant gap between the capabilities of two models of quantum information: the conventional model, where bipartite systems are represented by tens…
View article: Discrete-query quantum algorithm for NAND trees. (arXiv:quant-ph/0702160v2 UPDATED)
Discrete-query quantum algorithm for NAND trees. (arXiv:quant-ph/0702160v2 UPDATED) Open
Recently, Farhi, Goldstone, and Gutmann gave a quantum algorithm for evaluating NAND trees that runs in time O(sqrt(N log N)) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorith…
View article: Quantum fast-forwarding: Markov chains and graph property testing
Quantum fast-forwarding: Markov chains and graph property testing Open
We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with P the Markov chain transition matr…
View article: Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement
Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement Open
We consider a bipartite transformation that we call self-embezzlement and use it to prove a constant gap between the capabilities of two models of quantum information: the conventional model, where bipartite systems are represented by tens…
View article: Efficient Quantum Algorithms for Simulating Lindblad Evolution
Efficient Quantum Algorithms for Simulating Lindblad Evolution Open
We consider the natural generalization of the Schrodinger equation to Markovian open system dynamics: the so-called the Lindblad equation. We give a quantum algorithm for simulating the evolution of an n-qubit system for time t within prec…
View article: EXPONENTIAL IMPROVEMENT IN PRECISION FOR SIMULATING SPARSE HAMILTONIANS
EXPONENTIAL IMPROVEMENT IN PRECISION FOR SIMULATING SPARSE HAMILTONIANS Open
We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a $d$ -sparse Hamiltonian $…
View article: Perfect commuting-operator strategies for linear system games
Perfect commuting-operator strategies for linear system games Open
Linear system games are a generalization of Mermin’s magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional o…
View article: Efficient Quantum Algorithms for Simulating Lindblad Evolution
Efficient Quantum Algorithms for Simulating Lindblad Evolution Open
We consider the natural generalization of the Schrödinger equation to Markovian open system dynamics: the so-called the Lindblad equation. We give a quantum algorithm for simulating the evolution of an $n$-qubit system for time $t$ within …
View article: Simulating Hamiltonian Dynamics with a Truncated Taylor Series
Simulating Hamiltonian Dynamics with a Truncated Taylor Series Open
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physic…
View article: Near-linear constructions of exact unitary 2-designs
Near-linear constructions of exact unitary 2-designs Open
A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be impl…