Gate simulation and lower bounds on the simulation time
arXiv:quant-ph/0403082 · doi:10.1103/PhysRevA.70.032319
Abstract
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common versions of this task are known as Hamiltonian simulation and gate simulation, where Hamiltonian simulation can be seen as an infinitesimal version of the general task of gate simulation. We present a Lie-theoretic approach to Hamiltonian simulation and gate simulation. From this, we derive lower bounds on the time complexity in the n-qubit case, generalizing known results to both even and odd n. To achieve this we develop a generalization of the so-called magic basis for two-qubits. As a corollary, we note a connection to entanglement measures of concurrence-type.
17 pages
References in corpus (44)
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Mixed State Entanglement and Quantum Error Correction
- Concentrating Partial Entanglement by Local Operations
- Entanglement of a Pair of Quantum Bits
- Distributed Entanglement
- Universal state inversion and concurrence in arbitrary dimensions
- Time Optimal Control in Spin Systems
- Optimal Creation of Entanglement Using a Two--Qubit Gate
- Thermodynamics and the Measure of Entanglement
- Fidelity and Concurrence of conjugated states
- A geometric theory of non-local two-qubit operations
- Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations
- Universal Control of Decoupled Quantum Systems
- A potential multipartide entanglement measure
- A practical scheme for quantum computation with any two-qubit entangling gate
- Normal forms and entanglement measures for multipartite quantum states
- Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
- A Note on Invariants and Entanglements
- Variational Characterisations of Separability and Entanglement of Formation
- Entanglement capabilities of non-local Hamiltonians
- Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries
- Universal simulation of Hamiltonian dynamics for qudits
- Optimal simulation of two-qubit Hamiltonians using general local operations
- Efficient Refocussing of One Spin and Two Spin Interactions for NMR Quantum Computation
- Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices
- Characterization of non-local gates
- Interaction cost of non-local gates
- Entanglement, Mixedness, and Spin-Flip Symmetry in Multiple-Qubit Systems
- Quantify entanglement by concurrence hierarchy
- Lower Bound on Entanglement of Formation for the Qubit-Qudit System
- Suppression of arbitrary internal coupling in a quantum register
- Concurrence in arbitrary dimensions
- Simulating Hamiltonians in Quantum Networks: Efficient Schemes and Complexity Bounds
- Why Two Qubits Are Special
- Canonical Decompositions of n-qubit Quantum Computations and Concurrence
- A multi-photon Stokes-parameter invariant for entangled states
- Lower bounds on the complexity of simulating quantum gates
- Catalysis in non--local quantum operations
- Entanglement of 2xK quantum systems
- Fungible dynamics: there are only two types of entangling multiple-qubit interactions
- Optimal simulation of nonlocal Hamiltonians using local operations and classical communication
- Reversible simulation of bipartite product Hamiltonians
- Complexity of decoupling and time-reversal for n spins with pair-interactions: Arrow of time in quantum control
- On the practicality of time-optimal two-qubit Hamiltonian simulation
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- Training Schrödinger's cat: quantum optimal control
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- Optimal Control-Based Efficient Synthesis of Building Blocks of Quantum Algorithms Seen in Perspective from Network Complexity towards Time Complexity
- Symmetry Principles in Quantum Systems Theory
- Time Optimal Control of Coupled Qubits Under Non-Stationary Interactions
- Conditions for optimal construction of two-qubit non-local gates
- Symmetry criteria for quantum simulability of effective interactions
- Elliptic functions and efficient control of Ising spin chains with unequal couplings
- Controlling Several Atoms in a Cavity
- Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
- Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system
- Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control
- Ultrastrong time-dependent light-matter interactions are gauge-relative
- Quantum brachistochrone problem for two spins-1/2 with anisotropic Heisenberg interaction
- Compensating for non-linear distortions in controlled quantum systems
- Time-optimal polarization transfer from an electron spin to a nuclear spin
- An upper bound on the time required to implement unitary operations