Adiabatic Quantum State Generation

  title={Adiabatic Quantum State Generation},
  author={Dorit Aharonov and Amnon Ta-Shma},
  journal={SIAM J. Comput.},
The design of new quantum algorithms has proven to be an extremely difficult task. This paper considers a different approach to this task by studying the problem of quantum state generation. We motivate this problem by showing that the entire class of statistical zero knowledge, which contains natural candidates for efficient quantum algorithms such as graph isomorphism and lattice problems, can be reduced to the problem of quantum state generation. To study quantum state generation, we define… 

Figures from this paper

Quantum walks and ground state problems

Since the appearance of Shor's factoring algorithm in 1994, the search for novel quantum computer algorithms has proved surprisingly difficult. Two design approaches that have yielded some progress

Quantum algorithm for structured problems

It is shown that this quantum algorithm achieves exponential speedup over classical algorithms in solving some structured problems, including problems that can be reduced to both the Abelian and the non-Abelian HSP.

Quantum computation and communication in strongly interacting systems

A novel, low-control way of performing a two-qubit gate on qubits encoded in a decoherence-free subspace is found, making use of many-body interactions that may already be present, and a very different model from the normal circuit model is focus, combining ideas from measurement-based quantum computation and holonomic quantum computation, showing that all MBQC patterns with a property called gflow can be converted into a holonomic computation.

At the intersection of quantum computing and quantum chemistry

Quantum chemistry is concerned with solving the Schrodinger equation for chemically relevant systems. This is typically done by making useful and systematic approximations which form the basis for

A study of heuristic guesses for adiabatic quantum computation

This work introduces a simple form of heuristics: the ability to start the quantum evolution with a state which is a guess to the solution of the problem, and explains the viability of this approach and the needed modifications to the conventional AQC (CAQC) algorithm.

Site-by-site quantum state preparation algorithm for preparing vacua of fermionic lattice field theories

This paper presents a heuristic algorithm that can prepare the vacuum of fermionic systems in more general cases and more efficiently than previous methods and numerically demonstrates the effectiveness of this method for the 1+1 dimensional Gross-Neveu model.

Approximability of Optimization Problems through Adiabatic Quantum Computation

This book investigates the computational simulation of AQC algorithms applied to the MAX-SAT problem and shows that every monadic second-order logic (MSOL) expression has associated pseudo-Boolean maps that can be obtained by expanding the given expression, and also can be reduced to quadratic forms.

Adiabatic graph-state quantum computation

Measurement-based quantum computation (MBQC) and holonomic quantum computation (HQC) are two very different computational methods. The computation in MBQC is driven by adaptive measurements executed

Preparation of many-body states for quantum simulation.

The present algorithm is able to prepare general pure and mixed many-particle states of any number of particles and operates in time that is polynomial in all the essential descriptors of the system, the number ofarticles, the resolution of the lattice, and the inverse of the maximum final error.

Exponential rise of dynamical complexity in quantum computing through projections

It is shown that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation.



How powerful is adiabatic quantum computation?

It is argued that the adiabatic approach may be thought of as a kind of 'quantum local search', and a family of minimization problems that is hard for such local search heuristics are designed, and an exponential lower bound is established for the ad iabatic algorithm for these problems.

A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

For the small examples that the authors could simulate, the quantum adiabatic algorithm worked well, providing evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.

Quantum Computation by Adiabatic Evolution

We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that

A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability

Numerical results on randomly generated instances of an NP-complete problem and of a problem that can be solved classically in polynomial time are presented.

Quantum search by local adiabatic evolution

The adiabatic theorem has been recently used to design quantum algorithms of a new kind, where the quantum computer evolves slowly enough so that it remains near its instantaneous ground state, which

Adiabatic quantum computation is equivalent to standard quantum computation

The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown, so this result implies that the adiABatic computation model and the standard quantum circuit model are polynomially equivalent.

The quantum adiabatic optimization algorithm and local minima

It is proved that for a constant range of values for the transverse field, the spectral gap is exponentially small in the sector length, and there are exponentially many eigenvalues all exponentially close to the ground state energy.

A lattice problem in quantum NP

  • D. AharonovO. Regev
  • Mathematics
    44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.
  • 2003
This work gives a new characterization of QMA, called QMA+ formulation, and makes the important observation that autocorrelation functions are positive definite functions and using properties of such functions the authors severely restrict the prover's possibility to cheat.

Quantum search by measurement

We propose a quantum algorithm for solving combinatorial search problems that uses only a sequence of measurements. The algorithm is similar in spirit to quantum computation by adiabatic evolution,

The Adiabatic Theorem of Quantum Mechanics

We prove the adiabatic theorem for quantum evolution without the traditional gap condition. We show that the theorem holds essentially in all cases where it can be formulated. In particular, our