Energy barrier to decoherence

Abstract

We formulate a novel ground state quantum computation approach that requires no unitary evolution of qubits in time: the qubits are fixed in stationary states of the Hamiltonian. This formulation supplies a completely time-independent approach to realizing quantum computers. We give a concrete suggestion for a ground state quantum computer involving linked quantum dots.The discovery of efficient quantum mechanical factoring and database searching algorithms has fueled tremendous research interest in the field of quantum computing [1][2][3]. Much recent effort has been dedicated to the problem of realizing a quantum computer in the laboratory [4][5][6][7][8] . This problem is technically challenging, in part because it requires overcoming the decoherence of quantum mechanical variables as a result of interactions with the environment [9]. Several experimental systems have been proposed as candidates for quantum computers, and progress has been exciting, but fundamental obstacles still stand in the way of creating viable computers. In this letter, we formulate a novel approach to quantum computing that circumvents the problem of decoherence, which motivates new directions for quantum computer design. Our scheme works exclusively with quantum mechanical ground states, completely obviating the need for time-dependent control of a system. While researchers have considered using quantum mechanical ground states to perform classical computations [10][11][12], the idea of executing quantum algorithms using a ground state computer is an exciting unexplored possibility.In traditional quantum computation, one examines the development in time of a collection of quantum mechanical "qubits" under controlled unitary evolutions [13]. Each qubit is a two-state system, described by inner products of the quantum mechanical state |ψ(t) with basis states |0 and |1 associated with the 0 and 1 bit values. As an N -step quantum computation proceeds, the 0 and 1 states remain fixed. The state of the system progresses as |ψ(t i ) = U i |ψ(t i−1 ) , i = 1 to N , where U i is a unitary operator. The progress of the computation is described by the 2(N + 1) inner products 0|ψ(t i ) and 1|ψ(t i ) , which evolve according to the matrix equationIn our method, the qubits do not change in time; they are fixed in their ground states. The steps in the computation correspond, not to evolution between time points, but rather to development of the ground state between connected parts of the Hilbert space. Here a "qubit" is a single system with 2(N + 1) available states, grouped into (N + 1) two-state subspaces {|0 i , |1 i } one for each stage of the calculation. The ground state of the qubit is a superposition containing at least one component of each subspace, |ψ g = i |0 i 0 i |ψ g + |1 i 1 i |ψ g . The progress of the computation is then described in terms of the 2(N + 1) inner products 0 i |ψ g and 1 i |ψ g . As demonstrated below, proper choice of the Hamiltonian leads to a sequence of these inner products according to equation (1), in exact ana...

Universal Adiabatic Quantum Computation via the Space-Time Circuit-to-Hamiltonian Construction

“…The following lemma was used implicitly in reference [12]; here we quote a version of this lemma from [15] (proven in Section E.2 of that paper).…”

“…However, these techniques have the disadvantage of requiring impractically high variability in the coupling strengths which appear in the Hamiltonian (see, e.g., the analysis in [9]). Given this state of affairs, it is of interest to consider how to construct a universal adiabatic quantum computer with a simple Hamiltonian without using perturbative gadgets.An alternative type of circuit-to-Hamiltonian mapping which is conceptually distinct from the Feynman-Kitaev construction has been used by some authors [10][11][12][13][14][15][16]. In these works a quantum circuit is mapped to a Hamiltonian which acts on a Hilbert space with computational and "local" clock degrees of freedom associated with every qubit in the circuit.…”

“…An alternative type of circuit-to-Hamiltonian mapping which is conceptually distinct from the Feynman-Kitaev construction has been used by some authors [10][11][12][13][14][15][16]. In these works a quantum circuit is mapped to a Hamiltonian which acts on a Hilbert space with computational and "local" clock degrees of freedom associated with every qubit in the circuit.…”

Decoherence in adiabatic quantum computation

“…The more efficient local AQC, however, does not improve scaling of the computation time with the number of qubits n as in the decoherence-free case. The scaling improvement requires phase coherence throughout the computation, limiting the computation time and the problem size n.The adiabatic ground-state scheme of quantum computation [1,2] represents an important alternative to the gate-model approach. In adiabatic quantum computation (AQC) the Hamiltonian H S of the qubit register and its wave function |ψ undergo adiabatic evolution in such a way that, while the transformations of |ψ represent some meaningful computation, this state also remains close to the instantaneous ground state |ψ G of H S throughout the process.…”

Modeling an Adiabatic Quantum Computer via an Exact Map to a Gas of Particles

“…(2) is exact and applies to any CNOT gate.-Consider a specific example of an AQC. An arbitrary N-step, M-qubit quantum algorithm can be encoded in H 0 using the "ground state quantum computing" approach [15], whereby every qubit is represented by an array of 2 × (N + 1) quantum dots sharing a single electron. The state of the mth qubit on the (n + 1)st step of the algorithm is given by the probability amplitude to find the electron on either the quantum dot (m, n, 0) or (m, n, 1).…”