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...