Erratum: Polynomial-Time Simulation of Pairing Models on a Quantum Computer [Phys. Rev. Lett.89, 057904 (2002)]

Self-protected quantum algorithms based on quantum state tomography

“…Let us comment on precision issues in this context. Our QST-based method complements the scattering circuit method [28,29,30,31] and the quantum phase estimation algorithms [32,33,34] it subsumes, and the adiabatic method we previously introduced for pairing Hamiltonians [15]. As in our current method, these other methods scale polynomially in N , and this is commonly considered an exponential speedup over the currently known best classical algorithms for the same task.…”

“…Yet another class consists of algorithms for simulating quantum systems. Simulation algorithms can provide an exponential speed-up over any known classical algorithm for a variety of quantum systems [5,6,7,8,9,10,11,12,13,14,15] and are very promising for many applications in the physical sciences. These include atomic, molecular, solid state, and nuclear simulations and do not necessarily require a fully scalable quantum computing device [16].…”

Few-body spin couplings and their implications for universal quantum computation

“…By comparing the explicit matrix representations (26) and (28) it is clear that the crucial difference between U ′ 1 and U 1 is the appearance of the χ + terms on the diagonal of U ′ 1 (the difference between Ω and λ is irrelevant: it translates into a global phase). In order for U ′ 1 to act like U 1 , i.e., in order for it not to prepare a superposition of code states and the first four non-code states, χ + must vanish.…”

“…In these cases, the goal is to perform universal quantum computation using (EU:) only the most easily controllable interaction, or (DFS, supercoherence:) using only interactions that preserve the code subspace, since that subspace offers protection against certain types of decoherence. (Strong and fast exchange interaction pulses can further be used to suppress decoherence [25] and to eliminate decoherence-induced leakage [26]. ) We will refer to these cases collectively as "encoded quantum computation."…”

“…It turns out that universal quantum computation using only the Heisenberg exchange interaction is an extremely attractive possibility in encoded models, and we will consider it in detail below. After establishing that four-body interaction terms can arise in a Heisenberg exchange Hamiltonian, we investigate the question of neutralizing their effect by using encoded qubits [5,6,8,9,10,24,25,26,27,28,29]. By generalizing the work of Bacon [30], who showed that universal quantum computation was possible using encoded gates with two-body coupling Hamiltonians (i.e., assuming that the Heisenberg Hamiltonian was applicable even when coupling three or more dots at a time), we enumerate tuning conditions on experimental parameters that are needed for the four-body effects to cancel out.…”