Robust universal Hamiltonian quantum computing using two-body interactions

Abstract

We present a new scheme to perform noise resilient universal adiabatic quantum computation using two-body interactions. To achieve this, we introduce a new family of error detecting subsystem codes whose gauge generators and a set of their logical operators -capable of encoding universal Hamiltonian computations -can be implemented using two-body interactions. Logical operators of the code are used to encode any given computational Hamiltonian, and the gauge operators are used to construct a penalty Hamiltonian whose ground subspace is protected against local-errors. In contrast to previous approaches, the constructed penalty Hamiltonian does not necessarily commute with the encoded computational Hamiltonians, but for our construction the undesirable effect of the penalty Hamiltonian on the computation can be compensated by a simple modification of the implemented Hamiltonians.We also investigate whether a similar scheme can be constructed by encoding the computational Hamiltonian using only bare-logical operators of subsystem codes, to guarantee that computational Hamiltonian commutes with the penalty Hamiltonian. We prove a no-go theorem showing that restricting to two-body interactions and using any general CSS-type subsystem codes, such a construction cannot encode systems beyond an Ising chain in a transverse field. We point out that such a chain is universal for Hamiltonian-based quantum computation, but it is not universal for ground-state quantum computation.

Prospects for Quantum Enhancement with Diabatic Quantum Annealing

“…Most pressing in this regard would be the addition of a constant-in-time −XX coupling to the Hamiltonians in Eq. ( 1), since this would suffice in order to achieve fully two-local HES [196]. Hamiltonian error suppression is one of the clearest examples of a moonshot in modern quantum information science: if it works well (better than predicted by worst-case theoretical bounds) then it could dramatically reduce the expected overhead needed for implementing quantum algorithms at the application scale.…”

“…The ability to control arbitrary 2-local interactions would enable the emulation of nonstoquastic Hamiltonians as well as stoquastic Hamiltonians of a more general form than transversefield Ising models. This latter capability is the one needed for Hamiltonian error suppression using stabilizer subsystem codes [194][195][196], since to achieve universality they require both ±XX and ±ZZ interactions (though the penalty terms for the only fully two-local Hamiltonian error suppression protocol [196] are stoquastic). These error suppression protocols implemented in the setting of universal adiabatic quantum computing are arguably the most compelling reason to pursue qubit technologies that enable static dipole-dipole interactions along multiple vector components.…”

“…These capabilities enable arbitrarily long com-putations if the errors are below some fixed threshold, but depending on the finite size of applications and the expected speedup the overheads required may be prohibitive. Hamiltonian Error Suppression (HES) [77,80,[194][195][196][233][234][235][236][237][238][239][240][241][242][243][244][245][246] is an alternative to the standard approach that, in contrast, uses error detecting codes with a fixed or growing [240] distance, and does not require any intermediate measurements or classical processing. HES is designed for continuous-time Hamiltonian computation and enforces containment in a logical code space using energy penalties that suppress transitions to states outside of the code space.…”

“…This, however, requires four-local interactions for universality. A fully two-local scheme has also been developed, at the expense of giving up exponential error suppression [196].…”

Using copies to improve precision in continuous-time quantum computing

“…Despite the challenges, a variety of schemes for error correction and suppression in continuous-time quantum computing have been developed, generally referred to as Hamiltonian error suppression [16]. Most can be grouped into six categories: energy penalty Hamiltonians [23][24][25][26]; dynamical decoupling [27][28][29]; subsystem codes [30][31][32][33][34]; continuous-in-time techniques [20,35,36]; via qubit ensembles [37]; and the Zeno effect [38]. In addition to these techniques for explicit error suppression and/or correction, quantum annealing may be carried out in some circumstances without error correction, as long as sufficiently many repetitions are implemented [39][40][41][42][43].…”