01810nas a2200121 4500008004100000245006600041210006600107260001400173520141900187100002101606700002401627856003701651 2021 eng d00aPreparing Renormalization Group Fixed Points on NISQ Hardware0 aPreparing Renormalization Group Fixed Points on NISQ Hardware c9/20/20213 a

Noisy intermediate-scale quantum (NISQ) hardware is typically limited to low-depth quantum circuits to limit the number of opportunities for introduction of error by unreliable quantum gates. A less-explored alternative approach is to repeatedly apply a quantum channel with a desired quantum state as a stable fixed point. Increased circuit depth can in this case be beneficial rather than harmful due to dissipative self-correction. The quantum channels constructed from MERA circuits can be interpreted in terms of the renormalization group(RG), and their fixed points are RG fixed points, i.e. scale-invariant systems such as conformal field theories. Here, building upon the theoretical proposal of Kim and Swingle, we numerically and experimentally study the robust preparation of the ground state of the critical Ising model using circuits adapted from the work of Evenbly and White. The experimental implementation exhibits self-correction through renormalization seen in the convergence and stability of local observables, and makes essential use of the ability to measure and reset individual qubits afforded by the "quantum CCD" architecture of the Honeywell ion-trap. We also numerically test error mitigation by zero-noise extrapolation schemes specially adapted for renormalization circuits, which are able to outperform typical extrapolation schemes using lower gate overhead. 

1 aSewell, Troy, J.1 aJordan, Stephen, P. uhttps://arxiv.org/abs/2109.0978701973nas a2200145 4500008004100000245008000041210006900121260001400190490000800204520151100212100002201723700002101745700002401766856003701790 2019 eng d00aPolynomial Time Algorithms for Estimating Spectra of Adiabatic Hamiltonians0 aPolynomial Time Algorithms for Estimating Spectra of Adiabatic H c10/1/20200 v1003 a

Much research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians with Hamming symmetric potentials, such as the well studied "spike" example. Due to the large amount of symmetry in these potentials such problems are readily open to analysis both analytically and computationally. However, more realistic potentials do not have such a high degree of symmetry and may have many local minima. Here we present a somewhat more realistic class of problems consisting of many individually Hamming symmetric potential wells. For two or three such wells we demonstrate that such a problem can be solved exactly in time polynomial in the number of qubits and wells. For greater than three wells, we present a tight binding approach with which to efficiently analyze the performance of such Hamiltonians in an adiabatic computation. We provide several basic examples designed to highlight the usefulness of this toy model and to give insight into using the tight binding approach to examining it, including: (1) adiabatic unstructured search with a transverse field driver and a prior guess to the marked item and (2) a scheme for adiabatically simulating the ground states of small collections of strongly interacting spins, with an explicit demonstration for an Ising model Hamiltonian.

1 aBringewatt, Jacob1 aDorland, William1 aJordan, Stephen, P. uhttps://arxiv.org/abs/1905.0746101518nas a2200133 4500008004100000245005800041210005700099260001500156520111500171100001901286700002001305700002401325856003501349 2014 eng d00aPartial-indistinguishability obfuscation using braids0 aPartialindistinguishability obfuscation using braids c2014/08/213 a

An obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical progress has mainly been limited to no-go results. Recent works have proposed the first efficient obfuscation algorithms for classical logic circuits, based on a notion of indistinguishability against polynomial-time adversaries. In this work, we propose a new notion of obfuscation, which we call partial-indistinguishability. This notion is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions. We describe universal gate sets for both classical and quantum computation, in which our definition of obfuscation can be met by polynomial-time algorithms. We also discuss some potential applications to testing quantum computers. We stress that the cryptographic security of these obfuscators, especially when composed with translation from other gate sets, remains an open question.

1 aAlagic, Gorjan1 aJeffery, Stacey1 aJordan, Stephen, P. uhttp://arxiv.org/abs/1212.635801293nas a2200133 4500008004100000245003600041210003600077260001500113300001200128490000700140520094200147100002401089856004601113 2010 eng d00aPermutational Quantum Computing0 aPermutational Quantum Computing c2010/05/01 a470-4970 v103 a

In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle trajectory, and computes by permuting particles. Whereas topological quantum computation requires anyons, permutational quantum computation can be performed with ordinary spin-1/2 particles, using a variant of the spin-network scheme of Marzuoli and Rasetti. We do not know whether permutational computation is universal. It may represent a new complexity class within BQP. Nevertheless, permutational quantum computers can in polynomial time approximate matrix elements of certain irreducible representations of the symmetric group and simulate certain processes in the Ponzano-Regge spin foam model of quantum gravity. No polynomial time classical algorithms for these problems are known.

1 aJordan, Stephen, P. uhttp://dl.acm.org/citation.cfm?id=201136901152nas a2200133 4500008004100000245004500041210004500086260001400131490000700145520078700152100002400939700001800963856003700981 2008 eng d00aPerturbative Gadgets at Arbitrary Orders0 aPerturbative Gadgets at Arbitrary Orders c2008/6/190 v773 a Adiabatic quantum algorithms are often most easily formulated using many-body interactions. However, experimentally available interactions are generally two-body. In 2004, Kempe, Kitaev, and Regev introduced perturbative gadgets, by which arbitrary three-body effective interactions can be obtained using Hamiltonians consisting only of two-body interactions. These three-body effective interactions arise from the third order in perturbation theory. Since their introduction, perturbative gadgets have become a standard tool in the theory of quantum computation. Here we construct generalized gadgets so that one can directly obtain arbitrary k-body effective interactions from two-body Hamiltonians. These effective interactions arise from the kth order in perturbation theory. 1 aJordan, Stephen, P.1 aFarhi, Edward uhttp://arxiv.org/abs/0802.1874v401766nas a2200181 4500008004100000245008100041210006900122260001500191300001800206490000800224520121000232100001701442700002401459700002001483700002001503700002401523856003701547 2008 eng d00aPolynomial-time quantum algorithm for the simulation of chemical dynamics 0 aPolynomialtime quantum algorithm for the simulation of chemical  c2008/11/24 a18681 - 186860 v1053 a The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and inter-electronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the Born-Oppenheimer approximation, but faster and more efficient as well, for all reactions with more than about four atoms. This is the case even though the entire electronic wavefunction is propagated on a grid with appropriately short timesteps. Although the preparation and measurement of arbitrary states on a quantum computer is inefficient, here we demonstrate how to prepare states of chemical interest efficiently. We also show how to efficiently obtain chemically relevant observables, such as state-to-state transition probabilities and thermal reaction rates. Quantum computers using these techniques could outperform current classical computers with one hundred qubits. 1 aKassal, Ivan1 aJordan, Stephen, P.1 aLove, Peter, J.1 aMohseni, Masoud1 aAspuru-Guzik, Alán uhttp://arxiv.org/abs/0801.2986v3