arXiv subjects

Edwin Barnes

Publications and source records attributed to Edwin Barnes.

At least 91 records · Page 5Linked to original sources

arXiv2020

Teaching quantum information science to high-school and early undergraduate students

We present a simple, accessible, yet rigorous outreach/educational program focused on quantum information science and technology for high-school and early undergraduate students. This program allows students to perform meaningful hands-on calculations with quantum circuits and algorithms, without requiring knowledge of advanced mathematics. A combination of pen-and-paper exercises and IBM Q simulations helps students understand the structure of quantum gates and circuits, as well as the principles of superposition, entanglement, and measurement in quantum mechanics.

physics.ed-ph↗

arXiv2020

Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems

The ability to perform gates in multiqubit systems that are robust to noise is of crucial importance for the advancement of quantum information technologies. However, finding control pulses that cancel noise while performing a gate is made difficult by the intractability of the time-dependent Schrodinger equation, especially in multiqubit systems. Here, we show that this issue can be sidestepped by using a formalism in which the cumulative error during a gate is represented geometrically as a curve in a multi-dimensional Euclidean space. Cancellation of noise errors to leading order corresponds to closure of the curve, a condition that can be satisfied without solving the Schrodinger equation. We develop and uncover general properties of this geometric formalism, and derive a recursion relation that maps control fields to curvatures for Hamiltonians of arbitrary dimension. We demonstrate examples by using the geometric method to design dynamically corrected gates for a class of two-qubit Hamiltonians that is relevant for both superconducting transmon qubits and semiconductor spin qubits. We propose this geometric formalism as a general technique for pulse-induced error suppression in quantum computing gate operations.

quant-ph↗

arXiv2020

Coherent multi-spin exchange coupling in a quantum-dot spin chain

Heisenberg exchange coupling between neighboring electron spins in semiconductor quantum dots provides a powerful tool for quantum information processing and simulation. Although so far unrealized, extended Heisenberg spin chains can enable long-distance quantum information transfer and the generation of non-equilibrium quantum states. In this work, we implement simultaneous, coherent exchange coupling between all nearest-neighbor pairs of spins in a quadruple quantum dot. The main challenge in implementing simultaneous exchange couplings is the nonlinear and nonlocal dependence of the exchange couplings on gate voltages. Through a combination of electrostatic simulation and theoretical modeling, we show that this challenge arises primarily due to lateral shifts of the quantum dots during gate pulses. Building on this insight, we develop two models, which can be used to predict the confinement gate voltages for a desired set of exchange couplings. Although the model parameters depend on the number of exchange couplings desired (suggesting that effects in addition to lateral wavefunction shifts are important), the models are sufficient to enable simultaneous and independent control of all three exchange couplings in a quadruple quantum dot. We demonstrate two-, three-, and four-spin exchange oscillations, and our data agree with simulations.

cond-mat.mes-hall↗

arXiv2020

qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor

Quantum simulation, one of the most promising applications of a quantum computer, is currently being explored intensely using the variational quantum eigensolver. The feasibility and performance of this algorithm depend critically on the form of the wavefunction ansatz. Recently in Nat. Commun. 10, 3007 (2019), an algorithm termed ADAPT-VQE was introduced to build system-adapted ansätze with substantially fewer variational parameters compared to other approaches. This algorithm relies heavily on a predefined operator pool with which it builds the ansatz. However, Nat. Commun. 10, 3007 (2019) did not provide a prescription for how to select the pool, how many operators it must contain, or whether the resulting ansatz will succeed in converging to the ground state. In addition, the pool used in that work leads to state preparation circuits that are too deep for a practical application on near-term devices. Here, we address all these key outstanding issues of the algorithm. We present a hardware-efficient variant of ADAPT-VQE that drastically reduces circuit depths using an operator pool that is guaranteed to contain the operators necessary to construct exact ansätze. Moreover, we show that the minimal pool size that achieves this scales linearly with the number of qubits. Through numerical simulations on $\text{H}_4$, LiH and $\text{H}_6$, we show that our algorithm ("qubit-ADAPT") reduces the circuit depth by an order of magnitude while maintaining the same accuracy as the original ADAPT-VQE. A central result of our approach is that the additional measurement overhead of qubit-ADAPT compared to fixed-ansatz variational algorithms scales only linearly with the number of qubits. Our work provides a crucial step forward in running algorithms on near-term quantum devices.

quant-ph↗

arXiv2020

Landau poles in condensed matter systems

The existence or not of Landau poles is one of the oldest open questions in non-asymptotic quantum field theories. We investigate the Landau pole issue in two condensed matter systems whose long-wavelength physics is described by appropriate quantum field theories: the critical quantum magnet and Dirac fermions in graphene with long-range Coulomb interactions. The critical quantum magnet provides a classic example of a quantum phase transition, and it is well described by the $ϕ^4$ theory. We find that the irrelevant but symmetry-allowed couplings, such as the $ϕ^6$ potential, can significantly change the fate of the Landau pole in the $ϕ^4$ theory. We obtain the coupled beta functions of a $ϕ^4 + ϕ^6$ potential at both small and large orders. Already from the 1-loop calculation, the Landau pole is replaced by an ultraviolet fixed point. A Lipatov analysis at large orders reveals that the inclusion of a $ϕ^6$ term also has important repercussions for the high-order expansion of the beta functions. We also investigate the role of the Landau pole in 2+1 dimensional Dirac fermions with Coulomb interactions, e.g., graphene. Both the weak-coupling perturbation theory up to 2 loops and a low-order large-N calculation show the absence of a Landau pole. Furthermore, we calculate the asymptotic expansion coefficients of the beta function. We find that the asymptotic coefficient is bounded by that of a $ϕ^4$ theory, so graphene is free from Landau poles if the $ϕ^4$ theory does not manifest a Landau pole. We briefly discuss possible experiments that could potentially probe the existence of a Landau pole in these systems. Studying Landau poles in suitable condensed matter systems is of considerable fundamental importance since the relevant Landau pole energy scales in particle physics, whether it is quantum electrodynamics or Higgs physics, are completely unattainable.

cond-mat.str-el↗

arXiv2020

Fast noise-resistant control of donor nuclear spin qubits in silicon

A high degree of controllability and long coherence time make the nuclear spin of a phosphorus donor in isotopically purified silicon a promising candidate for a quantum bit. However, long-distance two-qubit coupling and fast, robust gates remain outstanding challenges for these systems. Here, following recent proposals for long-distance coupling via dipole-dipole interactions, we present a simple method to implement fast, high-fidelity arbitrary single- and two-qubit gates in the absence of charge noise. Moreover, we provide a method to make the single-qubit gates robust to moderate levels of charge noise to well within an error bound of $10^{-3}$.

quant-ph↗

arXiv2020

Interplay of exchange and superexchange in triple quantum dots

Recent experiments on semiconductor quantum dots have demonstrated the ability to utilize a large quantum dot to mediate superexchange interactions and generate entanglement between distant spins. This opens up a possible mechanism for selectively coupling pairs of remote spins in a larger network of quantum dots. Taking advantage of this opportunity requires a deeper understanding of how to control superexchange interactions in these systems. Here, we consider a triple-dot system arranged in linear and triangular geometries. We use configuration interaction calculations to investigate the interplay of superexchange and nearest-neighbor exchange interactions as the location, detuning, and electron number of the mediating dot are varied. We show that superexchange processes strongly enhance and increase the range of the net spin-spin exchange as the dots approach a linear configuration. Furthermore, we show that the strength of the exchange interaction depends sensitively on the number of electrons in the mediator. Our results can be used as a guide to assist further experimental efforts towards scaling up to larger, two-dimensional quantum dot arrays.

cond-mat.mes-hall↗

arXiv2020

Preserving Symmetries for Variational Quantum Eigensolvers in the Presence of Noise

One of the most promising applications of noisy intermediate-scale quantum computers is the simulation of molecular Hamiltonians using the variational quantum eigensolver. We show that encoding symmetries of the simulated Hamiltonian in the VQE ansatz reduces both classical and quantum resources compared to other, widely available ansatze. Through simulations of the H$_2$ molecule, we verify that these improvements persist in the presence of noise. This simulation is performed with IBM software using noise models from real devices. We also demonstrate how these techniques can be used to find molecular excited states of various symmetries using a noisy processor. We use error mitigation techniques to further improve the quality of our results.

quant-ph↗

arXiv2020

Is the Trotterized UCCSD Ansatz chemically well-defined?

The variational quantum eigensolver (VQE) has emerged as one of the most promising near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. However, unlike the original classical UCC theory, implementation on a quantum computer requires a finite-order Suzuki-Trotter decomposition to separate the exponentials of the large sum of Pauli operators. While previous literature has recognized the non-uniqueness of different orderings of the operators in the Trotterized form of UCC methods, the question of whether or not different orderings matter at the chemical scale has not been addressed. In this letter, we explore the effect of operator ordering on the Trotterized UCCSD ansatz, as well as the much more compact $k$-UpCCGSD ansatz recently proposed by Lee et al. We observe a significant, system-dependent variation in the energies of Trotterizations with different operator orderings. The energy variations occur on a chemical scale, sometimes on the order of hundreds of kcal/mol. This letter establishes the need to define not only the operators present in the ansatz, but also the order in which they appear. This is necessary for adhering to the quantum chemical notion of a ``model chemistry'', in addition to the general importance of scientific reproducibility. As a final note, we suggest a useful strategy to select out of the combinatorial number of possibilities, a single well-defined and effective ordering of the operators.

quant-ph↗

arXiv2020

Toward long-range entanglement between electrically driven single-molecule magnets

Over the past two decades, several molecules have been explored as possible building blocks of a quantum computer, a device that would provide exponential speedups for a number of problems, including the simulation of large, strongly correlated chemical systems. Achieving strong interactions and entanglement between molecular qubits remains an outstanding challenge. Here, we show that the TbPc$_2$ single-molecule magnet has the potential to overcome this obstacle due to its sensitivity to electric fields stemming from the hyperfine Stark effect. We show how this feature can be leveraged to achieve long-range entanglement between pairs of molecules using a superconducting resonator as a mediator. Our results suggest that the molecule-resonator interaction is near the edge of the strong-coupling regime and could potentially pass into it given a more detailed, quantitative understanding of the TbPc$_2$ molecule.

quant-ph↗

arXiv2020

Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm

The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multi-qubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that respect particle number, total spin, spin projection, and time-reversal symmetries. These circuits contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace dictated by the chemistry problem while avoiding all irrelevant sectors of Hilbert space. We show how to construct these circuits for arbitrary numbers of orbitals, electrons, and spin quantum numbers, and we provide explicit decompositions and gate counts in terms of standard gate sets in each case. We test our circuits in quantum simulations of the $H_2$ and $LiH$ molecules and find that they outperform standard state preparation methods in terms of both accuracy and circuit depth.

quant-ph↗

arXiv2019

Discrete time crystal in the gradient field Heisenberg model

We show that time crystal phases, which are known to exist for disorder-based many-body localized systems, also appear in systems where localization is due to strong magnetic field gradients. Specifically, we study a finite Heisenberg spin chain in the presence of a gradient field, which can be realized experimentally in quantum dot systems using micromagnets or nuclear spin polarization. Our numerical simulations reveal time crystalline order over a broad range of realistic quantum dot parameters, as evidenced by the long-time preservation of spin expectation values and the asymptotic form of the mutual information. We also consider the undriven system and present several diagnostics for many-body localization that are complementary to those recently studied. Our results show that these non-ergodic phases should be realizable in modest-sized quantum dot spin arrays using only demonstrated experimental capabilities.

quant-ph↗

arXiv2019

Long-distance entangling gates between quantum dot spins mediated by a superconducting resonator

Recent experiments with silicon qubits demonstrated strong coupling of a microwave resonator to the spin of a single electron in a double quantum dot, opening up the possibility of long-range spin-spin interactions. We present our theoretical calculation of effective interactions between distant quantum dot spins coupled by a resonator, and propose a protocol for fast, high-fidelity two-qubit gates consistent with experimentally demonstrated capabilities. Our simulations show that, in the presence of noise, spin-spin entangling gates significantly outperform cavity-mediated gates on charge qubits.

quant-ph↗

arXiv2019

Geometric formalism for constructing arbitrary single-qubit dynamically corrected gates

Implementing high-fidelity quantum control and reducing the effect of the coupling between a quantum system and its environment is a major challenge in developing quantum information technologies. Here, we show that there exists a geometrical structure hidden within the time-dependent Schrödinger equation that provides a simple way to view the entire solution space of pulses that suppress noise errors in a system's evolution. In this framework, any single-qubit gate that is robust against quasistatic noise to first order corresponds to a closed three-dimensional space curve, where the driving fields that implement the robust gate can be read off from the curvature and torsion of the space curve. Gates that are robust to second order are in one-to-one correspondence with closed curves whose projections onto three mutually orthogonal planes each enclose a vanishing net area. We use this formalism to derive new examples of dynamically corrected gates generated from smooth pulses. We also show how it can be employed to analyze the noise-cancellation properties of pulses generated from numerical algorithms such as GRAPE. A similar geometrical framework exists for quantum systems of arbitrary Hilbert space dimension.

quant-ph↗

arXiv2019

An adaptive variational algorithm for exact molecular simulations on a quantum computer

Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that instead of fixing an ansatz upfront, this algorithm grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware.

quant-ph↗

arXiv2019

Fast high-fidelity entangling gates for spin qubits in Si double quantum dots

Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work, we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters and initially assuming a noise-free environment, we present simple control pulses that generate CNOT, CPHASE, and CZ gates with average fidelities greater than 99.99\% and gate times as short as 45 ns. Moreover, using the local invariants of the system's evolution operator, we show that a simple square pulse generates a CNOT gate in less than 27 ns and with a fidelity greater than 99.99\%. Last, we use the same analytical methods to generate two-qubit gates locally equivalent to $\sqrt{\mathrm{CNOT}}$ and $\sqrt{\mathrm{CZ}}$ that are used to implement simple two-piece pulse sequences that produce high-fidelity CNOT and CZ gates in the presence of low-frequency noise.

quant-ph↗

arXiv2019

Generation of arbitrary all-photonic graph states from quantum emitters

We present protocols to generate arbitrary photonic graph states from quantum emitters that are in principle deterministic. We focus primarily on two-dimensional cluster states of arbitrary size due to their importance for measurement-based quantum computing. Our protocols for these and many other types of two-dimensional graph states require a linear array of emitters in which each emitter can be controllably pumped, rotated about certain axes, and entangled with its nearest neighbors. We show that an error on one emitter produces a localized region of errors in the resulting graph state, where the size of the region is determined by the coordination number of the graph. We describe how these protocols can be implemented for different types of emitters, including trapped ions, quantum dots, and nitrogen-vacancy centers in diamond.

quant-ph↗

arXiv2019

Enhancement of nuclear spin coherence times by driving dynamic nuclear polarization at defect centers in solids

The hyperpolarization of nuclear spins can enable powerful imaging and sensing techniques provided the hyperpolarization is sufficiently long-lived. Recent experiments on nanodiamond $^{13}$C nuclear spins demonstrate that relaxation times can be extended by three orders of magnitude by building up dynamic nuclear polarization (DNP) through the driving of electron-nuclear flip-flop processes at defect centers. This finding raises the question of whether the nuclear spin coherence times are also impacted by this hyperpolarization process. Here, we theoretically examine the effect of DNP on the nuclear spin coherence times as a function of the hyperpolarization drive time. We do this by developing a microscopic theory of DNP in a nuclear spin ensemble coupled to microwave-driven defect centers in solids and subject to spin diffusion mediated by internuclear dipolar interactions. We find that, similarly to relaxation times, the nuclear spin coherence times can be increased substantially by a few orders of magnitude depending on the driving time. Our theoretical model and results will be useful for current and future experiments on enhancing nuclear spin coherence times via DNP.

cond-mat.mes-hall↗