arXiv subjects

N. M. Linke

Publications and source records attributed to N. M. Linke.

At least 19 recordsLinked to original sources

arXiv2020

Many Body Thermodynamics on Quantum Computers via Partition Function Zeros

Interacting quantum systems illustrate complex phenomena including phase transitions to novel ordered phases. The universal nature of critical phenomena reduces their description to determining only the transition temperature and the critical exponents. Numerically calculating these results for systems in new universality classes is complicated due to critical slowing down, requiring increasing resources near the critical point. An alternative approach analytically continues the calculation onto the complex plane and determines the partition function via its zeros. Here we show how to robustly perform this analysis on noisy intermediate scale trapped ion quantum computers in a scalable manner, using the XXZ model as a prototype. We illustrate the transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the determination of critical phenomena for systems that cannot be solved otherwise.

quant-ph↗

arXiv2020

Probing many-body localization on a noisy quantum computer

A disordered system of interacting particles exhibits localized behavior when the disorder is large compared to the interaction strength. Studying this phenomenon on a quantum computer without error correction is challenging because even weak coupling to a thermal environment destroys most signatures of localization. Fortunately, spectral functions of local operators are known to contain features that can survive the presence of noise. In these spectra, discrete peaks and a soft gap at low frequencies compared to the thermal phase indicate localization. Here, we present the computation of spectral functions on a trapped-ion quantum computer for a one-dimensional Heisenberg model with disorder. Further, we design an error-mitigation technique which is effective at removing the noise from the measurement allowing clear signatures of localization to emerge as the disorder increases. Thus, we show that spectral functions can serve as a robust and scalable diagnostic of many-body localization on the current generation of quantum computers.

quant-ph↗

arXiv2020

Generation of Thermofield Double States and Critical Ground States with a Quantum Computer

Finite-temperature phases of many-body quantum systems are fundamental to phenomena ranging from condensed-matter physics to cosmology, yet they are generally difficult to simulate. Using an ion trap quantum computer and protocols motivated by the Quantum Approximate Optimization Algorithm (QAOA), we generate nontrivial thermal quantum states of the transverse-field Ising model (TFIM) by preparing thermofield double states at a variety of temperatures. We also prepare the critical state of the TFIM at zero temperature using quantum-classical hybrid optimization. The entanglement structure of thermofield double and critical states plays a key role in the study of black holes, and our work simulates such nontrivial structures on a quantum computer. Moreover, we find that the variational quantum circuits exhibit noise thresholds above which the lowest depth QAOA circuits provide the best results.

quant-ph↗

arXiv2020

Dynamical mean field theory algorithm and experiment on quantum computers

The developments of quantum computing algorithms and experiments for atomic scale simulations have largely focused on quantum chemistry for molecules, while their application in condensed matter systems is scarcely explored. Here we present a quantum algorithm to perform dynamical mean field theory (DMFT) calculations for condensed matter systems on currently available quantum computers, and demonstrate it on two quantum hardware platforms. DMFT is required to properly describe the large class of materials with strongly correlated electrons. The computationally challenging part arises from solving the effective problem of an interacting impurity coupled to a bath, which scales exponentially with system size on conventional computers. An exponential speedup is expected on quantum computers, but the algorithms proposed so far are based on real time evolution of the wavefunction, which requires high-depth circuits and hence very low noise levels in the quantum hardware. Here we propose an alternative approach, which uses the variational quantum eigensolver (VQE) method for ground and excited states to obtain the needed quantities as part of an exact diagonalization impurity solver. We present the algorithm for a two site DMFT system, which we benchmark using simulations on conventional computers as well as experiments on superconducting and trapped ion qubits, demonstrating that this method is suitable for running DMFT calculations on currently available quantum hardware.

quant-ph↗

arXiv2019

Training of Quantum Circuits on a Hybrid Quantum Computer

Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. We implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes data set using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer, and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm and Bayesian optimization to this task. We show that the convergence of the quantum circuit to the target distribution depends critically on both the quantum hardware and classical optimization strategy. Our study represents the first successful training of a high-dimensional universal quantum circuit, and highlights the promise and challenges associated with hybrid learning schemes.

quant-ph↗

arXiv2018

Parallel Entangling Operations on a Universal Ion Trap Quantum Computer

The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear efficiency gains in numerous quantum circuits as well as for entire algorithms such as Shor's factoring algorithm and quantum simulations. In cases such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time. More importantly, quantum gate parallelism is essential for the practical fault-tolerant error correction of qubits that suffer from idle errors. The implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions or cavity-coupled superconducting transmons. Here, we present the first experimental results for parallel 2-qubit entangling gates in an array of fully-connected trapped ion qubits. We demonstrate an application of this capability by performing a 1-bit full addition operation on a quantum computer using a depth-4 quantum circuit. These results exploit the power of highly connected qubit systems through classical control techniques, and provide an advance toward speeding up quantum circuits and achieving fault tolerance with trapped ion quantum computers.

quant-ph↗

arXiv2017

Observation of Hopping and Blockade of Bosons in a Trapped Ion Spin Chain

The local phonon modes in a Coulomb crystal of trapped ions can represent a Hubbard system of coupled bosons. We selectively prepare single excitations at each site and observe free hopping of a boson between sites, mediated by the long-range Coulomb interaction between ions. We then implement phonon blockades on targeted sites by driving a Jaynes-Cummings interaction on individually addressed ions to couple their internal spin to the local phonon mode. The resulting dressed states have energy splittings that can be tuned to suppress phonon hopping into the site. This new experimental approach opens up the possibility of realizing large-scale Hubbard systems from the bottom up with tunable interactions at the single-site level.

quant-ph↗

arXiv2017

Fault-tolerant quantum error detection

Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent detection or correction of errors without destroying the logical state itself through direct measurement. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. The advantage persists in the face of large added error rates and experimental calibration errors.

quant-ph↗

arXiv2017

High-fidelity spatial and polarization addressing of Ca-43 qubits using near-field microwave control

Individual addressing of qubits is essential for scalable quantum computation. Spatial addressing allows unlimited numbers of qubits to share the same frequency, whilst enabling arbitrary parallel operations. We demonstrate addressing of long-lived $^{43}\text{Ca}^+$ "atomic clock" qubits held in separate zones ($960μ$m apart) of a microfabricated surface trap with integrated microwave electrodes. Such zones could form part of a "quantum CCD" architecture for a large-scale quantum information processor. By coherently cancelling the microwave field in one zone we measure a ratio of Rabi frequencies between addressed and non-addressed qubits of up to 1400, from which we calculate a spin-flip probability on the qubit transition of the non-addressed ion of $1.3\times 10^{-6}$. Off-resonant excitation then becomes the dominant error process, at around $5 \times 10^{-3}$. It can be prevented either by working at higher magnetic field, or by polarization control of the microwave field. We implement polarization control with error $2 \times 10^{-5}$, which would suffice to suppress off-resonant excitation to the $\sim 10^{-9}$ level if combined with spatial addressing. Such polarization control could also enable fast microwave operations.

quant-ph↗

arXiv2017

Complete 3-Qubit Grover Search on a Programmable Quantum Computer

Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. It is an optimal search algorithm for a quantum computer, and has further applications as a subroutine for other quantum algorithms. Searches with two qubits have been demonstrated on a variety of platforms and proposed for others, but larger search spaces have only been demonstrated on a non-scalable NMR system. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state-marking scheme required to perform a classical search. All quantum solutions are shown to outperform their classical counterparts. We also report the first implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5% and 89.6%, respectively.

quant-ph↗

arXiv2017

Experimental Comparison of Two Quantum Computing Architectures

We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programmed in a way that is blind to the underlying hardware, thus allowing the first comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that employ more connectivity clearly benefit from a better connected system of qubits. While the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that co-designing particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.

quant-ph↗

arXiv2016

Demonstration of a small programmable quantum computer with atomic qubits

Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here, we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully-connected set of gate operations that are native to the hardware and have a mean fidelity of 98 %. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa (DJ) and Bernstein-Vazirani (BV) algorithms with average success rates of 95 % and 90 %, respectively. We also perform a coherent quantum Fourier transform (QFT) on five trappedion qubits for phase estimation and period finding with average fidelities of 62 % and 84 %, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

quant-ph↗

arXiv2015

Hybrid quantum logic and a test of Bell's inequality using two different atomic isotopes

Entanglement is one of the most fundamental properties of quantum mechanics, and is the key resource for quantum information processing. Bipartite entangled states of identical particles have been generated and studied in several experiments, and post-selected or heralded entangled states involving pairs of photons, single photons and single atoms, or different nuclei in the solid state, have also been produced. Here, we use a deterministic quantum logic gate to generate a "hybrid" entangled state of two trapped-ion qubits held in different isotopes of calcium, perform full tomography of the state produced, and make a test of Bell's inequality with non-identical atoms. We use a laser-driven two-qubit gate, whose mechanism is insensitive to the qubits' energy splittings, to produce a maximally-entangled state of one Ca-40 qubit and one Ca-43 qubit, held 3.5 microns apart in the same ion trap, with 99.8(6)% fidelity. We test the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality for this novel entangled state and find that it is violated by 15 standard deviations; in this test, we close the detection loophole but not the locality loophole. Mixed-species quantum logic is a powerful technique for the construction of a quantum computer based on trapped ions, as it allows protection of memory qubits while other qubits undergo logic operations, or are used as photonic interfaces to other processing units. The entangling gate mechanism used here can also be applied to qubits stored in different atomic elements; this would allow both memory and logic gate errors due to photon scattering to be reduced below the levels required for fault-tolerant quantum error correction, which is an essential pre-requisite for general-purpose quantum computing.

quant-ph↗

arXiv2014

High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit

We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine "atomic clock" states of $^{43}$Ca$^+$. We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of $T^*_2=50$ seconds, and an average single-qubit gate fidelity of 99.9999%. These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technical noise.

quant-ph↗

arXiv2014

High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions

We study the speed/fidelity trade-off for a two-qubit phase gate implemented in $^{43}$Ca$^+$ hyperfine trapped-ion qubits. We characterize various error sources contributing to the measured fidelity, allowing us to account for errors due to single-qubit state preparation, rotation and measurement (each at the $\sim0.1\%$ level), and to identify the leading sources of error in the two-qubit entangling operation. We achieve gate fidelities ranging between $97.1(2)\%$ (for a gate time $t_g=3.8μ$s) and $99.9(1)\%$ (for $t_g=100μ$s), representing respectively the fastest and lowest-error two-qubit gates reported between trapped-ion qubits by nearly an order of magnitude in each case.

quant-ph↗

arXiv2013

Injection locking of two frequency-doubled lasers with 3.2 GHz offset for driving Raman transitions with low photon scattering in $^{43}$Ca$^+$

We describe the injection locking of two infrared (794 nm) laser diodes which are each part of a frequency-doubled laser system. An acousto-optic modulator (AOM) in the injection path gives an offset of 1.6 GHz between the lasers for driving Raman transitions between states in the hyperfine split (by 3.2 GHz) ground level of $^{43}$Ca$^+$. The offset can be disabled for use in $^{40}$Ca$^+$. We measure the relative linewidth of the frequency-doubled beams to be 42 mHz in an optical heterodyne measurement. The use of both injection locking and frequency doubling combines spectral purity with high optical power. Our scheme is applicable for providing Raman beams across other ion species and neutral atoms where coherent optical manipulation is required.

physics.atom-ph↗

arXiv2013

Microwave control electrodes for scalable, parallel, single-qubit operations in a surface-electrode ion trap

We propose a surface ion trap design incorporating microwave control electrodes for near-field single-qubit control. The electrodes are arranged so as to provide arbitrary frequency, amplitude and polarization control of the microwave field in one trap zone, while a similar set of electrodes is used to null the residual microwave field in a neighbouring zone. The geometry is chosen to reduce the residual field to the 0.5% level without nulling fields; with nulling, the crosstalk may be kept close to the 0.01% level for realistic microwave amplitude and phase drift. Using standard photolithography and electroplating techniques, we have fabricated a proof-of-principle electrode array with two trapping zones. We discuss requirements for the microwave drive system and prospects for scalability to a large two-dimensional trap array.

quant-ph↗

arXiv2012

A microfabricated ion trap with integrated microwave circuitry

We describe the design, fabrication and testing of a surface-electrode ion trap, which incorporates microwave waveguides, resonators and coupling elements for the manipulation of trapped ion qubits using near-field microwaves. The trap is optimised to give a large microwave field gradient to allow state-dependent manipulation of the ions' motional degrees of freedom, the key to multiqubit entanglement. The microwave field near the centre of the trap is characterised by driving hyperfine transitions in a single laser-cooled 43Ca+ ion.

physics.atom-ph↗