Session G40: Noisy Intermediate Scale Quantum Computers V

NISQ Algorithm for Semidefinite Programming

Semidefinite programs (SDPs) are convex optimization programs with vast applications in control theory, quantum information and combinatorial optimization. Noisy intermediate-scale quantum (NISQ) algorithms aim to efficiently use the current generation of quantum hardware. However, optimizing variational quantum algorithms is a challenge as it is a NP-hard problem that in general requires an exponential time to solve and can contain many far from optimal local minima. 

Here, we present a NISQ algorithm for solving SDPs. The classical optimization program of our NISQ solver is another SDP over a lower dimensional ansatz space. Using the SDP formulation of the Hamiltonian ground state problem, we design a NISQ eigensolver. Unlike variational quantum eigensolvers, the classical optimization program of our eigensolver is convex, can be solved in polynomial time and every local minimum is a global minimum.

Further, we demonstrate the potential of our NISQ SDP solver by finding the largest eigenvalue of $2^{1000}$ dimensional matrices and solving graph problems related to quantum contextuality. We also discuss NISQ algorithms for rank-constrained SDPs. Our work extends the application of NISQ computers onto one of the most successful algorithmic frameworks of the past few decades.   

Testing Quantum Mechanics using Noisy Quantum Computers

We outline a proposal to test quantum mechanics using noisy intermediate-scale quantum (NISQ) devices in the high-complexity quantum advantage regime. We are motivated by the possibility that quantum mechanics is not fundamental, but instead emerges from a theory with less computational power, such as classical mechanics. We show that our proposal can significantly rule out this possibility with 2000 logical qubits and a modest gate infidelity of 10^-5, although useful experiments can already be conducted with e.g. 80 qubits and gate infidelity 10^-3. Our procedure involves simulating a non-Clifford random circuit, followed by its inverse, and then checking that the resulting state is the same as the initial state. We show that quantum mechanics predicts that the fidelity of this procedure decays exponentially with circuit depth (due to noise in NISQ computers). However, if quantum mechanics emerges from a theory with significantly less computational power, then we expect the fidelity to decay significantly more rapidly than the quantum mechanics prediction for sufficiently deep circuits, which is the experimental signature that we propose to search for.   

Detecting the footprint of central charge using IBM quantum simulator

Phase transitions are ubiquitous phenomena in physics. Physical systems close to phase transition are known to become scale-invariant and manifest universality. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations which can be solved exactly and the corresponding field theory description is known as conformal field theory (CFT). While the central charge is one of the characterizations of the underlying symmetry of the corresponding CFT's, they have not been experimentally detected. In this work, we measure the central charge associated with CFT corresponding to various spin chains such as the transverse-field Ising model and XXZ chain by preparing the IBM quantum system. We show that at and close to the critical point, Shannon entropy of measurable quantities such as formation probabilities manifest a footprint of central charge allowing us to extract the central charge. Leveraging on the power of variational algorithms such as Variational Quantum Eigensolver (VQE) and Adiabatically-Assisted Variational Quantum Eigensolver (AAVQE), we prepare the ground state of the transverse-field Ising model with periodic and open boundary conditions, at and near the critical point and perform our measurement for various system sizes.   

Using NISQ Computing Devices to Simulate, Optimize, and Design Near-Term Quantum Communication Networks

Computing the dynamics of quantum many-bodied systems is a key challenge in developing applications for future quantum communication networks. Quantum computers show promise in their ability to efficiently simulate comlex quantum networks. We develop a hybrid quantum-classical computing framework that uses NISQ computing devices to  simulate, optimize, and design near-term quantum communication networks. We implement our framework in a publicly available python library that uses the PennyLane quantum machine learning framework to intergrate quantum computing APIs with machine learning libraries. We demonstrate our hybrid computing framework's ability to simulate and optimize small quantum networks and analyze its performance on both quantum hardware and classical simulator. For small networks with fewer than 20 qubits, we find that classical simulation is most efficent. For larger networks, we discuss how parallelization across many NISQ computing devices can yield efficient optimization and simulation. Finally, we explore how this software can be used to help design quantum internet applications.

Work funded by NSF award DMR-1747426   

Performing cat-basis quantum logic on modulated coherent state pulses using a photonic NISQ-era processor

Universal quantum-logic manipulation of modulated quantum light underlies several quantum-enhanced classical communications and sensing applications. In quantum-limited optical communications with binary phase shift keyed (BPSK) coherent states, attaining quantum-enhanced superadditive capacity hinges on the ability to perform quantum operations in the approximate qubit subspace spanned by cat states associated with the BPSK states. Such logic capability would enable the implementation of structured quantum joint detection receivers, e.g., based on the recently proposed belief propagation with quantum messages (BPQM) algorithm that can in principle discriminate codeword blocks of coherent state pulses quantum optimally. We consider alternative approaches to realizing photonic cat basis logic using linear optics, ancilla cat states, and photon number and homodyne measurements that have been previously proposed. We analyze the gate fidelities as a function of single-mode squeezing required in Gaussian boson sampling-type circuits that we use to generate the ancilla cat states involved in the gates and report thresholds on the squeezing levels necessary to retain quantum enhancement in discriminating communication codewords of small example codes using the BPQM receiver.   

Realizing Fractional-Quantum-Hall Gravitons on Quantum Computers

Intermediate-scale quantum technologies provide unprecedented opportunities for scientific discoveries while posing the challenge of identifying important problems that can take advantage of them. There has been a significant interest in the solid state and particle physics models that can be implemented on such devices. In solid-state materials, fractional quantum Hall phases are one of the leading platforms for realizing graviton-like excitations. However, their direct observation remains an experimental challenge. In this talk, we discuss how to generate these excitations on the IBM quantum processor. We first identify an effective one-dimensional model that captures the geometric properties and graviton-like dynamics of fractional quantum Hall states. We then develop an efficient, optimal-control-based variational quantum algorithm to simulate geometric quench and the subsequent graviton dynamics, which we successfully implement on the IBM quantum computer. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models that lend themselves to direct implementations on the existing quantum hardware.   

Quantum simulation of quantum field theory in the light-front formulation

Quantum field theory is a natural target for simulation on future quantum computers. We will discuss such simulations in the light-front formulation of quantum field theory. This formulation has several appealing features for such simulations foremost of which are its similarities to quantum chemistry where much effort has already been expended in developing and optimizing quantum simulation techiniques. In previous work (2002.04016, 2105.10941), we demonstrated this by developing quantum algorithms based on simulating time evolution and adiabatic state preparation. These algorithms are suitable for future large-scale fault tolerant quantum computers. We also explain how to formulate the relativistic bound state problem as an instance of the Variational Quantum Eigensolver (VQE) algorithm using the Basis Light-Front Quantization (BLFQ) technique (2011.13443, 2009.07885). The BLFQ formulation provides an ideal framework for benchmarking NISQ devices and testing existing algorithms on physically relevant problems such as the calculation of hadronic spectra and parton distribution functions.   

Playing quantum nonlocal games with six noisy qubits on the cloud

Nonlocal games are extensions of Bell inequalities, aimed at demonstrating quantum advantage. These games are well suited for noisy quantum computers because they only require the preparation of a shallow circuit, followed by the measurement of non-commuting observable. Here, we consider the minimal implementation of the nonlocal game proposed in Science 362, 308 (2018). We test this game by preparing a 6-qubit cluster state using quantum computers on the cloud by IBM, Ionq, and Honeywell. Our approach includes several levels of optimization, such as circuit identities and error mitigation and allows us to cross the classical threshold and demonstrate quantum advantage in one quantum computer. We conclude by introducing a different inequality that allows us to observe quantum advantage in less accurate quantum computers, at the expense of probing a larger number of circuits.   

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We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining multi-dimensional energy surfaces for small molecules and a spin model. Our method solves related variational problems in parallel by exploiting the global nature of Bayesian optimisation and sharing information between different optimisers. Parallelisation makes our method ideally suited to the next generation of variational problems with many physical degrees of freedom. This addresses a key challenge in scaling-up quantum algorithms towards demonstrating quantum advantage for problems of real-world interest.   

Noise-Assisted Variational Quantum Thermalization

Preparing thermal states on a quantum computer can have a variety of applications, from simulating many-body quantum systems to training machine learning models. Variational circuits have been proposed for this task on near-term quantum computers, but several challenges remain such as finding a scalable cost-function, avoiding the need of purification, and mitigating noise effects. We propose a new algorithm for thermal state preparation that tackles those three challenges by exploiting the noise of quantum circuits. We consider a variational architecture containing a depolarizing channel after each gate, with the ability to directly control the level of noise. We derive a closed-form approximation for the free-energy of such circuit and use it as cost function for our variational algorithm. For a variety of Hamiltonians and system sizes, we show that the ability for our algorithm to learn the thermal state strongly depends on the temperature: while a high fidelity can be obtained for high and low temperatures, we identify a specific range of temperatures for which the problem becomes harder. We hope that this first study on noise-assisted thermal state preparation will spark interest in future research on exploiting noise in variational algorithms.    

Quantum simulation of the spin-boson model with noisy gate-based quantum computer

We consider noisy gate-based quantum computers for the purpose of simulating the spin-boson model. We establish a bosonic bath by an ensemble of qubits with finite coherence times. The energy-level broadening of qubits is mapped to broadening of the simulated bath spectral density. We study how desired forms of the spectral density can be constructed by optimizing simulated spin-bath couplings and bath energies. We study the effect of different gate decompositions and system connectivity on the quality of the mapping to the desired form. In the ideal situation, the spin-bath couplings can be decomposed using only variable angle two-qubit gates, such as a variable Mølmer-Sørensen gate. In other cases, qubit noise can get mapped to two-body noise in the simulated spin-bath system, which does not have exact correspondence in the original spin-boson formulation. We show a numeric comparison of the quality of the mapping for various decompositions. Furthermore we compare the full inclusion of the two-body noise terms with an approximate mapping of the effects on the spectral density of the simulated spin-boson problem.   

Demonstrating scalable synthesis of multi-qubit gates

Multi-qubit entangling gates are essential in many quantum applications. Although arbitrary quantum gates can be decomposed into sequences of universal single- and two-qubit gates, the huge cost in circuit depth obstructs any meaningful operation within limited coherence time. We propose a scalable method for low-depth synthesis of multi-qubit controlled gates, based on a hardware-efficient construction of quantum AND logic. We successfully demonstrate Toffoli gates with up to 8 qubits on a few-IO, low-crosstalk superconducting quantum processor. We also test our gates in Grover's search algorithm with multiple amplification cycles.   

Classical Variational Optimization of Gate Sequences for Time Evolution of Translational Invariant Systems

The simulation of time evolution of large quantum systems is a classically challenging and often intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation thereof, where a certain desired accuracy can be achieved by raising the gate count adequately. In this work, we introduce a variational algorithm which uses solutions of classical optimizations to predict efficient quantum circuits for time evolution of translational invariant quantum systems. Our strategy improves on the Trotter-Suzuki ansatz in accuracy by several orders of magnitude. Alternatively, one can trade the accuracy gain against a reduction of gate count. This is important in NISQ-applications where the fidelity of the output state decays exponentially with the number of gates. We also propose an extension of our strategy to construct algorithms for the evolution of open boundary systems with translation symmetry in the bulk.