Session M08: NISQ: Noise Resilience, Mitigation, and Characterization

Error-resilient Tensor Network-based Ansatz for a Noisy Quantum Computer

Quantum computers can approximately prepare the ground states of many physical systems without using an exponential amount of resources. A hybrid quantum-classical algorithm, such as the variational quantum eigensolver (VQE), is a promising candidate for simulating electronic structures on a near-term device. Simulating complex systems with VQE, however, poses serious challenges because of limited qubit coherence times and non-negligible error rates within near-term devices. To tackle this challenge, we integrate the geometric structure of Deep Multiscale Entanglement Renormalization Ansatz (DMERA) circuits with the low-cost verification of fermionic parity symmetry to simulate ground states of the Fermi-Hubbard model. Requiring only a gate depth logarithmic in the total system size and a number of qubits independent of the system size, this protocol enables us to study larger systems than are possible for approaches with different ansatzes. Results for the Fermi-Hubbard model indicate that the protocol effectively leverages the ability of near-term devices to simulate complex lattice models.   

Machine learning of noise-resilient quantum circuits

In this work, we study how machine learning can be applied to formulate noise-aware circuit compilations that can be executed on near-term quantum hardware to produce reliable results. We will demonstrate that experimentally derived noise models can be used to go beyond naive circuit compilations for several example quantum algorithms. There are two inputs to our Noise-Aware Circuit Learning (NACL) method: a task, and a noisy gate alphabet. The task is defined by either a set of classical training data or a desired output quantum state or unitary. The output of NACL is a quantum gate sequence that optimally accomplishes the inputted task in the presence of the inputted noise model. Neither an ansatz nor the circuit depth of the gate sequence is an input to NACL. This is because NACL optimizes over the circuit structure and depth, which is in the spirit of task-oriented programming. We implement NACL for several different problems, such as computing state overlap, preparing multi-body entangled states, and implementing the quantum Fourier transform. In each case, we find that our overall figure-of-merit is significantly lower for NACL than for standard methods of circuit compilation.   

Noise-Resilient Quantum Dynamics Using Symmetry-Preserving Ansatzes

We describe and demonstrate a method for the computation of quantum dynamics on small, noisy universal quantum computers. This method relies on the idea of `restarting' the dynamics; at least one approximate time step is taken on the quantum computer and then a parameterized quantum circuit ansatz is optimized to produce a state that well approximates the time-stepped results. The simulation is then restarted from the optimized state. By encoding knowledge of the form of the solution in the ansatz, such as ensuring that the ansatz has the appropriate symmetries of the Hamiltonian, the optimized ansatz can recover from the effects of decoherence. This allows for the quantum dynamics to proceed far beyond the standard gate depth limits of the underlying hardware, albeit incurring some error from the optimization, the quality of the ansatz, and the typical time step error. We demonstrate this methods on the Aubry-André model with interactions at half-filling, which shows interesting many-body localization effects in the long time limit. Our method is capable of performing high-fidelity Hamiltonian simulation hundred of time steps longer than the standard Trotter approach. These results demonstrate a path towards using small, lossy devices to calculate quantum dynamics.   

Error Mitigation in Data Driven Circuit Learning

Mitigating state preparation and measurement (SPAM) errors has been shown to improve the performance of noisy intermediate scale quantum (NISQ) devices. This talk focuses on the incorporation of matrix-based SPAM error mitigation into data-driven circuit learning for parameterized circuits implementing generative modeling tasks. We discuss how the choice of nonlinear optimization, loss function and the structure of the target distributions can affect the computational cost associated with gradient-based training of densely parameterized quantum circuits trained on NISQ hardware accessed via cloud-based queues.   

Preserving Symmetries for Variational Quantum Eigensolvers in the Presence of Noise

One of the most promising applications of noisy intermediate scale quantum computers (NISQ) is the simulation of molecular Hamiltonians using the variational quantum eigensolver (VQE) algorithm, which has already been demonstrated on small molecules. We show that encoding symmetries of the simulated Hamiltonian at the level of the ansatz used in the VQE provides improvements to both classical and quantum resources. We further verify that these improvements persist in the presence of noise by simulating such variational forms in noisy environments and evaluating their ability to find the correct ground state. To further improve the quality of our results, we implement state of the art error mitigation techniques. Finally, we demonstrate our results in experiment by using IBMQ quantum processors.   

Querying quantum computers with neural networks: precise measurements and noise reduction

In this talk I will introduce neural-network estimators for quantum observables, obtained by integrating the measurement apparatus of a quantum simulator with neural networks. Unsupervised learning of single-qubit measurement data can produce estimates of complex observables free of quantum noise. Precise estimates are achieved for quantum chemistry Hamiltonians, with a reduction of several orders of magnitude in the amount of measurements needed compared to standard estimators. Finally, I will show results on molecular systems obtained using IBM superconducting quantum processors, combining precise measurements with error mitigation strategies.   

Measurement Reduction in Variational Quantum Algorithms

Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in the Hamiltonian. The number of separate measurements required can become overwhelmingly large for problems at the scale of NISQ hardware that may soon be available. We approach this problem from the perspective of contextuality, and use unitary partitioning to define VQE procedures in which additional unitary operations are appended to the ansatz preparation circuit to reduce the number of terms one needs to measure. This approach may be tuned to hardware specifications in order to use all coherent resources available after ansatz preparation. We investigate this technique for a variety of Hamiltonian classes, in particular the electronic structure Hamiltonian from quantum chemistry. There, we prove that term reduction always scales at least linearly with respect to the number of orbitals, and we supplement this result with numerical studies.   

Noise Resilience of Variational Quantum Compiling

Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary U is compiled into a short-depth gate sequence V. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence V (i.e., the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver.   

Quantum Dynamical Complexity and Reliability of Analog Quantum Simulation

The NISQ era is characterized by the absence of fully fault-tolerant quantum simulators, which raises a question about the reliability of such devices. To address this, we seek to quantify the reliability of an analog quantum simulator, which doesn’t have access to error correction, in the presence of perturbations that make the dynamics quantum chaotic. In doing so we seek to identify the relationship between the robustness of the quantities that we seek to extract from the simulator and the dynamical complexity of the analog evolution. As one measure, we quantify the complexity by the number of variables that one must track to approximately yield the output within a desired accuracy. We address these questions by studying the basic paradigms such as the ground state and the excited state quantum phase transitions in the Lipkin-Meshkov-Glick (LMG) model[1].

References:
[1]Marco Távora, and Francisco Pérez-Bernal. "Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation." Physical Review A 94.1 (2016): 012113

  

Exploiting molecular point group symmetries for quantum simulation

Simulating molecules is believed to be one of the early-stage applications for quantum computers. Current
state-of-the-art quantum computers are limited in size and coherence, therefore optimizing resources to execute
quantum algorithms is crucial. In this work, we develop a formalism to reduce the number of qubits required
for simulating molecules using spatial symmetries, by finding qubit representations of irreducible symmetry
sectors. We present our results for various molecules and elucidate a formal connection of this work with a
previous technique that analyzed generic Z2 Pauli symmetries.   

Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware

We report on a quantum-classical simulation of a two-site dynamical mean-field theory (DMFT) calculation. We use IBM's superconducting qubit chip to compute the zero-temperature impurity Green's function in the time domain and a classical computer to fit the measured Green's function. We find that Trotter errors and noise from the quantum chip lead to inaccurate updates to impurity parameters, preventing the DMFT algorithm from converging to the correct solution. To mitigate this issue, we determine the update to the hybridization parameter by integrating the low-frequency peaks in the spectral function. This allows us to iterate the DMFT loop to self-consistency for a strongly Mott insulating system at half-filling.   

Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States

Many applications of quantum simulation require to prepare and then characterize quantum states by efficiently estimating k-body reduced density matrices (k-RDMs), from which observables of interest are obtained. Naive estimation of such RDMs require repeated state preparation for each matrix element. However, commuting matrix elements may be measured simultaneously, allowing for a significant cost reduction.
In this work we design schemes for such parallelization with near-optimal complexity in the system size N. We describe a scheme to sample all elements of a qubit k-RDM using only O(3^k log^k-1(N)) unique measurements. We detail a scheme to sample all elements of the fermionic 2-RDM using only O(N²) unique measurements, with O(N)-depth measurement circuit. We prove a lower bound of O(N^k) on the number of unique measurements required to directly sample all elements of a fermionic k-RDM, making our fermionic 2-RDM scheme asymptotically optimal. We finally construct circuits to sample the expectation value of a linear combination of ω anti-commuting 2-body fermionic operators with O(ω) gates on a linear array.   

Extracting state purity of a large system with limited control

As superconducting quantum devices with a large number of qubits become feasible, they offer an avenue for quantum simulation of equally large systems. The extraction of global information, such as a state's purity or entropy, remains a challenging prospect, generally requiring independent control of each qubit. Here, we propose a method of extracting the purity with limited control, applied through multiplexed dispersive readout. We consider the required control fidelity, and scaling of the number of measurements with system size.   

Evaluation of the classical sampling cost for noisy quantum circuits

In order to demonstrate quantum computational supremacy, quantum computers are being developed by Google, IBM and so on.
In an actual quantum device, there is a non-negligible amount of noise, which would deteriorate the advantage of quantum computation.
Therefore, it is necessary to evaluate overhead for classical simulation of quantum computation with taking the noise effect into account.
Recently, classical simulation algorithms such as stabilizer propagation and Pauli propagation.
In this work, we estimate the overhead for classical simulation of noisy quantum circuits in terms of Robustness of Magic (RoM) and stabilizer norm, and compare them.
Specifically, we study simulation costs of the noisy random quantum circuits and Trotterized quantum circuits.
We show that the Trotterized quantum circuits can be easily simulatable by adding small noise.