Domain-specific compilers for dynamic simulations of quantum materials on quantum computers

Abstract

Dynamic simulation of materials is a promising application for noisy intermediate-scale quantum (NISQ) computers. The difficulty in carrying out such simulations is that a quantum circuit must be executed for each time-step, and in general, these circuits grow in size with the number of time-steps simulated. NISQ computers can only produce high-fidelity results for circuits up to a given size due to gate error rates and qubit decoherence times, limiting the number of time-steps that can be successfully simulated. Here, we present a method for producing circuits that are constant in depth with increasing number of simulated time-steps for dynamic simulations of quantum materials for a specialized set of Hamiltonians derived from the one-dimensional Heisenberg model. We show how to build the constant-depth circuit structure for each system size, where the number of CNOT gates in the N -qubit constant-depth circuit structure grows only quadratically with N . The constantdepth circuits, which comprise an array of two-qubit matchgates on nearest-neighbor qubits, are constructed based on a set of multi-matchgate identities that we introduce as conjectures. Tutorials with the full code for generating our constant-depth circuits for the XY and transverse field Ising models are included. Using our constant-depth circuits, we are successfully able to demonstrate longtime dynamic simulations of quantum systems with up to five spins on available quantum hardware. Such constant-depth circuits could enable simulations of long-time dynamics for scientifically and technologically relevant quantum materials, enabling the observation of interesting and important atomic-level physics.

ArQTiC: A Full-stack Software Package for Simulating Materials on Quantum Computers

“…Thus, while the constant-depth results may not be exactly quantitatively accurate, they do demonstrate the trend of Anderson localization, while the IBM-compiled results do not. Figure 6 plots the total number of gates in the quantum circuit for each timestep for circuits compiled with IBM's native compiler (red dashed-dot line) versus using the domain-speciic, constant-depth circuit compilation technique [10] integrated into ArQTiC. While the circuits to obtain similar results to the red dashed-dot lines in Figure 5 can be achieved with other quantum software platforms, much greater eforts and domain-knowledge are required.…”

“…The default method is to use the native compiler of the target backend. In this case, the Hamiltonian of interest falls into the special subset of Hamiltonians for which a domain-speciic compiler [10] can be used, which can generate constant-depth circuits. The user may elect this compilation method by setting the constant_depth attribute to łTruež.…”

“…Here, domain-speciic refers to the fact that this circuit optimization technique can only be implemented for special subset of Hamiltonians, which are outlined in Ref. [10]. For generic Hamiltonians, circuits for real-time evolution are expected to grow at least linearly in size with simulation time.…”

VACSEN: A Visualization Approach for Noise Awareness in Quantum Computing

“…Second, a quantum algorithm can be compiled to various compiled circuits with significantly-different noise on the same quantum computer. For a large-scale quantum algorithm, the compiled circuits can be several hundreds [8,44]. The noise of compiled physical circuit needs to be evaluated from different perspectives, e.g., the circuit depths and the noise of involved qubits or quantum gates [6].…”

Evaluating low-depth quantum algorithms for time evolution on fermion-boson systems

“…In the second case, time evolution is recast into an optimisation problem via an appropriate variational principle, leading to the construction of the wavefunction through an ansatz quantum circuit. Examples of the * nathan.fitzpatrick@cambridgequantum.com first family include Variational Fast Forwarding [18,19], Incremental Structured Learning (ISL) [20], Variational Time Dependent Phase Estimation [21], circuit compilers for time dependent applications [22], Adaptive Product Formula [23], Quantum Imaginary Time Evolution [24] and truncated Dyson Series [25]. Examples of the second family of methods are Variational Quantum Simulation (VQS) [26][27][28][29], Hardware-Efficient Real Time Evolution [30], Quantum Assisted Simulation [31] and Truncated Taylor Series [32].…”