Energy Cost of Quantum Circuit Optimisation: Predicting That Optimising Shor’s Algorithm Circuit Uses 1 GWh

Quantum circuits are difficult to simulate, and their automated optimisation is complex as well. Significant optimisations have been achieved manually (pen and paper) and not by software. This is the first in-depth study on the cost of compiling and optimising large-scale quantum circuits with state-of-the-art quantum software. We propose a hierarchy of cost metrics covering the quantum software stack and use energy as the long-term cost of operating hardware. We are going to quantify optimisation costs by estimating the energy consumed by a CPU doing the quantum circuit optimisation. We use QUANTIFY, a tool based on Google Cirq, to optimise bucket brigade QRAM and multiplication circuits having between 32 and 8,192 qubits. Although our classical optimisation methods have polynomial complexity, we observe that their energy cost grows extremely fast with the number of qubits. We profile the methods and software and provide evidence that there are high constant costs associated to the operations performed during optimisation. The costs are the result of dynamically typed programming languages and the generic data structures used in the background. We conclude that state-of-the-art quantum software frameworks have to massively improve their scalability to be practical for large circuits.

Towards Compact Modeling of Noisy Quantum Computers: A Molecular-Spin-Qubit Case of Study

Classical simulation of Noisy Intermediate Scale Quantum computers is a crucial task for testing the expected performance of real hardware. The standard approach, based on solving Schrödinger and Lindblad equations, is demanding when scaling the number of qubits in terms of both execution time and memory. In this article, attempts in defining compact models for the simulation of quantum hardware are proposed, ensuring results close to those obtained with standard formalism. Molecular Nuclear Magnetic Resonance quantum hardware is the target technology, where three non-ideality phenomena—common to other quantum technologies—are taken into account: decoherence, off-resonance qubit evolution, and undesired qubit-qubit residual interaction. A model for each non-ideality phenomenon is embedded into a MATLAB simulation infrastructure of noisy quantum computers. The accuracy of the models is tested on a benchmark of quantum circuits, in the expected operating ranges of quantum hardware. The corresponding outcomes are compared with those obtained via numeric integration of the Schrödinger equation and the Qiskit’s QASMSimulator. The achieved results give evidence that this work is a step forward towards the definition of compact models able to provide fast results close to those obtained with the traditional physical simulation strategies, thus paving the way for their integration into a classical simulator of quantum computers.

Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds

Here we report a breakthrough in the fabrication of a long lifetime transmon qubit. We use tantalum films as the base superconductor. By using a dry etching process, we obtained transmon qubits with a best T1 lifetime of 503 μs. As a comparison, we also fabricated transmon qubits with other popular materials, including niobium and aluminum, under the same design and fabrication processes. After characterizing their coherence properties, we found that qubits prepared with tantalum films have the best performance. Since the dry etching process is stable and highly anisotropic, it is much more suitable for fabricating complex scalable quantum circuits, when compared to wet etching. As a result, the current breakthrough indicates that the dry etching process of tantalum film is a promising approach to fabricate medium- or large-scale superconducting quantum circuits with a much longer lifetime, meeting the requirements for building practical quantum computers.

Filling up complex spectral regions through non-Hermitian disordered chains

Eigenspectra that fill regions in the complex plane have been intriguing to many, inspiring research from random matrix theory to esoteric semi-infinite bounded non-Hermitian lattices. In this work, we propose a simple and robust ansatz for constructing models whose eigenspectra fill up generic prescribed regions. Our approach utilizes specially designed non-Hermitian random couplings that allow the co-existence of eigenstates with a continuum of localization lengths, mathematically emulating the effects of semi-infinite boundaries. While some of these couplings are necessarily long-ranged, they are still far more local than what is possible with known random matrix ensembles. Our ansatz can be feasibly implemented in physical platforms such as classical and quantum circuits, and harbors very high tolerance to imperfections due to its stochastic nature.

VQE method: a short survey and recent developments

The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by the choice of the variational ansatz used to represent the trial wave function. Hence, the construction of an efficient ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatzes for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing efficient ansatzes that fall into two categories—chemistry–inspired and hardware–efficient—that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

Collective unitary evolution with linear optics by Cartan decomposition

Unitary operation is an essential step for quantum information processing. We first propose an iterative procedure for decomposing a general unitary operation without resorting to controlled-NOT gate and single-qubit rotation library. Based on the results of decomposition, we design two compact architectures to deterministically implement arbitrary two-qubit polarization-spatial and spatial-polarization collective unitary operations, respectively. The involved linear optical elements are reduced from 25 to 20 and 21 to 20, respectively. Moreover, the parameterized quantum computation can be flexibly manipulated by wave plates and phase shifters. As an application, we construct the specific quantum circuits to realize two-dimensional quantum walk and quantum Fourier transformation. Our schemes are simple and feasible with the current technology.

Estimating Gibbs partition function with quantum Clifford sampling

The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its calculation generally involves summing over an exponential number of terms and can thus quickly grow to be intractable. Accurately and efficiently estimating the partition function of its corresponding system Hamiltonian then becomes the key in solving quantum many-body problems. In this paper we develop a hybrid quantumclassical algorithm to estimate the partition function, utilising a novel Clifford sampling technique. Note that previous works on quantum estimation of partition functions require O(1/ε√∆)-depth quantum circuits [17, 23], where ∆ is the minimum spectral gap of stochastic matrices and ε is the multiplicative error. Our algorithm requires only a shallow O(1)-depth quantum circuit, repeated O(n/ε2) times, to provide a comparable ε approximation. Shallow-depth quantum circuits are considered vitally important for currently available NISQ (Noisy Intermediate-Scale Quantum) devices.