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Register a new userQuantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators
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Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a non-unitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here we present a general algorithm for implementing the action of any non-unitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. The results are in agreement with classical calculations, showing promise in simulating non-unitary operations on intermediate-term and future quantum devices.
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Coupling a quantum many-body system to an external environment dramatically changes its dynamics and offers novel possibilities not found in closed systems. Of special interest are the properties of the steady state of such open quantum many-body systems, as well as the relaxation dynamics towards the steady state. However, new computational tools are required to simulate open quantum many-body systems, as methods developed for closed systems cannot be readily applied. We review several approaches to simulate open many-body systems and point out the advances made in recent years towards the simulation of large system sizes.
Quantum simulation on emerging quantum hardware is a topic of intense interest. While many studies focus on computing ground state properties or simulating unitary dynamics of closed systems, open quantum systems are an interesting target of study owing to their ubiquity and rich physical behavior. However, their non-unitary dynamics are also not natural to simulate on near-term quantum hardware. Here, we report algorithms for the digital quantum simulation of the dynamics of open quantum systems governed by a Lindblad equation using an adaptation of the quantum imaginary time evolution (QITE) algorithm. We demonstrate the algorithms on IBM Quantums hardware with simulations of the spontaneous emission of a two level system and the dissipative transverse field Ising model. Our work shows that the dynamics of open quantum systems can be efficiently simulated on near-term quantum hardware.
Quantum simulations of electronic structure with transformed ab initio Hamiltonians that include some electron correlation effects a priori are demonstrated. The transcorrelated Hamiltonians used in this work are efficiently constructed classically, at polynomial cost, by an approximate similarity transformation with an explicitly correlated two-body unitary operator; they are Hermitian, include up to two-particle interactions, and are free of electron-electron singularities. To investigate whether the use of such transformed Hamiltonians can reduce resource requirements for general quantum solvers for the Schrodinger equation, we explore the accuracy and the computational cost of the quantum variational eigensolver, based on the unitary coupled cluster with singles and doubles (q-UCCSD). Our results demonstrate that transcorrelated Hamiltonians, paired with extremely compact bases, produce explicitly correlated energies comparable to those from much larger bases. The use of transcorrelated Hamiltonians reduces the number of CNOT gates by up to two orders of magnitude, and the number of qubits by a factor of three.
A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single qubit quantum channels ${T_t}$ specified by a generator $mathcal{L}$. This algorithm requires only $mathcal{O}big((||mathcal{L}||_{(1rightarrow 1)} t)^{3/2}/epsilon^{1/2} big)$ single qubit and CNOT gates and approximates the channel $T_t = e^{tmathcal{L}}$ up to chosen accuracy $epsilon$. Inspired by developments in Hamiltonian simulation, a decomposition and recombination technique is utilised which allows for the exploitation of recently developed methods for the approximation of arbitrary single-qubit channels. In particular, as a result of these methods the algorithm requires only a single ancilla qubit, the minimal possible dilation for a non-unitary single-qubit quantum channel.
The emerging field of quantum simulation of many-body systems is widely recognized as a very important application of quantum computing. A crucial step towards its realization in the context of many-electron systems requires a rigorous quantum mechanical treatment of the different interactions. In this pilot study, we investigate the physical effects beyond the mean-field approximation, known as electron correlation, in the ground state energies of atomic systems using the classical-quantum hybrid variational quantum eigensolver (VQE) algorithm. To this end, we consider three isoelectronic species, namely Be, Li-, and B+. This unique choice spans three classes, a neutral atom, an anion, and a cation. We have employed the unitary coupled-cluster (UCC) ansatz to perform a rigorous analysis of two very important factors that could affect the precision of the simulations of electron correlation effects within a basis, namely mapping and backend simulator. We carry out our all-electron calculations with four such basis sets. The results obtained are compared with those calculated by using the full configuration interaction, traditional coupled-cluster and the UCC methods, on a classical computer, to assess the precision of our results. A salient feature of the study involves a detailed analysis to find the number of shots (the number of times a VQE algorithm is repeated to build statistics) required for calculations with IBM Qiskits QASM simulator backend, which mimics an ideal quantum computer. When more qubits become available, our study will serve as among the first steps taken towards computing other properties of interest to various applications such as new physics beyond the Standard Model of elementary particles and atomic clocks using the VQE algorithm.
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