Long-time simulations for fixed input states on quantum hardware

Abstract

Publicly accessible quantum computers open the exciting possibility of experimental dynamical quantum simulations. While rapidly improving, current devices have short coherence times, restricting the viable circuit depth. Despite these limitations, we demonstrate long-time, high fidelity simulations on current hardware. Specifically, we simulate an XY-model spin chain on Rigetti and IBM quantum computers, maintaining a fidelity over 0.9 for 150 times longer than is possible using the iterated Trotter method. Our simulations use an algorithm we call fixed state Variational Fast Forwarding (fsVFF). Recent work has shown an approximate diagonalization of a short time evolution unitary allows a fixed-depth simulation. fsVFF substantially reduces the required resources by only diagonalizing the energy subspace spanned by the initial state, rather than over the total Hilbert space. We further demonstrate the viability of fsVFF through large numerical simulations, and provide an analysis of the noise resilience and scaling of simulation errors.

Assisted quantum simulation of open quantum systems

“…For instance, the XY spin chain with Hamiltonian, , has unitary operators. 18 The Heisenberg n -qubit chain with open boundaries, , has unitary operators. 59 Note that the quantity J scales polynomially with the system size, , for certain Hamiltonians such as quantum systems with sparse interactions.…”

“…In the near term, the noisy intermediate-scale (50–100 qubit) quantum (NISQ) computers applying variational quantum algorithms (VQAs) avoid the implementation of QEC and have shallow quantum circuit compared with the FTQ computers. 14 A variety of high-impact applications of NISQ devices have been studied in many-body quantum system simulations 15 , 16 , 17 , 18 , 19 and machine learning. 20 , 21 However, there have been no corresponding VQAs for some special problems such as the direct estimation of energy difference between two structures in chemistry, although a promising UQA has been already developed.…”

Quantum Computation of Frequency-Domain Molecular Response Properties Using a Three-Qubit iToffoli Gate

“…Early experimental demonstrations of quantum simulation algorithms have focused on computing ground-and excited-state energies of small molecules [4][5][6][7] or few-site spin [6] and fermionic models [8]. More recently, the scale of quantum simulation experiments has increased in terms of numbers of qubits, diversity of gate sets, and complexity of algorithms, as manifested in simulation of models based on real molecules and materials [9][10][11], various phases of matter such as thermal [12,13], topological [14,15] and many-body localized states [16,17], as well as holographic quantum simulation using quantum tensor networks [18][19][20]. As quantum advantages in random sampling have been established on quantum hardware [21,22], focus has turned to the experimental demonstration of quantum advantages in problems of physical significance [23].…”

Generalization with quantum geometry for learning unitaries

“…This latter ability is called generalization and has been intensely studied recently [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Constructing models that generalize well is essential for quantum machine learning tasks such as variational learning of unitaries [18][19][20][21][22][23][24], which is applied to unitary compiling [11,25,26], quantum simulation [10,27,28], quantum autoencoders [29,30] and black-hole recovery protocols [31].…”

“…Model.-Let us consider a target unitary V , which we want to approximate with ansatz unitary U (θ) parameterized by M -dimensional parameter vector θ. We learn from a training set S L = {|ψ , V |ψ } L =1 of L states which are randomly drawn from a distribution of states |ψ ∈ W [10,28,59]. We learn by minimizing the cost function given by the fidelity…”