In situ upgrade of quantum simulators to universal computers

Abstract

Quantum simulators, machines that can replicate the dynamics of quantum systems, are being built as useful devices and are seen as a stepping stone to universal quantum computers. A key difference between the two is that computers have the ability to perform the logic gates that make up algorithms. We propose a method for learning how to construct these gates efficiently by using the simulator to perform optimal control on itself. This bypasses two major problems of purely classical approaches to the control problem: the need to have an accurate model of the system, and a classical computer more powerful than the quantum one to carry out the required simulations. Strong evidence that the scheme scales polynomially in the number of qubits, for systems of up to 9 qubits with Ising interactions, is presented from numerical simulations carried out in different topologies. This suggests that this in situ approach is a practical way of upgrading quantum simulators to computers.Recent and ongoing work on building large quantum systems is leading to simulators that are able to model physical phenomena, allowing questions about the underlying science to be answered [1][2][3]. These machines contain a register of quantum particles, typically two level quantum systems (qubits) storing quantum information. The presence of interactions between these leads to dynamics that, by varying control parameters in the system Hamiltonian, can replicate the quantum behaviour of systems of interest. This, however, is less general than a quantum computer which is able is to perform a universal set of logic gates on the qubits [4].Provided some control parameters can be varied in time, it is in principle possible to do an arbitrary gate on a quantum many-body system such as a quantum simulator [5][6][7]. Finding the right time-dependency however relies almost exclusively on numerical methods, especially when physical constraints on the control fields are taken into account [8,9]. These methods require a very precise knowledge of the parameters of a system, a daunting task for a machine with a huge number of degrees of freedom. Furthermore, they are intractable on a classical computer if the quantum simulator we want to solve the problem for is large enough to do something beyond the capabilities of classical computers. These two difficulties provide a major obstacle in using quantum simulators to perform arbitrary computation.We circumvent these problems by showing how well-known existing numerical methods can be translated to run in situ on the quantum simulator itself, as illustrated in Fig.1. A mix of an-

Enhancing quantum control by bootstrapping a quantum processor of 12 qubits

“…The MQFC protocol can be modified to extract the desired fidelities and optimize the pulse sequence accordingly (details in Appendix B in [28]). Note that right after our work, a five-qubit implementation of a different quantum algorithm for gate optimization was reported [35].…”

Quantum-assisted quantum compiling

“…(b) The Local Hilbert-Schmidt Test, which is the same as the Hilbert-Schmidt Test except that only two of the 2n qubits are measured at the end. Shown is the measurement of the qubits A1 and B1, and the probability that both qubits are in the state |0 is given by (25) with j = 1.…”

Optimal quantum control with poor statistics

“…Typical examples for such figures of merit -also referred to as target functionals -include state-fidelities [27], gate fidelities [9,28,29], the expectation values of an entanglement witness, or also more non-linear quantities like entanglement measures [17,27,30,31] or the Fisher information [10,32]. Tunable control parameters often include piecewise constant amplitudes of external electric or magnetic fields [2][3][4][5][6]33], but temporal shapes of laser-or microwave pulse with parametrization in terms of Fourier series are also objects of optimization [7,8,27,[34][35][36].…”

“…This long product of binomial distributions is the explicit form of the general object P (D|f ) entering the Bayesian inference above in Eq. (2). With this modeling in hand one can explicitly construct the predictive probability density P (f (θ)|D), based on any level of measurement noise, including the extreme case of no repetitions, i.e.…”

“…Among the most popular methods to perform optimizations directly based on experimental outcomes, gradient-based routines [2][3][4][5][6] and Nelder-Mead [7][8][9][10][11] have the advantage of simplicity and fast convergence when the underlying optimization landscape is well-behaved. Their performance can however be limited in the presence of many local minima [12,13] or plateaus [14].…”