Superconducting qubit circuit emulation of a vector spin-1/2

Abstract

We propose a superconducting qubit that fully emulates a quantum spin-1/2, with an effective vector dipole moment whose three components obey the commutation relations of an angular momentum in the computational subspace. Each of these components of the dipole moment also couples approximately linearly to an independently-controllable external bias, emulating the linear Zeeman effect due to a fictitious, vector magnetic field over a broad range of effective total fields around zero. This capability, combined with established techniques for qubit coupling, should enable for the first time the direct, controllable hardware emulation of nearly arbitrary, interacting quantum spin-1/2 systems, including the canonical Heisenberg model. Furthermore, it constitutes a crucial step both towards realizing the full potential of quantum annealing, as well as exploring important quantum information processing capabilities that have so far been inaccessible to available hardware, such as quantum error suppression, Hamiltonian and holonomic quantum computing, and adiabatic quantum chemistry.Quantum spin-1/2 models serve as basic paradigms for a wide variety of physical systems in quantum statistical mechanics and many-body physics, and are among the most highly studied in the context of quantum phase transitions and topological order [1][2][3][4]. In addition, since the spin-1/2 in a magnetic field is one of the simplest realizations of a qubit, many quantum information processing paradigms draw heavily on concepts which originated from or are closely related to quantum magnetism. For example, quantum spin-1/2 language is used to describe nearly all of the constructions underlying quantum error-correction [5-7] and error-suppression [8,9] methods. It is also the most commonly-used framework for specifying engineered Hamiltonians in many other quantum protocols such as quantum annealing [10,11], adiabatic topological quantum computing [12], quantum simulation [13-17], Hamiltonian and holonomic quantum computing [9,[18][19][20][21], and quantum chemistry [22][23][24].The conventional method for simulating vector spin-1/2 Hamiltonians is based on the 'gate-model' quantum simulation paradigm, and uses pulsed, high-speed sequences of discrete, non-commuting gate operations [25-27] to approximate time-evolution under a desired Hamiltonian [28,29]. In this paradigm, simulating a different Hamiltonian simply requires reprogramming the hardware with a different sequence of gates, a desirable property so long as the error introduced by the discretization can be kept sufficiently low. Unfortunately, this becomes increasingly difficult as the required spin interactions become stronger and/or more complex, since for a fixed gate duration 1 , the discretization error grows both with the strength of the spinspin interactions, and with the number of mutually-noncommuting terms they contain. In addition, gate-based implementation necessarily implies that the system occupies Hilbert space far above its ground state, and the resulting information ...

Demonstration of a Nonstoquastic Hamiltonian in Coupled Superconducting Flux Qubits

“…The renormalized capacitances are defined as C 1(2) = C 1(2) + C 12 C 2(1) /(C 2(1) + C 12 ). Capacitive couping has been proposed and analyzed theoretically for flux qubits in [27][28][29][30] and is commonly used in transmon qubits [31,32].…”

Validating a two-qubit nonstoquastic Hamiltonian in quantum annealing

“…While the role of such ground states in improving the performance of quantum annealing remains an open research question, the known examples where such an improvement is possible [14,15,18] definitely generate ground states with both positive and negative amplitudes [18]. We hope our proposal will be relevant for testing next generation quantum annealers with such interactions [21].…”

“…Evidence that is often cited for this predicament is that standard quantum annealing implements a stoquastic Hamiltonian [8][9][10][11][12][13] throughout the anneal, which makes it amenable to classical simulation using Quantum Monte Carlo techniques. The introduction of novel interactions at intermediate points in the anneal that make the Hamiltonian non-stoquastic would prevent this, and it remains an open question to what extent this will improve the current situation [14][15][16][17][18] [19] Nevertheless, experimental realizations of such interactions are ongoing [20,21], and here we propose a method to validate the implementation of tunable antiferromagnetic XX interactions within the constraints of the quantum annealing protocol, i.e. the evolution terminates on a Hamiltonian H P that is diagonal in the computational basis, and only measurements in the computational basis at the end of the anneal are allowed.…”

Locally suppressed transverse-field protocol for diabatic quantum annealing

“…The need for increased flexibility of the annealing schedules, including independent control of the transverse fields, has been widely recognized (see Ref. [33] and references therein), putting such capabilities on the roadmap for future devices [29,31,34,44,45].…”

“…Furthermore, it has recently been argued that nonstoquasticity is an essential requirement of an annealing Hamiltonian for demonstrating such speedups [24]. As of yet, there is little work on the experimental implementation of hardware that provides nonstoquastic terms [28], and further the hardware required to implement tuneable nonstoquastic two-local interaction terms [29] is currently under development and is not expected to be available for some time. As such, little is known about how a quantum annealing processor will perform with a diabatic protocol, and it is expected that the environment will play a greater role in determining the feasibility of the method [20].…”