Universal Quantum Computation with the Exchange Interaction

Abstract

Experimental implementations of quantum computer architectures are now being investigated in many different physical settings. The full set of requirements that must be met to make quantum computing a reality in the laboratory [1] is daunting, involving capabilities well beyond the present state of the art. In this report we develop a significant simplification of these requirements that can be applied in many recent solid-state approaches, using quantum dots [2], and using donor-atom nuclear spins [3] or electron spins [4]. In these approaches, the basic two-qubit quantum gate is generated by a tunable Heisenberg interaction (the Hamiltonian is $H_{ij}=J(t){\vec{S}}_i\cdot {\vec{S}}_j$ between spins $i$ and $j$), while the one-qubit gates require the control of a local Zeeman field. Compared to the Heisenberg operation, the one-qubit operations are significantly slower and require substantially greater materials and device complexity, which may also contribute to increasing the decoherence rate. Here we introduce an explicit scheme in which the Heisenberg interaction alone suffices to exactly implement any quantum computer circuit, at a price of a factor of three in additional qubits and about a factor of ten in additional two-qubit operations. Even at this cost, the ability to eliminate the complexity of one-qubit operations should accelerate progress towards these solid-state implementations of quantum computation.

revtex, 2 figures, this version appeared in Nature

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• The computational power of matchgates and the XY interaction on arbitrary graphs
• On the robustness of the hybrid qubit computational gates through simulated randomized benchmarking protocols
• Leakage and dephasing in ${}^{28}$Si-based exchange-only spin qubits
• Erasure conversion for singlet-triplet spin qubits enables high-performance shuttling-based quantum error correction
• Various correlations in a Heisenberg XXZ spin chain both in thermal equilibrium and under the intrinsic decoherence
• Two-qubit logical operations in three quantum dots system
• Recipes for the Digital Quantum Simulation of Lattice Spin Systems
• Supercomputer simulations of transmon quantum computers
• Computational Complexity of Some Quantum Theories in $1+1$ Dimensions
• Negative refraction index of the mesoscopic left-handed transmission line in the thermal Fock state
• Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation
• Implementing controlled-NOT gate based on free spin qubits with semiconductor quantum-dot array
• Continuous dynamical decoupling and decoherence-free subspaces for qubits with tunable interaction
• Operating two exchange-only qubits in parallel
• Quantum Computers and Decoherence: Exorcising the Demon from the Machine
• Latched readout for the quantum dot hybrid qubit
• Observation of low-lying excitations of electrons in coupled quantum dots
• Emergence of robust gaps in 2D antiferromagnets via additional spin-1/2 probes
• Multi-qubit DC gates over an inhomogeneous array of quantum dots
• Universal control of superexchange in linear triple quantum dots with an empty mediator
• Proposal for a cavity-induced measurement of the exchange coupling in quantum dots
• Pauli Spin Blockade in a Resonant Triple Quantum Dot Molecule
• Topological quantum compilation of two-qubit gates
• Negative refraction index of the quantum lossy left-handed transmission lines affected by the displaced squeezed Fock state and dissipation
• Two-qubit sweet spots for capacitively coupled exchange-only spin qubits
• Fast quantum computing with semiconductor quantum dots in a microcavity
• Dynamics of quantum entanglement in the reservoir with memory effects
• Derivation of the robustness from the concurrence
• Functional renormalization group study of parallel double quantum dots: Effects of asymmetric dot-lead couplings
• Long range universal quantum computation in large-size coupled cavity array independent of cavity number
• A Chain-Boson Model for the Decoherence and Relaxation of a Few Coupled SQUIDs in a Phonon Bath
• Charge qubit entanglement via conditional single-electron transfer in an array of quantum dots
• Geometry of quantum state manifolds generated by the Lie algebra operators
• Circular-polarization sensitive metamaterial based on triple quantum-dot molecules
• Designed defects in 2D antidot lattices for quantum information processing
• Entangling spin and charge degrees of freedom in semiconductor quantum dots
• A Low Complexity Scheme for Entanglement Distributor Buses
• Switching the sign of photon induced exchange interactions in semiconductor microcavities with finite quality factors
• Self-Quenching of Nuclear Spin Dynamics in Central Spin Problem
• Minimal Non-orthogonal Gate Decomposition for Qubits with Limited Control
• Exchange-Symmetrized Qudit Bell Bases and Bell-State Distinguishability
• Development of research network on Quantum Annealing Computation and Information using Google Scholar data
• SU(d)-Symmetric Random Unitaries: Quantum Scrambling, Error Correction, and Machine Learning
• Ab initio modelling of quantum dot qubits: Coupling, gate dynamics and robustness versus charge noise
• Universality of swap for qudits: a representation theory approach
• Fast optical control of a coded qubit in a triple quantum dot
• Reductions in finite-dimensional quantum mechanics: from symmetries to operator algebras and beyond
• Universal quantum logic gates in a scalable Ising spin quantum computer
• True decoherence-free-subspace derived from a semiconductor double quantum dot Heisenberg spin-trimer
• Dressed basis sets for the modeling of exchange interactions in double quantum dots
• On the validity of microscopic calculations of double-quantum-dot spin qubits based on Fock-Darwin states
• Mutual information-energy inequality for thermal states of a bipartite quantum system
• Finding and classifying an infinite number of cases of the marginal phase transition in one-dimensional Ising models
• Impact of the valley orbit coupling on exchange gate for spin qubits in silicon quantum dots
• Encoded Universality of Quantum Computations on the Multi-Atomic Ensembles in the QED Cavity
• Simulating decoherence of two coupled spins using the generalized cluster correlation expansion
• The Spin Density Matrix I: General Theory and Exact Master Equations
• Decoherence and fidelity enhancement during shuttling of entangled spin qubits
• Universal Quantum Computation and Leakage Reduction in the 3-Qubit Decoherence Free Subsystem
• Magnetic Field Detection Using a Two-Qubit System Under Noisy Heisenberg Interaction
• Approaches to Quantum Error Correction
• Spin Diffusion and Relaxation in Solid State Spin Quantum Computer
• Dzyaloshinskii-Moriya-type spin-spin interaction from mixed-parity superconductivity
• Probing a Single Nuclear Spin in a Silicon Single Electron Transistor
• Transport-induced suppression of nuclear field fluctuations in multi-quantum-dot systems
• Entanglement creation in semiconductor quantum dot charge qubit
• Quantum computer with atomic logical qubits encoded on macroscopic three-level systems in common quantum electrodynamic cavity
• Quantum entanglement response to pulsed gate modulation
• Quantum Gates Between Two Spins in a Triple Dot System with an Empty Dot
• Generation of robust entangled states in a non-hermitian periodically driven two-band Bose-Hubbard system
• The Computational Power of Non-interacting Particles
• Quantum Computing on Multi-atomic Ensembles in Quantum Electrodynamics Cavity
• Artificial versus Natural Atoms: The uncanny capability of the many-body Schrödinger equation to produce emergent behavior
• Creating Quantum Cluster States embedded in ancillary baths
• Synthesis of Energy-Conserving Quantum Circuits with XY interaction
• Landau-Zener Transitions in Spin Qubit Encoded in Three Quantum Dots
• Quantum Dots: Coulomb Blockade, Mesoscopic Fluctuations, and Qubit Decoherence
• Measuring and correcting nanosecond pulse distortions in quantum-dot spin qubits
• Harnessing subspace controllability: Dynamical generation of Dicke states in Heisenberg-coupled qubit arrays with a single local control
• Quantum dynamics of spin-J particles in static and rotating magnetic fields: Entanglement resonances and kinks
• Efficient Implementation of a Single-Qutrit Gate Set via Coherent Control
• Jenga-Krotov algorithm: Efficient compilation of multi-qubit gates for exchange-only qubits
• Generation of chiral spin state by quantum simulation
• Protected Rabi oscillation induced by natural interactions among physical qubits
• Monochromatic composite right/left handedness achieved in the quantized composite right/left handed transmission line
• Work-sharing of qubits in topological error corrections