Implementation Of Quantum Computation Research Articles

Limitations on transversal computation through quantum homomorphic encryption

Transversality is a simple and effective method for implementing quantum computation fault-tolerantly. However, no quantum error-correcting code (QECC) can transversally implement a quantum universal gate set (Eastin and Knill, {\em Phys. Rev. Lett.}, 102, 110502). Since reversible classical computation is often a dominating part of useful quantum computation, whether or not it can be implemented transversally is an important open problem. We show that, other than a small set of non-additive codes that we cannot rule out, no binary QECC can transversally implement a classical reversible universal gate set. In particular, no such QECC can implement the Toffoli gate transversally.}{We prove our result by constructing an information theoretically secure (but inefficient) quantum homomorphic encryption (ITS-QHE) scheme inspired by Ouyang {\em et al.} (arXiv:1508.00938). Homomorphic encryption allows the implementation of certain functions directly on encrypted data, i.e. homomorphically. Our scheme builds on almost any QECC, and implements that code's transversal gate set homomorphically. We observe a restriction imposed by Nayak's bound ({\em FOCS} 1999) on ITS-QHE, implying that any ITS quantum {\em fully} homomorphic scheme (ITS-QFHE) implementing the full set of classical reversible functions must be highly inefficient. While our scheme incurs exponential overhead, any such QECC implementing Toffoli transversally would still violate this lower bound through our scheme.

Noise analysis for high-fidelity quantum entangling gates in an anharmonic linear Paul trap

The realization of high fidelity quantum gates in a multi-qubit system, with a typical target set at 99.9%, is a critical requirement for the implementation of fault-tolerant quantum computation. To reach this level of fidelity, one needs to carefully analyze the noises and imperfections in the experimental system and optimize the gate operations to mitigate their effects. Here, we consider one of the leading experimental systems for the fault-tolerant quantum computation, ions in an anharmonic linear Paul trap, and optimize entangling quantum gates using segmented laser pulses with the assistance of all the collective transverse phonon modes of the ion crystal. We present detailed analyses of the effects of various kinds of intrinsic experimental noises as well as errors from imperfect experimental controls. Through explicit calculations, we find the requirements on these relevant noise levels and control precisions to achieve the targeted high fidelity of 99.9% for the entangling quantum gates in a multi-ion crystal.

Self-guaranteed measurement-based quantum computation

In order to guarantee the output of a quantum computation, we usually assume that the component devices are trusted. However, when the total computation process is large, it is not easy to guarantee the whole system when we have scaling effects, unexpected noise, or unaccounted correlations between several subsystems. If we do not trust the measurement basis nor the prepared entangled state, we do need to be worried about such uncertainties. To this end, we proposes a "self-guaranteed" protocol for verification of quantum computation under the scheme of measurement-based quantum computation where no prior-trusted devices (measurement basis nor entangled state) are needed. The approach we present enables the implementation of verifiable quantum computation using the measurement-based model in the context of a particular instance of delegated quantum computation where the server prepares the initial computational resource and sends it to the client who drives the computation by single-qubit measurements. Applying self-testing procedures we are able to verify the initial resource as well as the operation of the quantum devices, and hence the computation itself. The overhead of our protocol scales as the size of the initial resource state to the power of 4 times the natural logarithm of the initial state's size.

Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of Bell states

High-fidelity entangled Bell states are of great interest in quantum physics. Entanglement of ultracold neutral atoms in two spatially separated optical dipole traps is promising for implementation of quantum computing and quantum simulation and for investigation of Bell states of material objects. We propose a new method to entangle two atoms via long-range Rydberg-Rydberg interaction. Alternatively to previous approaches, based on Rydberg blockade, we consider radiofrequency-assisted Stark-tuned F\"{o}rster resonances in Rb Rydberg atoms. To reduce the sensitivity of the fidelity of Bell states to the fluctuations of interatomic distance, we propose to use the double adiabatic passage across the radiofrequency-assisted Stark-tuned F\"{o}rster resonances, which results in a deterministic phase shift of the two-atom state.

Rydberg-atom-based scheme of nonadiabatic geometric quantum computation

Nonadiabatic geometric quantum computation provides a means to perform fast and robust quantum gates. It has been implemented in various physical systems, such as trapped ions, nuclear magnetic resonance and superconducting circuits. Another system being adequate for implementation of nonadiabatic geometric quantum computation may be Rydberg atoms, since their internal states have very long coherence time and the Rydberg-mediated interaction facilitates the implementation of a two-qubit gate. Here, we propose a scheme of nonadiabatic geometric quantum computation based on Rydberg atoms, which combines the robustness of nonadiabatic geometric gates with the merits of Rydberg atoms.

One-step generation of continuous-variable quadripartite cluster states in a circuit QED system

We propose a dissipative scheme for one-step generation of continuous-variable quadripartite cluster states in a circuit QED setup consisting of four superconducting coplanar waveguide resonators and a gap-tunable superconducting flux qubit. With external driving fields to adjust the desired qubit-resonator and resonator-resonator interactions, we show that continuous-variable quadripartite cluster states of the four resonators can be generated with the assistance of energy relaxation of the qubit. By comparison with the previous proposals, the distinct advantage of our scheme is that only one step of quantum operation is needed to realize the quantum state engineering. This makes our scheme simpler and more feasible in experiment. Our result may have useful application for implementing quantum computation in solid-state circuit QED systems.

Invariants-based shortcuts for fast generating Greenberger–Horne–Zeilinger state among three superconducting qubits**Project supported by the National Natural Science Foundation of China (Grant No. 11464046).

As one of the most promising candidates for implementing quantum computers, superconducting qubits (SQs) are adopted for fast generating the Greenberger–Horne–Zeilinger (GHZ) state by using invariants-based shortcuts. Three SQs are separated and connected by two coplanar waveguide resonators (CPWRs) capacitively. The complicated system is skillfully simplified to a three-state system, and a GHZ state among three SQs is fast generated with a very high fidelity and simple driving pulses. Numerical simulations indicate the scheme is insensitive to parameter deviations. Besides, the robustness of the scheme against decoherence is discussed in detail.

Long-range interaction between charge and spin qubits in quantum dots

We analyze and give estimates for the long-distance coupling via floating metallic gates between different types of spin qubits in quantum dots made of different commonly used materials. In particular, we consider the hybrid, the singlet-triplet, and the spin-$1/2$ qubits, and the pairwise coupling between each type of these qubits with another hybrid qubit in GaAs, InAs, Si, and $\mathrm{Si_{0.9}Ge_{0.1}}$. We show that hybrid qubits can be capacitively coupled strongly enough to implement two-qubit gates, as long as the distance of the dots from the metallic gates is small enough. Thus, hybrid qubits are good candidates for scalable implementations of quantum computing in semiconducting nanostructures.

Nonadiabatic Holonomic Quantum Computation with Dressed-State Qubits

Implementing holonomic quantum computation is a challenging task as it requires complicated interaction among multilevel systems. Here we propose to implement nonadiabatic holonomic quantum computation based on dressed-state qubits in circuit QED. An arbitrary holonomic single-qubit gate can be conveniently achieved using external microwave fields and tuning their amplitudes and phases. Meanwhile, nontrivial two-qubit gates can be implemented in a coupled-cavities scenario assisted by a grounding SQUID with tunable interaction, where the tuning is achieved by modulating the ac flux threaded through the SQUID. In addition, our proposal is directly scalable, up to a two-dimensional lattice configuration. In the present scheme, the dressed states involve only the lowest two levels of each transmon qubit and the effective interactions exploited are all of resonant nature. Therefore, we release the main difficulties for physical implementation of holonomic quantum computation on superconducting circuits.

Models of optical quantum computing

AbstractI review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.

Surface code error correction on a defective lattice

The yield of physical qubits fabricated in the laboratory is much lower than that of classical transistors in production semiconductor fabrication. Actual implementations of quantum computers will be susceptible to loss in the form of physically faulty qubits. Though these physical faults must negatively affect the computation, we can deal with them by adapting error-correction schemes. In this paper we have simulated statically placed single-fault lattices and lattices with randomly placed faults at functional qubit yields of 80%, 90%, and 95%, showing practical performance of a defective surface code by employing actual circuit constructions and realistic errors on every gate, including identity gates. We extend Stace et al's superplaquettes solution against dynamic losses for the surface code to handle static losses such as physically faulty qubits []. The single-fault analysis shows that a static loss at the periphery of the lattice has less negative effect than a static loss at the center. The randomly faulty analysis shows that 95% yield is good enough to build a large-scale quantum computer. The local gate error rate threshold is , and a code distance of seven suppresses the residual error rate below the original error rate at . 90% yield is also good enough when we discard badly fabricated quantum computation chips, while 80% yield does not show enough error suppression even when discarding 90% of the chips. We evaluated several metrics for predicting chip performance, and found that the average of the product of the number of data qubits and the cycle time of a stabilizer measurement of stabilizers gave the strongest correlation with logical error rates. Our analysis will help with selecting usable quantum computation chips from among the pool of all fabricated chips.

Optimized designs of reversible arithmetic logic unit

Reversible logic has emerged as a promising paradigm in various domains, such as low power VLSI design, quantum cellular automata, and nanotechnology-based systems. The arithmetic logic unit (ALU) is one of the main components of any central processing unit. In this paper we propose two new reversible ALUs using elementary quantum gates, with more functions compared to the existing designs. The results show that the proposed designs are better than the existing counterparts in terms of cost-metrics and the number of functions generated. The proposed reversible ALUs can be used in the implementation of quantum computers. All the designs are with nanometric scales.

The Ellenbogen's "Matter as Software" Concept for Quantum Computer Implementation: IV. The X@C60 Molecular Building Blocks (MBBs) and Computing System Lifetime Estimation

The problem of approximate lifetimes of individual X@C60 MBBs and tip-based nanofabricated quantum computing device systems is discussed under the conservative assumption of single-point failure. A single chemical transformation of the C60 cage into high-energy opened o-C60 isomer which forms the communication canal for the low energy transfer of an X atom from X@C60 MBB to the outside environment was studied. According to the PM7 method, the energy of o-C60 isomer is about 2.47 eV higher than that of C60 in the ground state. The estimated activation barrier between C60 and o-C60 isomer lies at 2.48 eV above the ground state of C60. A search for an individual activation barrier of the guest X atom was performed for the elements ranging between H and Bi, excluding Tc and lanthanides. Four X elements (Ru, Rh, Pd and Os) have been excluded from the available set of X@C60 MBBs because of their tendency to form stable insertion products with the wall of C60 cage.

The Ellenbogen's "Matter as Software" Concept for Quantum Computer Implementation: III. Selection of X@C<SUB>60</SUB> Molecular Building Blocks (MBBs) for Tip-Based Nanofabrication (TBN) of Trapped Neutral Atom Quantum Computing Devices

The Ellenbogen's "Matter as Software" Concept for Quantum Computer Implementation: III. Selection of X@C<SUB>60</SUB> Molecular Building Blocks (MBBs) for Tip-Based Nanofabrication (TBN) of Trapped Neutral Atom Quantum Computing Devices

The Ellenbogen's "Matter as Software" Concept for Quantum Computer Implementation: II. Bonding Between the C<SUB>60</SUB> and X@C<SUB>60</SUB> Molecules as Available Molecular Building Blocks (MBBs) for Tip-Based Nanofabrication (TBN) of Quantum Computing Devices

The Ellenbogen's "Matter as Software" Concept for Quantum Computer Implementation: II. Bonding Between the C<SUB>60</SUB> and X@C<SUB>60</SUB> Molecules as Available Molecular Building Blocks (MBBs) for Tip-Based Nanofabrication (TBN) of Quantum Computing Devices

Nonadiabatic holonomic quantum computation with all-resonant control

The implementation of holonomic quantum computation on superconducting quantum circuits is challenging due to the general requirement of controllable complicated coupling between multilevel systems. Here we solve this problem by proposing a scalable circuit QED lattice with simple realization of a universal set of nonadiabatic holonomic quantum gates. Compared with the existing proposals, we can achieve both the single and two logical qubit gates in an tunable and all-resonant way through a hybrid transmon-transmission-line encoding of the logical qubits in the decoherence-free subspaces. This distinct advantage thus leads to quantum gates with very fast speeds and consequently very high fidelities. Therefore, our scheme paves a promising way towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.

Self-testing through EPR-steering

The verification of quantum devices is an important aspect of quantum information, especially with the emergence of more advanced experimental implementations of quantum computation and secure communication. Within this, the theory of device-independent robust self-testing via Bell tests has reached a level of maturity now that many quantum states and measurements can be verified without direct access to the quantum systems: interaction with the devices is solely classical. However, the requirements for this robust level of verification are daunting and require high levels of experimental accuracy. In this paper we discuss the possibility of self-testing where we only have direct access to one part of the quantum device. This motivates the study of self-testing via EPR-steering, an intermediate form of entanglement verification between full state tomography and Bell tests. Quantum non-locality implies EPR-steering so results in the former can apply in the latter, but we ask what advantages may be gleaned from the latter over the former given that one can do partial state tomography? We show that in the case of self-testing a maximally entangled two-qubit state, or ebit, EPR-steering allows for simpler analysis and better error tolerance than in the case of full device-independence. On the other hand, this improvement is only a constant improvement and (up to constants) is the best one can hope for. Finally, we indicate that the main advantage in self-testing based on EPR-steering could be in the case of self-testing multi-partite quantum states and measurements. For example, it may be easier to establish a tensor product structure for a particular party’s Hilbert space even if we do not have access to their part of the global quantum system.

Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy

Intrinsic noise is unavoidable in quantum devices and represents a hindrance to implementing quantum computation. Despite the presence of noise, a quantum-annealing algorithm that involves quantum tunneling may provide computational advantages over simulated annealing.

Parallelizing quantum circuit synthesis

Quantum circuit synthesis is the process in which an arbitrary unitary operation is decomposed into a sequence of gates from a universal set, typically one which a quantum computer can implement both efficiently and fault-tolerantly. As physical implementations of quantum computers improve, the need is growing for tools that can effectively synthesize components of the circuits and algorithms they will run. Existing algorithms for exact, multi-qubit circuit synthesis scale exponentially in the number of qubits and circuit depth, leaving synthesis intractable for circuits on more than a handful of qubits. Even modest improvements in circuit synthesis procedures may lead to significant advances, pushing forward the boundaries of not only the size of solvable circuit synthesis problems, but also in what can be realized physically as a result of having more efficient circuits. We present a method for quantum circuit synthesis using deterministic walks. Also termed pseudorandom walks, these are walks in which once a starting point is chosen, its path is completely determined. We apply our method to construct a parallel framework for circuit synthesis, and implement one such version performing optimal T-count synthesis over the Clifford+T gate set. We use our software to present examples where parallelization offers a significant speedup on the runtime, as well as directly confirm that the 4-qubit 1-bit full adder has optimal T-count 7 and T-depth 3.

Non-adiabatic holonomic quantum computation in linear system-bath coupling.

Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of . The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.