Simon Charles Benjamin

• DPhil in Physics
• Professor at University of Oxford

We present the Virtual Quantum Device (VQD) platform, a system based on the QuEST quantum emulator. Through the use of VQDs, non-expert users can emulate specific quantum computers with detailed error models, bespoke gate sets and connectivities. The platform boasts an intuitive interface, powerful visualisation, and compatibility with high-perform...

Recent demonstrations indicate that silicon-spin QPUs will be able to shuttle physical qubits rapidly and with high fidelity - a desirable feature for maximising logical connectivity, supporting new codes, and routing around damage. However it may seem that shuttling at the logical level is unwise: static defects in the device may 'scratch' a logic...

Artificial intelligence (AI) advancements over the past few years have had an unprecedented and revolutionary impact across everyday application areas. Its significance also extends to technical challenges within science and engineering, including the nascent field of quantum computing (QC). The counterintuitive nature and high-dimensional mathemat...

Quantum computing requires a universal set of gate operations; regarding gates as rotations, any rotation angle must be possible. However a real device may only be capable of B bits of resolution, i.e., it might support only 2 B possible variants of a given physical gate. Naive discretization of an algorithm’s gates to the nearest available options...

For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors that occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum fault tolerance can provide an answer in the long term, but in the coming era of noisy intermediate-scale quantum...

Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union–Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the growth and merger of data structures through nearest-neighbour steps; this naturally suggests the possibility of...

Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using hardware-specific operations and connectivity. Therefore, ab initio creation of circuits within a machine, eit...

Variational methods offer a highly promising route to exploiting quantum computers for chemistry tasks. Here we employ methods described in a sister paper to the present report, entitled ab initio machine synthesis of quantum circuits, in order to solve problems using adaptively evolving quantum circuits. Consistent with prior authors we find that...

We present the Virtual Quantum Device (VQD) platform, a system based on the QuEST quantum emulator. Through the use of VQDs, non-expert users can emulate specific quantum computers with detailed error models, bespoke gate sets and connectivities. The platform boasts an intuitive interface, powerful visualisation, and compatibility with high-perform...

Quantum computing requires a universal set of gate operations; regarding gates as rotations, any rotation angle must be possible. However a real device may only be capable of $B$ bits of resolution, i.e. it might support only $2^B$ possible variants of a given physical gate. Naive discretization of an algorithm's gates to the nearest available opti...

First-quantized, grid-based methods for chemistry modeling are a natural and elegant fit for quantum computers. However, it is infeasible to use today's quantum prototypes to explore the power of this approach because it requires a substantial number of near-perfect qubits. Here, we use exactly emulated quantum computers with up to 36 qubits to exe...

In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial scale but by pushing the envelope as far as possible through optimal choices of algorithms and hardware the val...

Variational quantum algorithms are promising tools whose efficacy depends on their optimization method. For noise-free unitary circuits, the quantum generalization of natural gradient descent has been introduced and shown to be equivalent to imaginary time evolution: the approach is effective due to a metric tensor reconciling the classical paramet...

The preparation of Hamiltonian eigenstates is essential for many applications in quantum computing; the efficiency with which this can be done is of key interest. A canonical approach exploits the quantum phase estimation (QPE) algorithm. We adopt ideas from variants of this method to implement a resource-frugal iterative scheme, and provide analyt...

Any architecture for practical quantum computing must be scalable. An attractive approach is to create multiple cores, computing regions of fixed size that are well spaced but interlinked with communication channels. This exploded architecture can relax the demands associated with a single monolithic device: the complexity of control, cooling and p...

For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors which occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum fault tolerance can provide an answer in the long term, but in the coming era of `NISQ' machines we must seek to...

Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using hardware-specific operations and connectivity. Here we explore methods for the ab initio creation of circuits...

Variational methods offer a highly promising route to exploiting quantum computers for chemistry tasks. Here we employ methods described in a sister paper to the present report, entitled ab initio machine synthesis of quantum circuits, in order to solve problems using adaptively evolving quantum circuits. Consistent with prior authors we find that...

Variational algorithms have particular relevance for near-term quantum computers but require nontrivial parameter optimizations. Here we propose analytic descent: Given that the energy landscape must have a certain simple form in the local region around any reference point, it can be efficiently approximated in its entirety by a classical model - w...

We explore grid-based techniques for simulating multi-electron dynamics using a quantum computer, an approach sometimes called first quantized chemistry. Using a split-operator Fourier transform (SO-FT) method on exactly-emulated quantum computers with up to 36 qubits, we model the dynamics of 2D and 3D atoms with single and paired particles intera...

We explore a method for automatically recompiling a quantum circuit $\mathcal{A}$ into a target circuit $\mathcal{B}$, with the goal that both circuits have the same action on a specific input i.e. $\mathcal{B}{\mid{in}\rangle}=\mathcal{A}{\mid{in}\rangle}$. This is of particular relevance to hybrid, NISQ-era algorithms for dynamical simulation or...

Any architecture for practical quantum computing must be scalable. An attractive approach is to create multiple cores, computing regions of fixed size that are well-spaced but interlinked with communication channels. This exploded architecture can relax the demands associated with a single monolithic device: the complexity of control, cooling and p...

Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers, owing to the extremely high computational cost. Quantum computers promise a solution, although fault-tolerant quantum computers will probably not be available in the near future. Current quantum de...

Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices. We show that the solution...

Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are typically not “optimal” either in terms of the circuit depth (and therefore the error burden) or the specifics o...

Quantum computers can exploit a Hilbert space whose dimension increases exponentially with the number of qubits. In experiment, quantum supremacy has recently been achieved by the Google team by using a noisy intermediate-scale quantum (NISQ) device with over 50 qubits. However, the question of what can be implemented on NISQ devices is still not f...

Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum (NISQ) devices. While most conventional QEM schemes assume discrete gate-based circuits with noise appearing either before or after each gate, the assumptions are inappropriate for describing realistic noise that may have strong gate dependence and complicated nonlocal eff...

Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal quantum error correcting code, with the subsequent verification of all key features including the identificati...

Applications such as simulating large quantum systems or solving large-scale linear algebra problems are immensely challenging for classical computers due their extremely high computational cost. Quantum computers promise to unlock these applications, although fault-tolerant quantum computers will likely not be available for several years. Currentl...

Adiabatic quantum computing enables the preparation of many-body ground states. Realization poses major experimental challenges: Direct analog implementation requires complex Hamiltonian engineering, while the digitized version needs deep quantum gate circuits. To bypass these obstacles, we suggest an adiabatic variational hybrid algorithm, which e...

Quantum variational algorithms are applicable to a range of tasks and have particular relevance for near-term quantum computers. The approach involves adjusting the parameterised elements of a quantum circuit to minimise the expected energy of the output state with respect to a Hamiltonian encoding the task. Typically the parameter space is navigat...

Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is estimated in the presence of statistical errors using entangled quantum states. We present a novel approach for findin...

Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks—generalized time evolution with a non-Hermitian Hamiltonian, linear algebra problems, and open quantum system dynamics. The algorithm for gener...

We introduce QuESTlink,pronounced 'quest link', an open-source Mathematicapackage which efficiently emulates quantum computers. By integratingwith the Quantum Exact Simulation Toolkit (QuEST), QuESTlink offers ahigh-level, expressive and usable interface to a high-performance, hardware-accelerated emulator. Requiring no installation, QuESTlink stre...

One of the most promising suggested applications of quantum computing is solving classically intractable chemistry problems. This may help to answer unresolved questions about phenomena such as high temperature superconductivity, solid-state physics, transition metal catalysis, and certain biochemical reactions. In turn, this increased understandin...

We introduce QuESTlink, pronounced "quest link", an open-source Mathematica package which efficiently emulates quantum computers. By integrating with the Quantum Exact Simulation Toolkit (QuEST), QuESTlink offers a high-level, expressive and usable interface to a high-performance, hardware-accelerated emulator. Requiring no installation, QuESTlink...

Spin qubits in silicon quantum dots are one of the most promising building blocks for large scale quantum computers thanks to their high qubit density and compatibility with the existing semiconductor technologies. High fidelity single-qubit gates exceeding the threshold of error correction codes like the surface code have been demonstrated, while...

We consider an approach to fault tolerant quantum computing based on a simple error-detecting code operating as the substrate for a conventional surface code. We anticipate that the approach will be efficient when the noise in the hardware is skewed towards one channel (e.g., phase), or alternatively when the hardware is modular in such a fashion t...

Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are typically not optimal either in terms of the circuit depth (and therefore the error burden) or the specifics of...

The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and simulating real and imaginary time dynamics. In this work, we first review the conventional variational principles,...

Quantum algorithms have been developed for efficiently solving linear algebra tasks. However they generally require deep circuits and therefore universal fault-tolerant quantum computers. In this work, we propose variational algorithms for linear algebra tasks that are compatible with Noisy Intermediate Scaled Quantum devices. We show that the solu...

Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum computers can efficiently simulate quantum systems, but not non-unitary imaginary time evolution. We propose a...

Twirling is a technique widely used for converting arbitrary noise channels into Pauli channels in error threshold estimations of quantum error correction codes. It is vitally useful both in real experiments and in classical quantum simulations. Minimising the size of the twirling gate set increases the efficiency of simulations and in experiments...

Coherent noise can be much more damaging than incoherent (probabilistic) noise in the context of quantum error correction. One solution is to use twirling to turn coherent noise into incoherent Pauli channels. In this article, we argue that if twirling can improve the logical fidelity versus a given noise model, we can always achieve an even higher...

Adiabatic quantum computing enables the preparation of many-body ground states. This is key for applications in chemistry, materials science, and beyond. Realisation poses major experimental challenges: Direct analog implementation requires complex Hamiltonian engineering, while the digitised version needs deep quantum gate circuits. To bypass thes...

A design for a large-scale surface code quantum processor based on a node/network approach is introduced for semiconductor quantum dot spin qubits. The minimal node contains only seven quantum dots, and nodes are separated on the micron scale, creating useful space for wiring interconnects and integration of conventional transistor circuits. Entang...

We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We anticipate that the approach will be efficient when the noise in the hardware is skewed towards one channel (e.g. phase), or alternatively when the hardware is modular in such a fashion th...

A design for a large-scale surface code quantum processor based on a node/network approach is introduced for semiconductor quantum dot spin qubits. The minimal node contains only 7 quantum dots, and nodes are separated on the micron scale, creating useful space for wiring interconnects and integration of conventional transistor circuits. Entangleme...

Rapidly developing experiments across multiple platforms now aim to realise small quantum codes, and so demonstrate a memory within which a logical qubit can be protected from noise. There is a need to benchmark the achievements in these diverse systems, and to compare the inherent power of the codes they rely upon. We describe a recently-introduce...

It is vital to minimise the impact of errors for near-future quantum devices that will lack the resources for full fault tolerance. Two quantum error mitigation (QEM) techniques have been introduced recently, namely error extrapolation [Li2017,Temme2017] and quasi-probability decomposition [Temme2017]. To enable practical implementation of these id...

We investigate the performance of a quantum algorithm for solving classical 3-SAT problems. A cycle of post-selected measurements drives the computer's register monotonically toward a steady state which is correlated to the classical solution(s). An internal parameter $\theta$ determines both the degree of correlation and the success probability, t...

Memristive systems are generalizations of memristors, which are resistors with memory. In this paper, we present a quantum description of quantum dot memristive systems. Using this model we propose and experimentally demonstrate a simple and practical scheme for realizing memristive systems with quantum dots. The approach harnesses a phenomenon tha...

Rapidly developing experiments across multiple platforms now aim to realise small quantum codes, and so demonstrate a memory within which a logical qubit can be protected from noise. There is a need to benchmark the achievements in these diverse systems, and to compare the inherent power of the codes they rely upon. We describe a recently-introduce...

The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realised in systems which support Hamiltonian evolution, rather than discrete gates. We explore an alternative approach in which slowly varying measurements are used to mimi...

The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realised in systems which support Hamiltonian evolution, rather than discrete gates. We explore an alternative approach in which slowly varying measurements are used to mimi...

The potential impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable real-world imperfections necessitate means to improve remote entanglement by local quantum operations. Here we realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit no...

The potential impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable real-world imperfections necessitate means to improve remote entanglement by local quantum operations. Here we realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit no...

Memristive systems are generalisations of memristors, which are resistors with memory. In this paper, we present a quantum description of memristive systems. Using this model we propose and experimentally demonstrate a simple and practical scheme for realising memristive systems with quantum dots. The approach harnesses a phenomenon that is commonl...

Optically linked ion traps are promising as components of network-based quantum technologies, including communication systems and modular computers. Experimental results achieved to date indicate that the fidelity of operations within each ion trap module will be far higher than the fidelity of operations involving the links; fortunately internal s...

We introduce a new analytical method for studying the open quantum systems problem of a discrete system weakly coupled to an environment of harmonic oscillators. Our approach is based on a phase space representation of the density matrix for a system coupled to a two-tiered environment. The dynamics of the system and its immediate environment are r...

An important challenge in quantum science is to fully understand the efficiency of energy flow in networks. Here we present a simple and intuitive explanation for the intriguing observation that optimally efficient networks are not purely quantum, but are assisted by some interaction with a ‘noisy’ classical environment. By considering the system's...

Resonant manipulation of carbon nanotube valley-spin qubits by an electric field is investigated theoretically. We develop a new analysis of electrically driven spin resonance exploiting fixed physical characteristics of the nanotube: a bend and inhomogeneous disorder. The spectrum is simulated for an electron valley-spin qubit coupled to a hole va...

We study the feasibility of a novel solid-state device engineered from first principles for surface code quantum computing. Quantum information is stored within an array of well-separated impurity spins in a lattice. A second set of `probe' spins are mechanically separate from the data qubits and move in-and-out of their proximity. The spin dipole-...

Exquisite quantum control has now been achieved in small ion traps, in nitrogen-vacancy centres and in superconducting qubit clusters. We can regard such a system as a universal cell with diverse technological uses from communication to large-scale computing, provided that the cell is able to network with others and overcome any noise in the interl...

We introduce a new analytical method for studying the open quantum systems problem of a discrete system weakly coupled to an environment of harmonic oscillators. Our approach is based on a phase space representation of the density matrix, employing neither the Markov nor the Born approximation. We are able to treat cases where the modes of the imme...

An important challenge in quantum science is to fully understand the efficiency of energy flow in networks. Here we present a simple and intuitive explanation for the intriguing observation that optimally efficient networks are not purely quantum, but are assisted by some interaction with a `noisy' classical environment. By considering the system's...

DOI:https://doi.org/10.1103/PhysRevA.88.019906

Almost 60 years ago Dicke introduced the term superradiance to describe a signature quantum effect: N atoms can collectively emit light at a rate proportional to N^2. Even for moderate N this represents a significant increase over the prediction of classical physics, and the effect has found applications ranging from probing exciton delocalisation...

Supplementary Figures S1-S2, Supplementary Tables S1-S3, Supplementary Notes 1-3 and Supplementary Methods

In a recent Letter [Phys. Rev. Lett. 109, 110502 (2012), arXiv:1204.6528], Bandyopadhyay, Paterek and Kaszlikowski report their analysis of spin coherence time in the radical pair involved in avian magnetoreception, concluding that is of the order of a microsecond. However, a combination of an erroneous numerical calculation together with an incorr...

In a recent Letter [Phys. Rev. Lett. 109, 110502 (2012), arXiv:1204.6528], Bandyopadhyay, Paterek and Kaszlikowski report their analysis of spin coherence time in the radical pair involved in avian magnetoreception, concluding that is of the order of a microsecond. However, a combination of an erroneous numerical calculation together with an incorr...

Coupled spin chains are promising candidates for wiring up qubits in solid-state quantum computing (QC). In particular, two nitrogen-vacancy centers in diamond can be connected by a chain of implanted nitrogen impurities; when driven by suitable global fields the chain can potentially enable quantum state transfer at room temperature. However, our...

We introduce a protocol to distribute entanglement between remote parties. Our protocol is based on a chain of repeater stations, and exploits topological encoding to tolerate very high levels of defects and errors. The repeater stations may employ probabilistic entanglement operations which usually fail; ours is the first protocol to explicitly al...

A scalable quantum computer could be built by networking together many simple processor cells, thus avoiding the need to create a single complex structure. The difficulty is that realistic quantum links are very error prone. A solution is for cells to repeatedly communicate with each other and so 'purify' any imperfections; however prior studies su...

Sensors that harness exclusively quantum phenomena (such as entanglement) can achieve superior performance compared to those employing only classical principles. Recently, a technique based on postselected, weakly-performed measurements has emerged as a method of overcoming technical noise in the detection and estimation of small interaction parame...

Coupled spin chains are promising candidates for 'wiring up' qubits in solid-state quantum computing (QC). In particular, two nitrogen-vacancy centers in diamond can be connected by a chain of implanted nitrogen impurities; when driven by a suitable global fields the chain can potentially enable quantum state transfer at room temperature. However,...

In the distributed quantum computing paradigm, well-controlled few-qubit `nodes' are networked together by connections which are relatively noisy and failure prone. A practical scheme must offer high tolerance to errors while requiring only simple (i.e. few-qubit) nodes. Here we show that relatively modest, three-qubit nodes can support advanced pu...

A recent paper by Souza, Oliveira and Sarthour (SOS) reports the experimental violation of a Leggett-Garg inequality (sometimes referred to as a temporal Bell inequality). The inequality tests for quantum mechanical superposition: if the inequality is violated, the dynamics cannot be explained by a large class of classical theories under the headin...

This chapter begins with a short introduction to the topic of quantum information processing. We presume only a very limited familiarity with quantum mechanics; in fact, all the really essential ideas, terminology and formalism will be introduced as we go along. The introduction will discuss classical and quantum information, the qubit, entanglemen...

A recent paper by Souza, Oliveira and Sarthour (SOS) reports the experimental violation of a Leggett–Garg (LG) inequality (sometimes referred to as a temporal Bell inequality). The inequality tests for quantum mechanical superposition: if the inequality is violated, the dynamics cannot be explained by a large class of classical theories under the h...

Certain migratory birds can sense the Earth's magnetic field. The nature of this process is not yet properly understood. Here we offer a simple explanation according to which birds literally see the local magnetic field through the impact of a physical rather than a chemical signature of the radical pair: a transient, long-lived electric dipole mom...

Sensors based on crystal defects, especially nitrogen vacancy (NV) centres in nanodiamond, can achieve detection of single magnetic moments. Here we show that this exquisite control can be utilized to entangle remote electronic spins for applications in quantum computing; the mobile sensor provides a `flying' qubit while the act of sensing the loca...

Supplementary Methods and Supplementary References

The quantum superposition principle states that an entity can exist in two different states simultaneously, counter to our 'classical' intuition. Is it possible to understand a given system's behaviour without such a concept? A test designed by Leggett and Garg can rule out this possibility. The test, originally intended for macroscopic objects, ha...

Recently a new form of quantum memory has been proposed. The storage medium is an ensemble of electron spins, coupled to a stripline cavity and an ancillary readout system. Theoretical studies suggest that the system should be capable of storing numerous qubits within the ensemble, and an experimental proof-of-concept has already been performed. He...

Defects in diamond crystals possess rare physical properties that can enable new forms of technology. Unlocking this potential requires rapid quantum-state measurement, a 'quantum snapshot', which has now been achieved.

Recently there have been several theoretical and experimental studies of the prospects for magnetic field sensors based on crystal defects, especially nitrogen vacancy (NV) centers in diamond. Such systems could potentially be incorporated into an atomic force microscopy-like apparatus in order to map the magnetic properties of a surface at the sin...

Electron and nuclear spins have been employed in many of the early demonstrations of quantum technology. However, applications in real world quantum technology are limited by the difficulty of measuring single spins. Here we show that it is possible to rapidly and robustly amplify a spin state using a lattice of ancillary spins. The model we employ...

The quantum superposition principle states that an entity can exist in two different states simultaneously, counter to our 'classical' intuition. Is it possible to understand a given system's behaviour without such a concept? A test designed by Leggett and Garg can rule out this possibility. The test, originally intended for macroscopic objects, ha...

In artificial systems, quantum superposition and entanglement typically decay rapidly unless cryogenic temperatures are used. Could life have evolved to exploit such delicate phenomena? Certain migratory birds have the ability to sense very subtle variations in Earth's magnetic field. Here we apply quantum information theory and the widely accepted...

Entangled states can potentially be used to outperform the standard quantum limit which every classical sensor is bounded by. However, entangled states are very susceptible to decoherence, and so it is not clear whether one can really create a superior sensor to classical technology via a quantum strategy which is subject to the effect of realistic...

The field of quantum metrology promisesmeasurement devices that are fundamentally superior to conventional technologies. Specifically, when quantum entanglement is harnessed, the precision achieved is supposed to scale more favorably with the resources employed, such as system size and time required. Here, we consider measurement of magnetic-field...

In distributed quantum computation, small devices composed of a single or a few qubits are networker together to achieve a scalable machine. Typically there is an optically active matter qubit at each node, so that photons are exploited to achieve remote entanglement. However, in many systems the optically active states are unstable or poorly defin...

In certain approaches to quantum computing the operations between qubits are non-deterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components; operations between components should assumed to be failure prone. In the logical limit of this architecture each compo...

Molecular nanostructures may constitute the fabric of future quantum technologies, if their degrees of freedom can be fully harnessed. Ideally one might use nuclear spins as low-decoherence qubits and optical excitations for fast controllable interactions. Here, we present a method for entangling two nuclear spins through their mutual coupling to a...