# James D. Whitfield's research while affiliated with Dartmouth College and other places

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## Publications (27)

We establish the theoretical foundation of the Floquet graphene antidot lattice, whereby massless Dirac fermions are driven periodically by a circularly polarized electromagnetic field while having their motion excluded from an array of nanoholes. The properties of interest are encoded in the quasienergy spectra, which are computed nonperturbativel...

We establish the theoretical foundation of the Floquet graphene antidot lattice, whereby massless Dirac fermions are driven periodically by a circularly polarized electromagnetic field, while having their motion excluded from an array of nanoholes. The properties of interest are encoded in the quasienergy spectra, which are computed non-perturbativ...

Quantum algorithms are touted as a way around some classically intractable problems such as the simulation of quantum mechanics. At the end of all quantum algorithms is a quantum measurement whereby classical data is extracted and utilized. In fact, many of the modern hybrid-classical approaches are essentially quantum measurements of states with s...

The Hartree–Fock problem provides the conceptual and mathematical underpinning of a large portion of quantum chemistry. As efforts in quantum technology aim to enhance computational chemistry algorithms, the Hartree–Fock method, central to many other numerical approaches, is a natural target for quantum enhanced algorithms. While quantum computers...

Simulating a fermionic system on a quantum computer requires encoding the anti-commuting fermionic variables into the operators acting on the qubit Hilbert space. The most familiar of which, the Jordan-Wigner transformation, encodes fermionic operators into non-local qubit operators. As non-local operators lead to a slower quantum simulation, recen...

Simulating molecules is believed to be one of the early-stage applications for quantum computers. Current state-of-the-art quantum computers are limited in size and coherence, therefore optimizing resources to execute quantum algorithms is crucial. In this work, we develop a formalism to reduce the number of qubits required for simulating molecules...

One route to numerically propagating quantum systems is time-dependent density functional theory (TDDFT). The application of TDDFT to a particular system’s time evolution is predicated on V-representability which we have analyzed in a previous publication. Here we describe a newly developed solver for the scalar time-dependent Kohn-Sham potential....

The Hartree-Fock problem provides the conceptual and mathematical underpinning of a large portion of quantum chemistry. As efforts in quantum technology aim to enhance computational chemistry algorithms, the fundamental Hartree-Fock problem is a natural target. While quantum computers and quantum simulation offer many prospects for the future of mo...

PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This paper explains the design and philosophy behind PySCF that enables it to meet these twin objectives. With several...

Quantum technology is seeing a remarkable explosion in interest due to a wave of successful commercial technology. As a wider array of engineers and scientists are needed, it is time we rethink quantum educational paradigms. Current approaches often start from classical physics, linear algebra, or differential equations. This chapter advocates for...

PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows. The present paper explains the design and philosophy behind PYSCF that enables it to meet these twin objectives....

Simulating molecules is believed to be one of the early-stage applications for quantum computers. Current state-of-the-art quantum computers are limited in size and coherence, therefore optimizing resources to execute quantum algorithms is crucial. In this work, we develop a formalism to reduce the number of qubits required for simulating molecules...

Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the superfast encoding introduced by Kitaev and one of the authors. This encoding maps a target fermionic Hamiltonian with two-body interactions on a graph of degree d to a qubit simulator Hamilto...

In our recent work, we examined various fermion-to-qubit mappings in the context of quantum simulation including the original Bravyi-Kitaev superfast encoding (OSE) as well as a generalized version (GSE). We return to OSE and compare it against the Jordan-Wigner (JW) transform for quantum chemistry considering the number of qubits required, the Pau...

Quantum algorithms are touted as a way around some classically intractable problems such as the simulation of quantum mechanics. At the end of all quantum algorithms is a quantum measurement whereby classical data is extracted and utilized. In fact, many of the modern hybrid-classical approaches are essentially quantum measurements of states with s...

There are many ways to numerically represent chemical systems in order to compute their electronic structure. Basis functions may be localized in real-space (atomic orbitals), in momentum-space (plane waves), or in both components of phase-space. Such phase-space localized basis functions in the form of wavelets have been used for many years in the...

In our recent work, we have examined various fermion to qubit mappings in the context of quantum simulation including the original Bravyi-Kitaev Superfast encoding (OSE) as well as a generalized version (GSE). We return to OSE and compare it against the Jordan-Wigner (JW) transform for quantum chemistry considering the number of qubits required, th...

Quantum chemistry often considers atoms and molecules with non-zero spin. In such cases, the need for proper spin functions results in the theory of configuration state functions. Here, we consider the construction of such wavefunctions using the symmetric group and more specifically Young projectors. We discuss the formalism and detail an example...

One route to numerically propagating quantum systems is time-dependent density functional theory (TDDFT). The application of TDDFT to a particular system's time evolution is predicated on $V$-representability which we have analyzed in a previous publication. Here we describe a newly developed solver for the scalar time-dependent Kohn-Sham potential...

There are many ways to numerical represent of chemical systems in order to compute their electronic structure. Basis functions may be localized either in real-space (atomic orbital), localized in momentum-space (plane waves), or may be local in both components of phase-space. Such phase-space localized basis functions in the form of wavelets, have...

Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the Superfast Encoding introduced by Kitaev and one of the authors. This encoding maps a target fermionic Hamiltonian with two-body interactions on a graph of degree $d$ to a qubit simulator Hamil...

Present quantum computers often work with distinguishable qubits as their computational units. In order to simulate indistinguishable fermionic particles, it is first required to map the fermionic state to the state of the qubits. The Bravyi-Kitaev Superfast (BKSF) algorithm can be used to accomplish this mapping. The BKSF mapping has connections t...

Present quantum computers often work with distinguishable qubits as their computational units. In order to simulate indistinguishable fermionic particles, it is first required to map the fermionic state to the state of the qubits. The Bravyi-Kitaev Superfast (BKSF) algorithm can be used to accomplish this mapping. The BKSF mapping has connections t...

The natural occupation numbers of fermionic systems are subject to non-trivial constraints, which include and extend the original Pauli principle. Several decades after the first generalized Pauli constraints had been found, a recent mathematical breakthrough has clarified their mathematical structure and has opened up the possibility of a systemat...

In digital quantum simulation of fermionic models with qubits, one requires the use of non-local maps for encoding. Such maps require linear or logarithmic overhead in circuit depth which could render the simulation useless, for a given decoherence time. Here we show how one can use a cavity-QED system to perform digital quantum simulation of fermi...

Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of qubits. This overhead can be a hindrance to implementation of qubit-based quantum simulators, especially in t...

Digital quantum simulation of fermionic systems is important in the context of chemistry and physics. Simulating fermionic models on general purpose quantum computers requires imposing a fermionic algebra on spins. The previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two techniques for accomplishing this task. Here we re-exami...

## Citations

... Similar to the effect of the long-range hopping, the topological phases with large topological numbers also can be obtained by the Periodic driving. As we all know, Periodic driving has been used as a powerful control tool to achieve coherent control of quantum states [53][54][55][56][57], and artificially create exotic topological phases in systems of ultracold atoms [58][59][60][61][62][63], photonics [64,65], superconductor qubits [66,67] and graphene [68][69][70][71]. Periodic driven engineering can not only realize topological phases that are difficult to achieve in static systems, but also provide effective control of topological phase transitions [72][73][74][75], to realize many topological states that do not exist in static systems [76][77][78][79]. ...

... However, since the time step δt must be very small depending on the strength of correlation in the system, the resulting number of operations makes the time necessary to solve for even small molecules extremely long. This is true of other classical solution techniques such as Hartree-Fock [13]. This is expected based on the complexity of solving quantum chemistry systems [14]. ...

... Although circuit depth is one of the most critical metrics for NISQ devices, the number of physical qubits on the actual quantum chip (circuit width) is the necessary condition that limits the problem that can be solved. Several techniques based on symmetries presented in the Hamiltonian have been used to reduce the number of qubits [48][49][50][51] . But these techniques can only reduce a few qubits and have certain symmetry requirements. ...

... The same methodology can be applied to both the groundstate and time-dependent reverse-engineering problems, however the former requires iterative solutions of the time-independent Kohn-Sham equations, whereas the latter requires repeated iterative application of the time-evolution operator to the Kohn-Sham states. A number of iterative algorithms have been proposed in recent literature to realise the inverse density-to-potential map in time-dependent and ground-state DFT [224][225][226][227][228][229]. For example, some of these approaches consider iterative schemes derived from the continuity equation of time-dependent DFT [225,226], whereas the original timedependent reverse-engineering algorithm in iDEA utilised iterative updates of the vector potential in the context of time-dependent current DFT (matching the current densities) [218]. ...

... whose trace defines density of states (DOS). We implemented -point CCGF approach in PySCF quantum chemistry software package [44] using a hybrid MPI+OpenMP parallelization scheme. To avoid solvingpoint Λ equations, we approximate the Λ amplitudes as the complex conjugate of amplitudes. ...

... In recent years, we have witnessed a strong renewed interest in methods for simulating fermionic systems through a set of local qubit gates [5,[13][14][15][16][17][18][19]. Compared to earlier methods (such as Refs. ...

... Ref. [255] shows that SFBK results in lower gate depth than Jordan-Wigner, but higher than Bravyi-Kitaev on a small molecular system. Chien et al. [313] also show that Jordan-Wigner can outperform SFBK in terms of gate count under certain conditions on the Hamiltonian studied. One can expect GSE to perform better due to its lower Pauli weight, however for a relevant comparison, one would need to incorporate equivalent error mitigation techniques into Jordan-Wigner or Bravyi-Kitaev to balance quantum resources required to achieve a given accuracy. ...

... In recent years, we have witnessed a strong renewed interest in methods for simulating fermionic systems through a set of local qubit gates [5,[13][14][15][16][17][18][19]. Compared to earlier methods (such as Refs. ...

... Generalization of the transformation to higher dimensions using lattice gauge fields have also been proposed [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Such exact bosonization mappings are also important form the quantum simulation perspective, for they address the possibility of simulating a quantum many-body fermionic systems using a bosonic quantum computer [21][22][23][24][25][26]. Symmetries, however, may not remain manifest under the transformation. ...

... Finally, let us note that the analysis of the so-called generalized Pauli constraints [105][106][107][108][109][110][111][112] (GPC) of the ONs obtained when using some nonrelativistic functional approximations has attracted some attention [113] in the last few years. These conditions serve to approach to the possibility of obtaining pure N -representable 1-RDMs. ...